Héloïse Beutier

Béatrice Hechler

Ophélie Godon

Yu Wang

Caitlin M Gillis

Luc De Chaisemartin

Aurélie Gouel-Chéron

Stéphanie Magnenat

Lynn E Macdonald

Andrew J Murphy

NASA Sylvie Chollet-Martin

Dan Longrois

Christian Gachet

Pierre Bruhns
email: bruhns@pasteur.fr

Friederike Jönsson
email: joensson@pasteur.fr

CD32A-expressing platelets determine the severity of experimental anaphylaxis

[Main Text: ] Introduction

Anaphylaxis is an acute and life-threatening multisystem allergic reaction. It results from inappropriate cellular responses triggered by antibodies to generally inoffensive antigens, and is characterized by massive mediator release [START_REF] Strait | Ingested allergens must be absorbed systemically to induce systemic anaphylaxis[END_REF], and rapidly occurring vascular and organ dysfunction. Experimental models have elucidated two different antibody-dependent anaphylaxis pathways. The 'classical' pathway relies on antibodies of the IgE class, which, when bound to the high affinity FcRI receptor on basophils and mast cells, trigger cell activation upon exposure to the causative allergen [START_REF] Kalesnikoff | New developments in mast cell biology[END_REF][START_REF] Galli | Pathogenesis and management of anaphylaxis: current status and future challenges[END_REF]. The 'alternative' anaphylaxis pathway is engaged by IgG antibodies, which, when aggregated by a specific antigen, activate myeloid cells via IgG receptors (FcRs) [START_REF] Finkelman | Molecular mechanisms of anaphylaxis: lessons from studies with murine models[END_REF][START_REF] Karasuyama | Newly discovered roles for basophils: a neglected minority gains new respect[END_REF][START_REF] Gillis | Contribution of Human FcgammaRs to Disease with Evidence from Human Polymorphisms and Transgenic Animal Studies[END_REF]. Even though human anaphylaxis has been classically viewed as an IgE antibody-dependent reaction, accumulating evidence indicates that IgG antibody-dependent reactions may be responsible for human anaphylaxis cases, particularly in the context of druginduced anaphylaxis [START_REF] Finkelman | Human IgE-independent systemic anaphylaxis[END_REF].

Both clinical and experimental anaphylaxis are associated with immediate release of histamine and lipid mediators. Notably, the lipid mediator platelet-activating factor (PAF) has been proposed to contribute to the severity of anaphylaxis in humans [START_REF] Vadas | Platelet-activating factor, PAF acetylhydrolase, and severe anaphylaxis[END_REF] and in several experimental models [START_REF] Strait | Pathways of anaphylaxis in the mouse[END_REF][START_REF] Jönsson | Mouse and human neutrophils induce anaphylaxis[END_REF][START_REF] Gillis | Mechanisms of anaphylaxis in human low-affinity IgG receptor locus knock-in mice[END_REF]. The cellular source and target(s) of PAF in such reactions remain unknown, but it is reasonably established that IgG anaphylaxis induction entails the FcγRdependent activation of myeloid cells that can release PAF. In particular, both resident cellsmast cells and macrophages-and circulating cells -neutrophils, monocytes and basophils-have been found to contribute to anaphylaxis, but to largely varying degrees depending on the animal model and the inciting allergic agent used [START_REF] Finkelman | Molecular mechanisms of anaphylaxis: lessons from studies with murine models[END_REF][START_REF] Gillis | Contribution of Human FcgammaRs to Disease with Evidence from Human Polymorphisms and Transgenic Animal Studies[END_REF][START_REF] Jonsson | Neutrophils in local and systemic antibody-dependent inflammatory and anaphylactic reactions[END_REF].

Among the five classical human FcγRs (FcγRI, FcγRIIA, FcγRIIB, FcγRIIIA, FcγRIIIB) [START_REF] Bruhns | Properties of mouse and human IgG receptors and their contribution to disease models[END_REF], hFcγRIIA/CD32A is the most widely expressed FcγR in humans; an activating IgG receptor present on all cells of myeloid origin, including platelets. When expressed in transgenic mice, hFcγRIIA can induce severe IgG-dependent anaphylaxis that relies on the contribution of neutrophils and monocytes/macrophages [START_REF] Jönsson | Human FcgammaRIIA induces anaphylactic and allergic reactions[END_REF]. Mice expressing four human FcγRs (FcγRIIA, FcγRIIB, FcγRIIIA and FcγRIIIB) in place of endogenous mouse FcγRIIB, FcγRIII and FcγRIV, also demonstrated severe systemic IgG-induced anaphylaxis that was abolished following hFcγRIIA blockade [START_REF] Gillis | Mechanisms of anaphylaxis in human low-affinity IgG receptor locus knock-in mice[END_REF], suggesting a major role for hFcγRIIA in IgG-dependent anaphylaxis induction, even when several other human FcγRs are expressed.

On human platelets, hFcγRIIA is expressed as the sole FcγR [START_REF] Bruhns | Mouse and human FcR effector functions[END_REF]. Considering that wildtype mice do not express any IgG receptor on platelets, we hypothesized that a putative platelet contribution to human IgG-induced anaphylaxis might have been overlooked due to the inappropriateness of classical mouse models. Indeed, platelets are equipped with a plethora of bioactive molecules, which they release upon activation. Among them, serotonin is a prime candidate to contribute to clinical signs of anaphylaxis, since serotonin can increase vascular permeability [START_REF] Majno | Studies on inflammation. 1. The effect of histamine and serotonin on vascular permeability: an electron microscopic study[END_REF][START_REF] Cloutier | Platelets can enhance vascular permeability[END_REF], trigger vasoconstriction or vasodilation [START_REF] Watts | Serotonin and blood pressure regulation[END_REF], and induce bronchoconstriction in the context of allergic asthma [START_REF] Lechin | Increased levels of free serotonin in plasma of symptomatic asthmatic patients[END_REF].

To test whether hFcγRIIA-expressing platelets actively contribute to IgG anaphylaxis, we developed new mouse models expressing either only hFcγRIIA and no other FcγR, or mice recapitulating the human FcγR complexity in place of mouse FcγRs. We then corroborated our findings with patient samples from clinical cases of drug-induced anaphylaxis.

Our results demonstrate that platelets are critical players in hFcγRIIA-induced anaphylaxis. Human FcγRIIA-expressing platelets were directly activated by aggregated hIgG in vitro and in vivo and were sufficient to restore susceptibility to anaphylaxis in resistant mice. Activated platelets released serotonin, which contributed to the severity of anaphylaxis; accordingly, thrombocytemia aggravated IgG-dependent anaphylaxis, whereas thrombocytopenia was protective. Data from a clinical study on perioperative drug-induced anaphylaxis further support the notion that platelets contribute to human anaphylaxis.

Results

Platelets are required for hFcγRIIA-induced anaphylaxis

In mice expressing human FcγRs in place of endogenous mouse FcγRs, whether as transgenes or knock-in inserts, anaphylaxis can be induced by injection of heat-aggregated human IgG (HA-hIgG), as a surrogate for human IgG-immune complexes [START_REF] Gillis | Mechanisms of anaphylaxis in human low-affinity IgG receptor locus knock-in mice[END_REF][START_REF] Jönsson | Human FcgammaRIIA induces anaphylactic and allergic reactions[END_REF][START_REF] Smith | Mouse model recapitulating human Fcgamma receptor structural and functional diversity[END_REF]. As expected, hFcγRIIA tg mice (on a FcγR null background, thus expressing only hFcγRIIA and no other mouse or human FcγRs) developed a rapid hypothermia upon HA-hIgG injection, a primary readout for anaphylaxis, associated with hemoconcentration and augmented vascular permeability (Fig. S1A-B). Surprisingly, the reaction was accompanied by a profound thrombocytopenia (Fig. 1A), detectable as early as 5 minutes following anaphylaxis induction, and that persisted for 24 hours (Fig. 1B). As expected, FcγR null mice (expressing no FcγRs) suffered no hypothermia, vascular leakage or hemoconcentration and only a mild and transient decrease in platelet counts (Fig. 1A-B/S1A-B). To test whether thrombocytopenia was merely a marker of systemic cell activation or if platelets were critical for anaphylaxis induction, we depleted platelets 72 h before anaphylaxis induction using anti-GPIb mAbs. Antibody-dependent platelet clearance was efficient even in FcγR null mice (Fig. S1C), demonstrating that this depletion method is FcγR-independent [START_REF] Li | Desialylation is a mechanism of Fc-independent platelet clearance and a therapeutic target in immune thrombocytopenia[END_REF], and therefore should not interfere with FcγRdependent cell activation thereafter. Platelet depletion abolished hypothermia in hFcγRIIA tg mice (Fig. 1C/S1C-D), suggesting that platelets are required for IgG-dependent anaphylaxis. We then tested whether an increase in platelet numbers would lead to an escalation in anaphylaxis severity. hFcγRIIA tg mice treated with a thrombopoietin receptor agonist, romiplostim, exhibited a 3-fold increase in circulating platelet numbers as compared to untreated mice (Fig. 1D) [START_REF] Leon | Romiplostim administration shows reduced megakaryocyte responsecapacity and increased myelofibrosis in a mouse model of MYH9-RD[END_REF]. This increase in platelet counts rendered hFcγRIIA tg mice extremely sensitive to anaphylaxis induction, with a high accompanying mortality (Fig. 1E). Importantly, thrombocythemia alone was not sufficient to augment sensitivity to anaphylaxis, as thrombocythemic FcγR null mice remained resistant (Fig. 1D-E).

hFcγRIIA tg -expressing platelets are sufficient to induce anaphylaxis in resistant mice

Platelet activation during anaphylaxis may result from direct engagement with circulating HA-hIgG and could therefore contribute to -or even be responsible for -anaphylaxis induction.

Washed platelets from hFcγRIIA tg mice aggregated in vitro upon incubation with HA-hIgG in a dose-dependent manner, and to the extent reached by classical inducers of platelet aggregation, i.e. thrombin or adenosine 5′-diphosphate (ADP) (Fig. 2A). Markers of platelet activation accompanied in vitro aggregation: expression of both CD62P and activated IIb3 integrin were significantly increased on the platelet surface (Fig. 2B). Importantly, washed platelets from FcγR null mice aggregated and exhibited markers of activation only upon stimulation with thrombin or ADP, but not with HA-hIgG (Fig. S2A/B), indicating that the effect of the latter requires IgG receptor expression. Supporting this observation, blocking hFcγRIIA with an anti-hFcγRIIA Fab-fragment prevented activation and aggregation of washed platelets from hFcγRIIA tg mice by HA-hIgG (Fig. 2A/B). These data demonstrate that IgG immune complexes can directly activate hFcγRIIA tg -expressing mouse platelets in vitro, and suggest that this may also occur in vivo.

Accordingly, 30 minutes after injection of HA-hIgG, circulating platelets in hFcγRIIA tg mice, but not in FcγR null mice, exhibited increased CD62P expression whether present as single platelets or as platelet-neutrophil aggregates (Fig. 2C/D). About 80% of circulating neutrophils (Fig. 2E) and >90% of Ly6C hi monocytes (Fig. S2C/E) in hFcγRIIA tg but not FcγR null mice were covered with platelets during anaphylaxis (t=30 minutes) but not after the reaction (t=5 hours). In addition, single neutrophils in circulation of hFcγRIIA tg mice, but not of FcγR null mice, displayed an activated phenotype as reflected by their reduced CD62L expression (Fig. 2F). This suggests that both hFcγRIIA tg -expressing platelets and neutrophils become activated during HA-hIgG anaphylaxis independently of their association. Indeed, injection of an anti-CD62P antibody abolished the formation of platelet-myeloid cell aggregates following injection of HA-hIgG (Fig. 2G/Fig. S2E), without affecting anaphylaxis severity (Fig. 2H), or neutrophil (Fig. S2F) and platelet activation (Fig. S2G/H).

We next evaluated whether expression of hFcγRIIA exclusively on platelets may be sufficient to induce anaphylaxis, without the requirement of other FcγR-mediated myeloid cell activation. We therefore devised an in vivo model in which the anaphylactic inducer, i.e. HA-hIgG, could engage only platelets: we transferred washed platelets from hFcγRIIA tg mice, or from FcγR null mice as a negative control, into FcγR null mice prior to injection with HA-hIgG.

Platelets from hFcγRIIA tg mice, but not from FcγR null mice, conferred FcγR null mice with a susceptibility to hypothermia in response to HA-hIgG injection (Fig. 2I). Therefore, hFcγRIIA-mediated activation of platelets is sufficient for anaphylaxis induction in resistant mice, in the absence of other FcγR-mediated myeloid cell activation.

Platelet-released serotonin contributes to hypothermia in mice undergoing HA-hIgGanaphylaxis

We next investigated whether platelets activated via hFcγRIIA release mediators that are able to directly induce a hypothermic response. Isolated platelets from hFcRIIA tg mice were stimulated in vitro with HA-hIgG to induce platelet aggregation and secretion, and the supernatant containing the entire platelet releasate was recovered by centrifugation. The releasate from HA-hIgG-activated platelets, but not the buffer alone, induced significant hypothermia when injected i.v. into recipient FcγR null mice (Fig. 3A). This releasate contained significant levels of serotonin, but only minute quantities of histamine (33752ng serotonin versus 1.70.2 ng histamine /10 9 platelets) (Fig. S3A). Furthermore, a 15-fold increase in serotonin concentration was observed in the circulation of hFcγRIIA tg mice 5 minutes after anaphylaxis onset, whereas histamine levels were barely increased (Fig. S3B). To test whether serotonin contributes to HA-hIgG-induced anaphylaxis, we inhibited serotonin biosynthesis in hFcγRIIA tg mice prior to anaphylaxis induction by repeated injections of 4-chloro-phenylalanine (PCPA), an inhibitor of the essential enzyme tryptophan hydroxylase [START_REF] Koe | p-Chlorophenylalanine: a specific depletor of brain serotonin[END_REF]. Pre-treatment with PCPA reduced anaphylactic hypothermia in hFcγRIIA tg mice more than 2-fold (Fig. 3B) without altering platelet consumption (Fig. 3C), indicating that serotonin indeed contributes to HA-hIgG anaphylaxis.

Accordingly, intravenous injection of serotonin led to a dose-dependent hypothermia in WT mice (Fig. 3D). Finally, the transfer of the releasate from serotonin-deprived HA-hIgG-activated washed platelets (Fig. S3C) induced a milder temperature drop in recipient FcγR null mice than that from serotonin-sufficient platelets (Fig. 3A). Together these results indicate that hFcγRIIAexpressing platelets release serotonin upon activation with HA-hIgG, which contributes to hypothermic symptoms of HA-hIgG-induced anaphylaxis.

Platelets contribute to IgG-anaphylaxis in a mouse model reproducing human FcγR complexity

hFcγRIIA is one of four human activating IgG receptors, along with hFcγRI, hFcγRIIIA and hFcγRIIIB, in addition to the inhibitory IgG receptor hFcγRIIB. We therefore investigated if platelet activation contributes also to anaphylaxis induction in the context of full human FcγR complexity by using a novel mouse model knocked-in for all human FcγRs (hFcγR KI ), which recapitulates hFcγR expression (Fig. S4/S5). These mice are susceptible to hIgG-induced anaphylaxis, demonstrating rapid hypothermia following HA-hIgG injection, which was likewise accompanied by a profound thrombocytopenia (Fig. 4A). Blocking hFcγRIIA in vivo was sufficient to abolish hypothermia and thrombocytopenia in HA-hIgG-injected hFcγR KI mice (Fig. 4B), illustrating that hFcγRIIA is the FcγR dominantly contributing to anaphylaxis induction, as was suggested by our previous studies using another mouse model [START_REF] Gillis | Mechanisms of anaphylaxis in human low-affinity IgG receptor locus knock-in mice[END_REF]. Platelet depletion in hFcγR KI mice reduced the nadir of hypothermia 2-fold (Fig. 4C/Fig. S1C), confirming the contribution of platelets to anaphylaxis, albeit that this effect was less pronounced than in hFcγRIIA tg mice, in which platelet depletion abolished hypothermia (Fig. 1C). As observed in hFcγRIIA tg mice (Fig. 2), platelets rapidly associated with neutrophils during HA-hIgG-induced anaphylaxis in hFcγR KI mice (Fig. S6A), and pretreatment of hFcγR KI mice with an anti-CD62P antibody also abolished the formation of these aggregates (Fig. S6A) without affecting the anaphylaxis outcome (Fig. S6B) or platelet consumption (Fig. S6C). These data confirm the contribution of platelets to anaphylaxis pathophysiology, in a more complex model of cognate hFcR expression, while simultaneously arguing for the additional activation of other cellular pathways [START_REF] Strait | Pathways of anaphylaxis in the mouse[END_REF][START_REF] Jönsson | Human FcgammaRIIA induces anaphylactic and allergic reactions[END_REF][START_REF] Gillis | Mechanisms of anaphylaxis in human low-affinity IgG receptor locus knock-in mice[END_REF].

Releasate from HA-hIgG-activated human platelets induces hypothermia in mice

Having demonstrated the crucial role of hFcγRIIA-expressing mouse platelets in HA-IgG anaphylaxis, we next investigated whether this was also the case for human platelets. As observed with hFcγRIIA-expressing mouse platelets (Fig. 2A), washed human platelets aggregated in vitro upon incubation with HA-hIgG in a dose-dependent manner, and to the extent reached by classical inducers of platelet aggregation, i.e. thrombin or ADP (Fig. 5A). In vitro aggregation was accompanied by upregulation of platelet activation markers: expression of P-selectin (Fig. 5B) and of activated IIb3 integrin as revealed by PAC-1 antibody binding (Fig. 5C). hFcγRIIA was required for the activation of human platelets by HA-hIgG; as blocking hFcγRIIA prevented aggregation and expression of P-selectin and activated IIb3 integrin on the platelet surface (Fig. 5A-C). These data demonstrate that IgG immune complexes can directly activate human platelets via hFcγRIIA in vitro, and suggest that this may also occur during anaphylactic reactions in humans without the requirement of accessory cells.

We next investigated if human platelets activated with HA-hIgG release mediators that can induce a temperature drop in vivo. Transfer of the releasate from washed human platelets activated with HA-hIgG induced significant hypothermia in recipient mice, which was not observed upon injection of HA-hIgG-containing buffer alone (Fig. 5D). As observed in the releasate of hFcγRIIA-expressing mouse platelets (Fig. 3), human platelet releasate contained significant serotonin concentrations (17745 ng/10 9 platelets), but only a minute amount of histamine (71 ng/10 9 platelets) (Fig. 5E). Thus, serotonin released from HA-hIgG-activated human platelets may contribute to hypothermia in recipient mice.

Evidence for platelet activation during human drug-induced anaphylaxis

Having demonstrated that hFcγRIIA-expressing platelets contribute to IgG anaphylaxis severity in mouse models, we sought to evaluate the translation of these findings to the clinic. To this end, we investigated circulating platelet numbers and activation status in blood samples from 67 patients suffering from mild or severe anaphylaxis to perioperative neuromuscular blocking agent (NMBA) administration and their matched controls, in the case-control "NASA" study (https://clinicaltrials.gov/ct2/show/NCT01637220). Significantly fewer single platelets, identified as CD61 + /FSC lo cells by flow cytometry (Fig. S7), were detected 30 minutes after anaphylaxis induction (i.e. NMBA injection) in the blood of patients suffering from severe versus mild anaphylaxis (1.30±0.14×10 4 /L versus 1.76±0.18×10 4 /L), or compared to matched control patients undergoing anesthesia without anaphylaxis (1.80±0.09×10 4 /L). Six-to-eight weeks post-anaphylaxis, platelet counts from patients that had suffered a severe anaphylactic reaction were comparable (2.06±0.15×10 4 /L) to those of controls (Fig. 6A), indicating that this phenotype was not inherent to this patient group. Of note, the platelet counts represented herein are unusual as only single CD61 + /FSC lo cells were considered (thus excluding platelets in aggregates) and because blood was drawn on heparin in this clinical protocol, which is known to affect platelet responsiveness [START_REF] Gao | Heparin promotes platelet responsiveness by potentiating alphaIIbbeta3mediated outside-in signaling[END_REF]. The sampling method should not, however, be responsible for the variations we observe between patient groups, since all blood was sampled identically.

Nonetheless, to complement this analysis we took advantage of four case/control pairs among all patients in this study, who underwent cardiac surgery and therefore assessment of their differential blood counts before, during and after surgery. In this patient sub-group, we could confirm thrombocytopenia in anaphylactic patients compared to controls, particularly in the +3/4h interval following anesthesia (Fig. 6B). This effect could not be accounted for merely by hemodilution, since simultaneously monitored leukocyte counts did not change significantly (Fig. 6C). Finally, and similar to results from our pre-clinical models, platelet CD62P expression and the percentage of CD62P-positive platelets were significantly higher in patients suffering from severe versus mild NMBA-induced anaphylaxis, or versus control groups (Fig. 6D), indicating that human platelets are activated during anaphylaxis.

Discussion

This work identifies platelets as critical novel players in the effector phase of IgG anaphylaxis using two different pre-clinical mouse models sharing the particularity of expressing the activating human IgG receptor hFcγRIIA (CD32A) on platelets. Severe thrombocytopenia and platelet activation required hFcγRIIA expression on platelets, whereas anaphylaxis severity increased with augmented platelet numbers and was reduced in their absence. hFcγRIIAexpressing platelets were directly activated by aggregated hIgG in vitro and in vivo and were sufficient to restore susceptibility to anaphylaxis in resistant mice. Activated platelets released serotonin, which contributed to anaphylaxis severity. These observations were partly corroborated by clinical data from a cohort of patients suffering from drug-induced anaphylaxis, showing that platelet activation was associated with anaphylaxis severity and that anaphylaxis occurrence was accompanied by a reduction in circulating platelet numbers.

Our analysis identifies platelet-derived serotonin as a mediator in hFcRIIA-induced anaphylaxis. Serotonin is released by both human and mouse platelets following HA-hIgG activation: the releasate from HA-hIgG-activated human or mouse platelets contained high concentrations of serotonin, and was able to induce significant hypothermia when transferred into recipient mice, whereas the releasate from serotonin-depleted platelets induced only a mild hypothermia. Mice exhibited elevated circulating serotonin concentrations rapidly after anaphylaxis induction, and developed only a mild hypothermia when serotonin biosynthesis was inhibited in vivo prior to anaphylaxis induction. Furthermore, injection of serotonin alone into mice induced a hypothermic response. Supporting our findings, release of platelet serotonin was observed following incubation of neuromuscular blockers with blood samples of patients who had previously an anaphylactic reaction to a neuromuscular blocker [START_REF] Bermejo | Platelet serotonin is a mediator potentially involved in anaphylactic reaction to neuromuscular blocking drugs[END_REF]. Serotonin has also been described to trigger bronchoconstriction when released in the lungs of asthmatic patients [START_REF] Lechin | Increased levels of free serotonin in plasma of symptomatic asthmatic patients[END_REF], to induce either vasoconstriction or vasodilation depending on the type of serotonin receptor and vascular bed [START_REF] Watts | Serotonin and blood pressure regulation[END_REF] and to increase vascular permeability through the formation of gaps in the endothelium [START_REF] Majno | Studies on inflammation. 1. The effect of histamine and serotonin on vascular permeability: an electron microscopic study[END_REF][START_REF] Cloutier | Platelets can enhance vascular permeability[END_REF], suggestive of pleiotropic effects when released during anaphylaxis.

Depletion of platelet serotonin stores by inhibition of serotonin biosynthesis attenuated but did not totally protect mice from anaphylaxis, indicating that serotonin is not the sole mediator of anaphylaxis in the pre-clinical models used herein. Circulating histamine concentrations did not change significantly during anaphylaxis in our models, and antihistamine pretreatment had no effect on anaphylaxis severity (Fig. S6D). PAF receptor antagonists, however, attenuated HA-hIgG-induced anaphylaxis in hFcR KI mice, as reported for other models of IgG anaphylaxis [START_REF] Strait | Pathways of anaphylaxis in the mouse[END_REF][START_REF] Jönsson | Mouse and human neutrophils induce anaphylaxis[END_REF][START_REF] Gillis | Mechanisms of anaphylaxis in human low-affinity IgG receptor locus knock-in mice[END_REF], suggesting that PAF, but not histamine, may contribute along with serotonin to IgG anaphylaxis. Whether PAF originates from platelets and/or from independently activated myeloid cells remains an open question.

Experimental anaphylaxis in hFcγRIIA-expressing mice was associated with transient hypothermia, augmented vascular permeability and hemoconcentration, and was accompanied by a rapid and severe thrombocytopenia. Importantly, anaphylaxis-induced thrombocytopenia occurred within minutes and preceded significant hypothermia in our models, suggesting that thrombocytopenia is an early sign of anaphylaxis triggered by direct platelet activation. In support of the notion that platelets may trigger anaphylaxis induction, IgG receptor expression exclusively on platelets was sufficient to induce hypothermia. Furthermore, these results may explain the dominance of hFcγRIIA over other human FcγRs in anaphylaxis induction in hFcγR KI mice (expressing hFcγRI, hFcγRIIA, hFcγRIIB, hFcγRIIIA and hFcγRIIIB), or in mice expressing a more restricted set of hFcγRs, as reported previously [START_REF] Gillis | Mechanisms of anaphylaxis in human low-affinity IgG receptor locus knock-in mice[END_REF], as hFcγRIIA is the only activating IgG receptor expressed by platelets [START_REF] Bruhns | Mouse and human FcR effector functions[END_REF].

The role of hFcγRIIA-induced platelet activation is best established in the pathophysiology of immune-mediated thrombocytopenia and thrombosis, a group of pathologies that encompass thrombosis triggered by certain therapeutic monoclonal antibodies and sepsisassociated or heparin-induced thrombocytopenia [START_REF] Meyer | Bevacizumab immune complexes activate platelets and induce thrombosis in FCGR2A transgenic mice[END_REF][START_REF] Cox | Platelets and the innate immune system: mechanisms of bacterial-induced platelet activation[END_REF][START_REF] Mckenzie | Advances in the pathophysiology and treatment of heparin-induced thrombocytopenia[END_REF][START_REF] Stolla | CalDAG-GEFI deficiency protects mice in a novel model of Fcgamma RIIA-mediated thrombosis and thrombocytopenia[END_REF]. In most of these conditions, diseasecausing IgG is binding via its antigen-recognition site to the surface of platelets, thereby facilitating interactions of its Fc portion with platelet hFcγRIIA. Whether this is a general requirement for hFcγRIIA activation is not known. It may, however, imply that in the context of IgG-dependent anaphylaxis, IgG complexes must first be retained by one hFcγRIIA molecule on the platelet surface to then be able to trigger platelet activation via another hFcγRIIA molecule on the same or adjacent platelet (i.e. in cis or trans). Indeed, hIgG readily bound to the platelet surface in hFcγRIIA tg mice injected with HA-hIgG, in a dose dependent manner, which led to a corresponding reduction in detectable hFcγRIIA expression on platelets (Fig. S8).

Other studies investigating IgG-induced inflammatory reactions reported that platelets might rather play a regulatory role, preventing exaggerated neutrophil-mediated inflammation or inducing anti-inflammatory cytokine (e.g. IL-10) production by monocytes [START_REF] Gros | Single platelets seal neutrophil-induced vascular breaches via GPVI during immune-complex-mediated inflammation in mice[END_REF][START_REF] Inui | Platelets convert peripheral blood circulating monocytes to regulatory cells via immunoglobulin G and activating-type Fcgamma receptors[END_REF]. Importantly, however, these studies have been performed in mice expressing mouse FcγRs, and therefore in the absence of the sole activating IgG receptor on platelets, hFcγRIIA. In light of the data presented herein and previous reports on hFcγRIIA function in vivo, it may be pertinent to reevaluate the role of platelets during inflammation using hFcγRIIA-expressing mice, to ascertain whether protective or regulatory functions are preserved when platelets express hFcγRIIA.

We found that the large majority of circulating neutrophils and Ly6C hi -monocytes were covered with activated platelets; which, however, neither accounted for the reduction in circulating platelet numbers nor for the activation of either platelets or myeloid cells, because anti-CD62P antibodies blocked these interactions yet had no significant effect on anaphylaxis severity or thrombocytopenia. Other phenomena in vivo such as platelet-platelet aggregation, phagocytosis or adhesion to the vascular endothelium (33) may contribute to the thrombocytopenia observed during anaphylaxis. Also, our data imply that activation of platelets (increased CD62P expression) and neutrophils (CD62L shedding) occurs independently of their association. Prior studies on platelet-neutrophil interactions have suggested that platelet binding to neutrophils may facilitate neutrophil effector functions, such as extravasation into inflamed tissues and the formation of neutrophil extracellular traps [START_REF] Clark | Platelet TLR4 activates neutrophil extracellular traps to ensnare bacteria in septic blood[END_REF][START_REF] Caudrillier | Platelets induce neutrophil extracellular traps in transfusion-related acute lung injury[END_REF][START_REF] Sreeramkumar | Neutrophils scan for activated platelets to initiate inflammation[END_REF]. Our data indicate that these physical interactions are not required for anaphylaxis induction, but rather that platelets and myeloid cells are each activated through direct FcR engagement. Indeed we have shown previously that antibody-mediated neutrophil depletion had a beneficial effect on IgG anaphylaxis in hFcγRIIA tg mice [START_REF] Jönsson | Human FcgammaRIIA induces anaphylactic and allergic reactions[END_REF] and in mice expressing a more restricted set of human FcγRs [START_REF] Gillis | Mechanisms of anaphylaxis in human low-affinity IgG receptor locus knock-in mice[END_REF] than that of hFcγR KI mice.

Inherently, data obtained using engineered mouse models may over-or underestimate pathways leading to disease. Platelet contribution to anaphylaxis was observed to be greater in the hFcγRIIA tg mice than in hFcγR KI mice. This may be attributed to differences in hFcγRIIA expression levels on platelets, which is greater in hFcγRIIA tg mice than in hFcγR KI mice.

Another possibility is that expression of multiple human IgG receptors compared to expression of a single IgG receptor (hFcγRIIA) might lead to the concurrent activation of additional cellular pathways in hFcγR KI mice compared to hFcγRIIA tg mice. Future clinical studies evaluating hFcγRIIA expression levels on platelets with respect to anaphylaxis susceptibility may resolve this distinction. Our data indicate that, regardless of whether high or moderate, hFcγRIIA expression on platelets promotes platelet contribution to anaphylaxis severity. Importantly, our in vivo data were supported by our in vitro studies on human washed platelets, which like their mouse counterparts, aggregated and expressed activation markers in response to hFcRIIA engagement by HA-hIgG. Furthermore, we observed reduced numbers of circulating platelets in severe anaphylactic cases, along with an activated platelet phenotype. Of note, these observations are consistent with the sole other report in the literature that studied platelet numbers during human anaphylaxis: in which two anaphylactic cases were accompanied by >60% reduction in circulating platelet counts [START_REF] Choi | Occurrence of disseminated intravascular coagulation (DIC) in active systemic anaphylaxis: role of platelet-activating factor[END_REF]. Thus, clinical data are in line with our data obtained in preclinical mouse models, and substantiate the premise that platelets contribute to human anaphylaxis. Further clinical studies will be necessary to comfort these observations and evaluate whether platelets or platelet-derived mediators such as serotonin may represent new targets to intervene and ameliorate anaphylactic reactions in patients. This report offers new insights into the mechanisms underlying anaphylaxis as it may occur in humans and identifies platelets and their serotonin release as critical players. Our work provides a rationale for future studies to assess the role of platelets in more complex clinical and pre-clinical settings, in which both IgE and IgG anti-allergen antibodies may contribute to anaphylaxis.

Materials and Methods

Clinical study design

Detailed description of the NASA clinical study design and cohort can be found in (38 and Jönsson, de Chaisemartin et al, submitted). In brief, the multi-center NASA ("Neutrophil Activation in Systemic Anaphylaxis") study involved 11 hospital anesthesia departments in the Ile-de-France region in France (https://clinicaltrials.gov/ct2/show/NCT01637220). The purpose of the NASA study was to evaluate the role of neutrophils during anaphylactic reactions to NMBA in humans through a case/control study design, with a 6-8 weeks' follow-up in cases, with clinical signs consistent with intra-anesthetic anaphylaxis to NMBA whatever the grade of the reaction. Patients were retrospectively classified in severity grade according to the Ring and Messmer (39) classification by two independent evaluations of clinician experts. A severe acute hypersensitivity reaction (AHR) was defined as a grade 3 or 4 (i.e. a severe organ failure or a cardiac/respiratory arrest). As case patients were not in a medical and psychological state to provide study consent during the AHR, their consent was obtained as soon as they were judged able. If the patients did not recover the day after the AHR, consent was obtained from a next of kin. Non-inclusion criteria were the absence of consent. The study protocol was approved by a local ethics committee (committee for the protection of Individuals "Ile-de-France X") and prospectively registered at ClinicalTrials.gov (Identifier: NCT0163722). The biological collection was approved and labeled by the National Health Authority, and registered within the French Ministry of Research and ARH ("Agences Régionales de l'Hospitalisation"). As recommended by International/National Guidelines [START_REF] Mertes | Reducing the risk of anaphylaxis during anesthesia: 2011 updated guidelines for clinical practice[END_REF][START_REF] Gouel-Chéron | Management of anaphylactic shock in the operating room[END_REF][START_REF] Simons | World Allergy Organization Anaphylaxis Guidelines: 2013 Update of the Evidence Base[END_REF] on management of perioperative AHR, a venous blood sample was collected 30 minutes following the onset of the AHR when the patient's condition had been stabilized. Platelet enumerations were performed by flow cytometry on diluted total human blood using anti-CD61 and anti-CD62P antibodies. All patients that suffered an AHR were treated following the French and international practice guidelines [START_REF] Mertes | Reducing the risk of anaphylaxis during anesthesia: 2011 updated guidelines for clinical practice[END_REF][START_REF] Gouel-Chéron | Management of anaphylactic shock in the operating room[END_REF][START_REF] Simons | update of the evidence base: World Allergy Organization anaphylaxis guidelines[END_REF][START_REF] Longrois | Traitement des réactions anaphylactiques survenant en cours d'anesthésie et en particulier du choc anaphylactique[END_REF].

Mice

hFcγR KI mice were generated by intercrossing of VG1543 mice [START_REF] Gillis | Mechanisms of anaphylaxis in human low-affinity IgG receptor locus knock-in mice[END_REF] with VG6074 mice (Fig. S4A) designed and generated by Regeneron Pharmaceuticals, Inc. on a mixed 62.5% C57BL/6N, 37.5% 129S6/SvEv genetic background, and backcrossed one generation to C57BL/6N. FcγR null mice were described previously [START_REF] Gillis | In vivo effector functions of high-affinity mouse IgG receptor FcgammaRI in disease and therapy models[END_REF]. Mice expressing the fcgr2a transgene [START_REF] Mckenzie | The role of the human Fc receptor Fc gamma RIIA in the immune clearance of platelets: a transgenic mouse model[END_REF] were bred to FcγR null mice to generate FcγRIIA tg FcγR null mice (referred to as hFcγRIIA tg herein). All mice were bred at Institut Pasteur and used for experiments at 7-11 weeks of age.

Antibodies and reagents

ADP (Adenosine 5′-diphosphate sodium), prostacyclin PGI 2 , apyrase, PAF, ACD (acidcitrate-dextrose) anticoagulant and p-chlorophenylalanine (PCPA) were obtained from Sigma Aldrich, TNP [START_REF] Li | Desialylation is a mechanism of Fc-independent platelet clearance and a therapeutic target in immune thrombocytopenia[END_REF][START_REF] Leon | Romiplostim administration shows reduced megakaryocyte responsecapacity and increased myelofibrosis in a mouse model of MYH9-RD[END_REF][START_REF] Koe | p-Chlorophenylalanine: a specific depletor of brain serotonin[END_REF][START_REF] Gillis | Mechanisms of anaphylaxis in human low-affinity IgG receptor locus knock-in mice[END_REF][START_REF] Gao | Heparin promotes platelet responsiveness by potentiating alphaIIbbeta3mediated outside-in signaling[END_REF][START_REF] Bermejo | Platelet serotonin is a mediator potentially involved in anaphylactic reaction to neuromuscular blocking drugs[END_REF][START_REF] Meyer | Bevacizumab immune complexes activate platelets and induce thrombosis in FCGR2A transgenic mice[END_REF][START_REF] Cox | Platelets and the innate immune system: mechanisms of bacterial-induced platelet activation[END_REF][START_REF] Mckenzie | Advances in the pathophysiology and treatment of heparin-induced thrombocytopenia[END_REF][START_REF] Stolla | CalDAG-GEFI deficiency protects mice in a novel model of Fcgamma RIIA-mediated thrombosis and thrombocytopenia[END_REF][START_REF] Gros | Single platelets seal neutrophil-induced vascular breaches via GPVI during immune-complex-mediated inflammation in mice[END_REF] -BSA from Santa Cruz, thrombin from Roche, anti-GPIbα (polyclonal rat IgG) and isotype control from Emfret Analytics and heparin from Tocris. Human albumin and fibrinogen were provided by LFB Biomédicaments (2014-01029). Anti-FcγRIIA (mouse IgG2b,

Preparation of washed platelet suspensions, in vitro stimulation and transfer

Preparation of washed human or mouse platelets. Washed platelets from mouse blood were prepared as previously described [START_REF] Cazenave | Preparation of washed platelet suspensions from human and rodent blood[END_REF]. Platelets were suspended in Tyrode's buffer (137 mM NaCl, 2 mM KCl, 12 mM NaHCO 3 , 0.3 mM NaH 2 PO 4 , 1 mM MgCl 2 , 2 mM CaCl 2 , 5.5 mM glucose, 5 mM Hepes, pH7.3) containing 0.35% human serum albumin and apyrase (0.02 U/ml). Suspension of washed platelets was adjusted at the indicated concentration and maintained at 37°C until use. For generation of serotonin-depleted washed platelets, mice received i.p. injections of p-chlorophenylalanine (PCPA, 300 mg/kg) or vehicle (PBS-Tween 20 5% (v/v)) for 5 consecutive days and were used for experiments on day 6.

In vitro stimulation. Platelet aggregation was measured at 37°C in an aggregometer APACT 4004 (ELITechGroup). A 270 µL aliquot of washed human (2×10 6 platelets/µL) or mouse (2×10 5 platelets/µL) platelets was stirred at 1,100 rpm and activated by addition of the appropriate agonist and human fibrinogen (0.8 mg/mL), in a final volume of 300 µL. The extent of aggregation was quantified by measuring the maximum curve height above baseline. For flow cytometric analysis washed human or mouse platelets were stimulated for 10 minutes at 37°C.

Transfer of washed mouse platelets. 1.7×10 9 washed mouse platelets in 300 L Tyrode's albumin buffer (or buffer alone) were injected i.v. into recipient mice 20 minutes before anaphylaxis induction.

Transfer of platelet releasates. Washed human or mouse platelets (6×10 6 platelets/µL) were activated by HA-hIgG (1 mg/mL) for 30 minutes, followed by centrifugation at 15 000 g for 10 minutes and releasates were collected for i.v. injection into recipient mice (200 μL/mouse). Tyrode's albumin buffer incubated with HA-hIgG (1 mg/mL) served as negative control.

Flow cytometric analysis of platelets, leukocytes and their aggregates

Flow cytometric analysis of NASA study patients: As recommended by International/National Guidelines [START_REF] Mertes | Reducing the risk of anaphylaxis during anesthesia: 2011 updated guidelines for clinical practice[END_REF][START_REF] Gouel-Chéron | Management of anaphylactic shock in the operating room[END_REF][START_REF] Simons | World Allergy Organization Anaphylaxis Guidelines: 2013 Update of the Evidence Base[END_REF] on management of perioperative AHR, a venous blood sample was collected 30 minutes following the onset of the AHR. It should be noted that platelets analysis was not an original objective of the NASA study and that blood samples were taken using heparin as anti-coagulant. Platelet enumerations and assessment of CD62P expression were performed by flow cytometry. Diluted total human blood was incubated for 15 min at room temperature in the dark in the presence of anti-CD61 antibodies, together with anti-CD62P antibodies or its isotype control (mIgG1). Mouse blood cells or washed human or mouse platelets were stained with indicated fluorescently-labeled mAbs for 15 minutes at room temperature. In mouse whole blood, single platelets were defined as FSC lo /CD41 + cells, neutrophils as CD45 + /CD11b + /Ly6G hi cells and Ly6C hi -monocytes as CD45 + /CD11b + /Ly6G lo /Ly6C hi cells. Within these populations, aggregates were identified using CD41 + as a marker. Platelet activation of single platelets and on aggregates was assessed by CD62P expression and neutrophil activation by CD62L shedding.

Statistical analysis

Mouse data and experiments with human washed platelets were analyzed using one-way

  hFcγR KI , FcγR null or hFcγRIIA tg mice demonstrate normal development and breeding patterns. Experiments using mice were validated by the CETEA ethics committee number 89 (Institut Pasteur, Paris, France) under #2013-0103, and by the French Ministry of Research under agreement #00513.02.

Fig. 1 .

 1 Fig. 1. Platelets are required for hFcγRIIA-induced anaphylaxis. (A/B) Change in body temperature (left) and platelet count (right) during HA-hIgG-anaphylaxis in hFcγRIIA tg (circles, n=4) and FcγR null (squares, n=4) mice. (C) HA-hIgG-anaphylaxis-induced changes in body temperature in hFcγRIIA tg (circles) and FcγR null (squares) mice (n=4), pretreated with anti-GPIbα antibody (red symbols) or isotype control (black symbols), (n=4). (D) Platelet counts in hFcγRIIA tg (circles) and FcγR null (squares) mice, pretreated (green symbols, n=5) or not (open symbols, n=4 or 5) with

Fig. 2 .

 2 Fig. 2. hFcγRIIA-expressing platelets are sufficient to induce anaphylaxis in resistant mice. (A) Maximal aggregation (%) of washed platelets from hFcγRIIA tg mice compared to baseline and

Fig. 3 .

 3 Fig. 3. Platelet-released serotonin contributes to hypothermia in mice undergoing HA-hIgGanaphylaxis. (A) Releasates (Rel.) from HA-hIgG-activated washed platelets from hFcγRIIA tg

Fig. 4 .Fig. 5 .

 45 Fig. 4. Platelets contribute to IgG-anaphylaxis in mouse models reproducing human FcR

Fig. 6 .

 6 Fig. 6. Evidence for platelet activation during human drug-induced anaphylaxis. (A) Platelet counts

  If not stated otherwise, data are represented as mean ± SEM. Statistical differences between different patient groups were assessed using a Kruskal-Wallis test with Dunn's correction for multiple testing ($), differences between measures acquired at two different time points in the same patients were assessed using a Wilcoxon test (#). If not stated otherwise, data are represented as mean ± SEM.

	or two-way ANOVA with Tukey's post-test or unpaired t-test for comparison of two groups of
	measurements. A p-value less than .05 was considered significant: (*p < .05; **p < .01; ***p <
	.001; ****p < .0001).

severe (n=29) patients during follow-up visit. (A/D) Statistically significant differences between groups of anesthetized subjects: $ P<0.05, $$$$ P<0.0001, and within a group of subjects comparing two different time points: ## P<0.01, ### P<0.001; #### P<0.0001.

Acknowledgments: We are thankful to our colleagues F. Abdallah, B. Iannascoli and O. Richard-Le Goff at Institut Pasteur, Paris for technical help. We are thankful to our colleagues for their generous gifts: M.P. Reilly and S. McKenzie (Jefferson Medical College, Philadelphia, PA) for FCGR2A-transgenic mice and LFB Biomédicaments (Les Ulis, France) for human albumin and fibrinogen. Funding: This work was supported by the European Research Council (ERC)-Seventh Frame-work Program (ERC-2013-CoG 616050), by a JCJC grant from the Agence National de la Recherche (ANR-16-CE15-0012-01), the Institut Pasteur, the Institut National de la Santé et de la Recherche Médicale (INSERM), the Société Française d'Allergologie (SFA; Soutien de la Recherche en Allergologie). H.B. was supported by a fellowship from the University Pierre et Marie Curie. C.M.G. was supported partly by a stipend from the Pasteur -Paris University (PPU) International PhD program and by the Institut Carnot Pasteur Maladies Infectieuses, and partly by the Balsan company. Y.W. holds a stipend from the Pasteur -Paris University (PPU) International PhD program. F.J. is an employee of the Centre National de la Recherche Scientifique (CNRS). Author contributions: H.B., F.J., B.H., O.G., C.M.G. Y.W. and S.M. performed and analyzed experiments; A.M. and L.E.M. designed mouse targeting and generated mouse strains; L.d.C. and A.G-C. provided data from cardiac surgery patients. S.C.M, P.B and D.L. initiated the NASA study, B.H. and C.G provided expertise on platelet biology, F.J. supervised and designed the research with help from P.B.; P.B. and F.J. provided funding; all authors were given the opportunity to discuss results and manuscript content. Competing interests: L.E.M. and A.M. are employees of Regeneron Pharmaceuticals, Inc. and hold stocks in the company.

All other authors declare no competing financial interests.

Platelet enumerations and hematocrit determination

In selected patients (4 cardiac surgery anaphylactic cases and 4 paired controls) platelets from EDTA-treated whole blood were enumerated using the Sysmex TS 500 Hemocytometer (Kobe, Japan). For analysis of mouse blood, 10 L of blood was collected at the tail vein directly in EDTA (20 mM final), and platelet numbers and hematocrit assessed using a hematometer (SCIL Vet abc Plus, Horiba Medical).

In vivo blocking, depletion, romiplostim treatment

For platelet depletion, mice were injected i.v. with 50 g/mouse of anti-GPIbα (anti-CD42b) or isotype control (rat IgG) 72 h before challenge. Blocking of FcγRIIA was achieved by i.v. injection of 40 g/mouse blocking anti-FcγRIIA mAb (clone IV.3) or isotype control (mIgG2b) 24 h and 12 h before challenge. For CD62P blocking experiments, 50 g/mouse of anti-CD62P REA antibody (clone REA344; Miltenyi) or an isotype control were injected 30 minutes before challenge. To induce neo-production of platelets, mice received s.c. injections of romiplostim (50 μg/kg of body weight; NPLATE ® Amgen) on day 0 and 3 and were used for experiments on day 6, adapted protocol from [START_REF] Leon | Romiplostim administration shows reduced megakaryocyte responsecapacity and increased myelofibrosis in a mouse model of MYH9-RD[END_REF]. For in vivo serotonin depletion, mice received i.p. injections of p-chlorophenylalanine (PCPA, 300 mg/kg) or vehicle (PBS-Tween 20 5% (v/v)) for 7 consecutive days. On the third day of treatment, a mild thrombocytopenia was induced with 5 g/mouse of anti-GPIbα mAb to remove serotonin-loaded platelets from the circulation. Mice were used for experiments on day 7 when platelet counts had recovered.

Supplementary Materials

Supplementary Materials:

NASA study group


Ichrak Toumi

Member, IEEE Valentin Emiya

Audio inpainting based on joint-sparse modeling

Keywords: Audio inpainting, sparse approximation, joint sparsity, matching pursuit

We present a new framework for the restoration of missing samples in audio signals. It consists in locating audio frames that share similar sparse structures and in applying a joint-sparse algorithm to estimate the missing samples. Such similar frames are found in audio signals due to the signals' intrinsic structures: across channels, in the temporal neighboring of each frame and, since patterns are repeated non-locally. We propose a fast and robust strategy for locating the similar frames by introducing a spectral cosine similarity that is more suitable than the usual correlation similarity. We present and compare the inpainting versions of three known joint-sparse algorithms and show how they lead to a better reconstruction of the missing parts. Experimental results reveal that by selecting only a few similar frames, joint-sparse audio inpainting outperform the state-of-the-art OMP inpainting method by up to 5 dB, and that improvements cumulatively result from non-local and interchannel joint decomposition.

I. INTRODUCTION

The audio inpainting framework aims at recovering the distored or missing parts in an audio signal based on the observed parts. In [START_REF] Adler | Audio inpainting[END_REF], the inpainting problem is formulated as an inverse problem in each audio frame. An inpainting algorithm based on a sparse decomposition was introduced, allowing the estimation of missing samples in audio frames from the approximated sparse support of the observed samples in a Gabor dictionary. The approach achieved competitive or better results compared to state-of-the-art methods like [START_REF] Janssen | Adaptive interpolation of discrete-time signals that can be modeled as autoregressive processes[END_REF].

However, methods such as [START_REF] Adler | Audio inpainting[END_REF] process each audio frame independently while audio signals like speech, music and other sounds are highly structured across frames. As illustrated in Figure 1, this kind of structures originates from at least three phenomena. First, slowly-varying contents result in local similarities in the temporal neighborhood of each frame. Second, non-local similarities are observed since audio signals are generally composed of patterns that occur several times like phonemes and musical notes or chords. Third, simultaneous frames from multiple channels also offer several versions of some common contents with only small gain and delay differences. In the case of sparse models, similarity is defined in terms of a common sparse support, as illustrated by vertical arrays in Figure 1, with white elements representing zero entries. Our research hypothesis is that the use of these similar frames is advantageous to better estimate model parameters and solve inverse problems. The idea have been already used in image processing [START_REF] Buades | A non-local algorithm for image denoising[END_REF] and has been made possible using joint (a.k.a. simultaneous) sparse models [START_REF] Mairal | Non-local sparse models for image restoration[END_REF], [START_REF] Li | Image denoising via robust simultaneous sparse coding[END_REF]: the authors I. Toumi and V. Emiya are with Aix Marseille Univ, Université de Toulon, CNRS, LIS, Marseille, France (e-mail: firstname.lastname@lis-lab.fr).

This work was supported by ANR JCJC program MAD (ANR-14-CE27-0002). Fig. 1. Illustration of the joint-sparse structure of an audio signal: a target frame (black dot in the left part) has similar joint-sparse frames (in blue) identified simultaneously across channels (left/top and right/bottom), in its neighboorhood (selected frames in the left part) and non-locally (selected frames in the center and right parts). assume that the similar image patches share the same supports and they apply an algorithm for joint-sparse decomposition.

Recently, this idea has motivated several works in audio processing [START_REF] Siedenburg | Audio declipping with social sparsity[END_REF]- [START_REF] Perraudin | Inpainting of long audio segments with similarity graphs[END_REF]. It has proved for audio declipping [START_REF] Siedenburg | Audio declipping with social sparsity[END_REF] where dependencies between neighboring coefficients are exploited to improve the declipping performance. The results confirm the interest in using similarity information for inpainting clipped data. This approach being limited to the joint modeling of neighboring frames, finding and exploiting non-local similar frames is not addressed. Another strategy is proposed in [START_REF] Manilow | Leveraging repetition to do audio imputation[END_REF] where repeated patterns are tracked in audio signals. This is performed in the particular case where the audio background is characterized by patterns repeated with a repeating period while the foreground has no repetition pattern. Non-local structures have been tracked using similarity graphs in [START_REF] Bahat | Self-content-based audio inpainting[END_REF], [START_REF] Perraudin | Inpainting of long audio segments with similarity graphs[END_REF] for inpainting large gaps in audio signals. In [START_REF] Perraudin | Inpainting of long audio segments with similarity graphs[END_REF], the inpainting of a large hole is achieved by comparing features extracted before and after the gap to other regions in order to find a region with similar contents to be copy-pasted inside the hole with smoothed transitions. In [START_REF] Bahat | Self-content-based audio inpainting[END_REF], more processing is proposed to adapt the contents of the pasted block with pitch, gain and time modifications, in the context of packet loss concealment.

In this paper, we propose to exploit similarity in audio signals in a sparse inpainting setting, in the continuity of [START_REF] Adler | Audio inpainting[END_REF], and extending preliminary works [START_REF] Toumi | Sparse non-local similarity modeling for audio inpainting[END_REF]. Given that the more missing samples, the less observations, the worse the sparse estimation, our research hypothesis is that finding similar regions for jointsparse decomposition will provide more observation in order to improve the estimation quality and the resulting inpainting performance. In such a context, the two main questions we address are:

1) In an audio signal with missing samples, how to locate regions that are similar in the sense that their latent sparse representations share a common support? 2) Given a set of regions similar to a target frame, which algorithms are appropriate for reconstructing the missing samples in this frame? This paper is organized as follows. The general processing framework and notations are introduced in section II. In section III, we introduce the joint-sparsity approach and extend several existing algorithms to deal with missing data by using frame-dependent dictionaries. In section IV, we study how to select similar frames, based on a joint-sparse model structuring audio signals. Extensive experiments are reported in section V and conclusions are drawn in section VI.

II. FRAME-BASED INPAINTING FRAMEWORK

We consider an audio signal s ∈ R L×C of length L with C channels. A known binary mask m ∈ {0, 1}

L×C is used to locate missing and observed samples, coded by 0 and 1 entries respectively, so that the observation is y = m s where is the Hadamard product. Signal s is segmented into

N L-L h overlapping frames of length L. For frame index n ∈ [N ] and channel c, s n,c = [s (nh + l, c)] l∈[L] ∈ R L denotes the n th frame in channel c,
where h is the hop size and [N ] {0, . . . , N -1}. The binary mask m and the observation vector y are segmented similarly as a set of frame masks {m n,c } and a set of observed frames {y n,c }. In order to simplify notations, we will also use index j = (n, c) as a double index for a frame s j , the related mask m j and observation y j .

Each frame is inpainted as a target frame, by means of the selection of other similar frames: the inpainting of a target frame given a set of similar frames is described in section III while the principle to select a set of similar frames is detailed in section IV. The restored signal can then be obtained from the reconstructed frames by a regular overlap-add procedure.

III. JOINT-SPARSE AUDIO INPAINTING

Starting from the formulation of the inpainting problem with a regular sparse model in section III-A, we introduce the formulation of the joint-sparse inpainting problem in section III-B. We propose several algorithms to obtain the joint-sparse decomposition from a set of frames with missing entries in section III-C.

A. Sparse problem formulation

In [START_REF] Adler | Audio inpainting[END_REF], each audio frame s is modeled using a sparse representation [START_REF] Elad | Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing[END_REF] as:

s = Dx + n (1)
where D ∈ R L×K is the so-called dictionary, x ∈ R K is the sparse representation and n ∈ R L is the noise. Given a mask m ∈ {0, 1} L for frame s in the inpainting context, the observation is y = m s and the inpainting optimization problem writes:

arg min x x 0 s.t. y -m Dx 2 2 < (2)
where > 0 is a tolerance on the residual energy. Since the 0 norm leads to an NP-hard problem, an approximated sparse solution may be obtained using a variant of the OMP algorithm [START_REF] Pati | Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition[END_REF] where all the dictionary columns are internally re-normalized to unit norm due to the partial observations. The unknown samples are then recovered from the given sparse solution x by reconstructing the frame as s D x.

B. Joint-sparse problem formulation

For a target frame s, let us assume that we have an index set S so that frame s is included in the set of frames indexed by S and the sparse decompositions x j of frames s j , j ∈ S have the same support. Many algorithms have been designed to obtain a joint-sparse decomposition X S = [x j ] j∈S (e.g., see [START_REF] Blanchard | Greedy algorithms for joint sparse recovery[END_REF]- [START_REF] Needell | Cosamp: Iterative signal recovery from incomplete and inaccurate samples[END_REF]). Joint-sparsity is typically promoted by minimizing the p,q mixed (pseudo-)norm X S p,q of matrix X S where the pair (p, q) usually takes the values (0, ∞) to count the number of non-zero rows or (1, 2) for a convex relaxation promoting joint sparsity.

In the inpainting case, the optimization problem can be formulated as arg min

X S X S 0,∞ s.t. Y S -M S DX S 2 F < S (3)
where S > 0, Y S [y j ] j∈S is the observation matrix in which each column is a selected observed frame y j = m j s j , M S [m j ] j∈S is the binary mask matrix, and X S 0,∞ j∈S supp(x j ) counts the number of non-zero rows in X S .

C. Algorithms for joint-sparse inpainting

We propose three algorithms for joint-sparse decomposition by extending their original formulation to the inpainting framework. The extension consists in building frame-dependent dictionaries to handle missing data as described in section III-C1. The three algorithms are detailed in sections III-C2, III-C3 and III-C4. The reconstruction of the frames is eventually described in section III-C5

1) Frame-dependent dictionaries: Since each selected frame has its own mask, one must use frame-dependent dictionaries instead of a unique dictionary for all frames. For j ∈ S, the normalized dictionary for frame j is defined as

D j diag(m j ) × D × W j (4)
where

W j diag m j d k -1 2 k∈[K]
is the normalization matrix. In eq. ( 4), the left product with diag(m j ) results in zeroing the rows of D related to missing coefficients and the right product by W j leads to atoms with unit l 2 -norms. Problem (3) can then be rewritten as arg min

X S X S 0,∞ s.t. j∈S y j -D j x j 2 2 < S (5)
whose solution X S = x j j∈S is related to the solution X S = [x j ] j∈S of (3) by the rescaling

x j = W j x j . (6)
2) Inpainting S-OMP: The Simultaneous Orthogonal Matching Pursuit (S-OMP) generalizes the OMP algorithm to the joint-sparsity case [START_REF] Tropp | Algorithms for Simultaneous Sparse Approximation: Part I: Greedy Pursuit[END_REF]. The inpainting version of S-OMP is described in Algorithm 1. It mainly consists in building the joint-sparse support Γ i in a greedy way, starting from the empty set (line 5) and adding one atom at each iteration (line 10). The atom is selected jointly across frames by adding up the absolute correlations between each frame residual and the frame-related atoms (lines 8 and 9). The residual is then updated independently for each frame (line 11).

Algorithm 1 S-OMP inpainting algorithm.

Inputs: Y S , M S , D = [d k ] k∈[K] , i max , S 1: for j ∈ S do 2:
Build frame-dependent normalized dictionary D j and normalization matrix W j from D and m j using eq. ( 4). 3: end for 4: Iteration counter i = 0 5: Support Γ 0 = ∅ 6: Residual r 0 j = y j , ∀j ∈ S 7: while i < i max and j∈S r i 2 2 ≥ S do 8:

c j = D H j r i j , ∀j ∈ S 9:
Select atom k = arg max

k∈[K] j∈S |c j (k)| 10: Update support Γ i+1 = Γ i ∪ k 11:
Update current solution and residuals r i+1 j = I -D j,Γ i+1 D + j,Γ i+1 y j , ∀j ∈ S 12:

i = i + 1 13: end while 14: for j ∈ S do 15:

Create output vectors:

x j 0 K 16:
Compute sparse representation:

x j Γ i D + j,Γ i y j 17:
Correct dictionary normalization: x j = W j x j 18: end for 19: return X S [x j ] j∈S 3) Inpainting S-IHT: The simultaneous Iterative Hard Thresholding algorithm (S-IHT) is an extension of the Iterative Hard Thresholding (IHT) algorithm to the case of joint sparse signals [START_REF] Blanchard | Greedy algorithms for joint sparse recovery[END_REF], [START_REF] Makhzani | Reconstruction of jointly sparse signals using iterative hard thresholding[END_REF]. The inpainting version given in Algorithm 2 relies on iteratively refining a sparse support Γ i and joint Tsparse vectors x i j . The sparse support is recomputed at each iteration, jointly across frames, by performing a gradient step (line 9), by adding up the absolute values of the result for all frames [START_REF] Toumi | Sparse non-local similarity modeling for audio inpainting[END_REF] and by retaining the location of T highest entries [START_REF] Elad | Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing[END_REF]. The update of the sparse representations is obtained independently for each frame by considering the gradient step in each frame and by keeping only the values indexed by the support Γ i , using the hard-thresholding operator H Γ i+1 (line 13). A faster version of the algorithm has been proposed in [START_REF] Makhzani | Reconstruction of jointly sparse signals using iterative hard thresholding[END_REF] where the step size is an adaptative scaling factor µ i j for each selected frame k and at each iteration i (line 15).

Algorithm 2 S-IHT inpainting algorithm.

Inputs: Y S , M S , D = [d k ] k∈[K] , T , i max , S 1: for j ∈ S do 2:
Build frame-dependent normalized dictionary D j and normalization matrix W j from D and m j using eq. ( 4). 3: end for 4: Iteration counter i = 0 5: Support Γ 0 = ∅ 6: Sparse coefficients x 0 j = 0 7: adaptative scaling factor µ 0 j = 1 L 8: while i < i max and j∈S y j -D jΓ i x i j 2 > S do 9:

z i+1 j = x i j + µ i j D T j (y j -D k x i k ) , ∀j ∈ S 10: w i+1 = 1 |S| j∈S z i+1 j 11:
Γ i+1 = indices of T largest coefficients of w i+1

12:

for j ∈ S do 13:

x i+1 j = H Γ i+1 x i j + µ i j D T j (y j -D j x i j )
14:

g j = D T j,Γ i+1 (y j -D j,Γ i+1 x i j )
15:

µ i+1 j = g T j,Γ i+1 g j,Γ i+1 g T j,Γ i+1 D T j,Γ i+1 D j,Γ i+1 g j,Γ i+1 16:
end for 17:

i = i + 1 18: end while 19: for j ∈ S do 20:
Create output vectors:

x j 0 K 21:
Compute sparse representation:

x j Γ i D + j,Γ i y j 22:
Correct dictionary normalization: x j = W j x j 23: end for 24: return X S [x j ] j∈S 4) Inpainting S-CoSaMP: The third algorithm is the extension of greedy algorithm CoSaMP [START_REF] Needell | Cosamp: Iterative signal recovery from incomplete and inaccurate samples[END_REF] to the joint-sparse case [START_REF] Blanchard | Greedy algorithms for joint sparse recovery[END_REF], [START_REF] Belmerhnia | Greedy methods for simultaneous sparse approximation[END_REF]. The inpainting version is given in Algorithm 3. A sparse support Γ i is iteratively refined, by extending it (line 11) with indexes of νT atoms that best correlate with the residuals, in a joint way across frames (lines 9 and 10). An orthogonal projection of the observed frames onto the extended set of atoms is then performed (lines 13 and 14) and the support update is then obtained by selecting the T largest coefficients (line 16). The residual update is eventually performed independently for each frame (line 17), similarly as in the S-OMP algorithm.

The extension of the support at each iteration is controled by the positive hyperparameter ν that must be adjusted by the user. In our case, a small value of ν is recommended to ensure a better stability of the pseudo-inverse at line 13.

5) Frame reconstruction: Each algorithm returns an approximate solution X S to problem (3). Since S contains the indexes of a target frame and of similar frames, one may only use the sparse representation x to reconstruct the target frame as s D x, discarding the other columns of X S .

IV. SELECTING FRAMES FOR JOINT-SPARSE

DECOMPOSITIONS

Our approach for joint-sparse decomposition and inpainting requires the prior selection of similar frames, which are identified by the index set S. Here, similarity should be understood

Algorithm 3 S-CoSaMP inpainting algorithm. Inputs: Y S , M S , D = [d k ] k∈[K] , T , ν, i max , S 1: for j ∈ S do 2:
Build frame-dependent normalized dictionary D j and normalization matrix W j from D and m j using eq. ( 4). 3: end for 4: Iteration counter i = 0 5: Support Γ 0 = ∅ 6: Sparse coefficients x 0 j = 0 7: Residual r 0 j = y j , ∀j ∈ S 8: while i < i max and j∈S r i j 2 > S do 9:

c j = D H j r i j , ∀j ∈ S 10:
Select support Ω = arg max

|Ω|≤νT k∈Ω j∈S |c j (k)| 2
11:

Q i = Γ i ∪ Ω 12:
for j ∈ S do 13:

b j Q i = D + j,Q i y j 14: b j Q i = 0) 15:
end for 16:

Select support Γ i+1 = arg max

|Γ|=T k∈Γ j∈S |b j (k)| 2 17: r i+1 j = I -D j,Γ i+1 D + j,Γ i+1 y j , ∀j ∈ S 18: i = i + 1 19: end while 20: for j ∈ S do 21:
Create output vectors:

x j 0 K 22:
Compute sparse representation:

x j Γ i D + j,Γ i y j 23:
Correct dictionary normalization: x j = W j x j 24: end for 25: return X S [x j ] j∈S in terms of a joint-sparse representation. In this section, we elaborate on how to build such a set. The main idea is that joint-sparsity is due to at least three phenomena: 1) in a multichannel recording (e.g., stereo), the contents in all channels is the same up to some variations that may not affect joint-sparsity; 2) the contents in successive frames is varying slowly compared to the frame length -which is generally chosen to obtain quasi-stationarity within frames; 3) multiple occurrences of the same audio item -such as phoneme or musical notes-are observed with significant delays between them.

As a result, we propose a triple joint-sparse model in which all those similarities are tracked. Interchannel joint sparsity is introduced in section IV-A in order to select similar frames from all channels. Joint sparsity in adjacent and non-local frames is described in section IV-B, resulting in a selection of frames at various frame indices.

A. Interchannel frame selection

Joint-sparsity across channels can be obtained if the sparse support is invariant to the actual interchannel differences. A global gain difference does not affect the sparse support in an undesirable way, since only the non-zero coefficients are modified, and possibly vanish. However in a more general, convolutive model of audio signal, the same sources are recorded in each channel after being filtered in a channel-dependent way, e.g., by Green functions or head-related transfer functions. As a result, the differences between channels are frequencydependent gain and phase variations, which may affect the sparse support. Hopefully, choosing a Fourier dictionary is suitable since it is not sensitive to those variations, besides being adapted to the sparse decomposition of audio signals.

Hence, the multichannel setting is a beneficial way to gather joint-sparse frames, which can be done by systematically selecting frames from all channels and decomposing them jointly in a Fourier dictionary.

B. Neighboring and non-local frame selection

Let us fix the index n of a target frame. The selection of frames that are similar to this target frame in its temporal neighboring and in possibly-far regions of the signal requires a selection criterion. Given a similarity measure γ and a set of candidate frames indexed by n ∈ [N ], one may build the index set of similar frames by selecting the most similar frames from all channels:

S = ∆ {(n, c) ; n ∈ [N ] , c ∈ [C] , γ(n, n ) ≥ γ S } (7)
where parameter γ S is adjusted to control the number of selected frames ζ which is equal to |S|. One important issue is the choice of a similarity measure that is suitable to the joint-sparse decomposition. The goal is to select a set of frames with sparse approximations sharing the same support as that of the target frame without having to compute their sparse decomposition. This requires a similarity measure that has the ability to act as a proxy to the comparison between the sparse supports. We propose and compare three different similarity criteria in order to find the most appropriate measure for a joint-sparse approximation in a redundant Fourier dictionary. 1) Proposed similarity measures: Similarity measures for the selection of non-local regions have been already used in image processing [START_REF] Buades | A non-local algorithm for image denoising[END_REF] and are generally based on the correlation between images patches, which would correspond to correlating audio frames in our setting. Starting from this criterion, we propose three different measures to assess the similarity between the target frame and a candidate frame, and study how they are suitable for a joint-sparse approximation in a redundant Fourier dictionary:

• the correlation may be viewed as the cosine of the angle between the K-point DFT y n,c and y n ,c of both frames:

γ corr (n, n ) c∈[C] y n,c y n,c 2 , y n ,c y n ,c 2 = c∈[C] y n,c y n,c 2 , y n ,c y n ,c 2 = c∈[C] cos ∠ y n,c , y n ,c (8)
• the spectral cosine similarity discards phase effects and is computed as the cosine similarity between the normalized modulus of the DFT vectors:

γ m (n, n ) c∈[C] cos ∠ y n,c , y n ,c (9)
• the Itakura-Saito (IS) similarity is defined as γ IS (n, n ) 1 -d IS (n, n ) from the IS divergence widely used for audio processing:

d IS (n, n ) 1 CK c∈[C] k y n,c (k) y n ,c (k) (10)
-log

y n,c (k) y n ,c (k) - 1
2) Selecting an appropriate similarity measure: We experimentally compare the ability of the proposed criteria to select the same frames with a reference method which computes the sparse decompositions of the frame supports to find the most similar ones (see Figure 2). We start by segmenting our signal into a set of overlapped frames {s j } with a hop size h. Missing data are artificially created at random locations to obtain observed frames y j . Then, on one hand, a groundtruth is designed as follows: we extract a sparse decomposition of the frames using OMP algorithm and compute the Hamming distance between their supports {x j }, resulting in a similarity matrix Γ ham . On the other hand, we compute the similarity matrices Γ corr ,Γ m ,Γ IS based on the different similarity measures presented above. For each target frame y, the ζ most similar frames among all the candidate frames y j are given by the ζ largest values for each measure. Then the intersection between the sets of indices (S corr , S m , S IS ) and groundtruth S ham is computed in order to select the best similarity measure. The process is repeated for different ratios of missing data, using the same experimental conditions as in Section V and for ζ = 4. Results are averaged for a speech and a piano examples and are shown in Table I.

The results show that the correlation measure is not appropriate and that the spectral cosine similarity seems to be more efficient than the IS similarity for all the considered ratios of missing data. To further understand these quantitative results, similarity maps are generated for the reference method and for each proposed measure showing the selected frames and how they are located. In Figure 3, we give an example for a small region in a speech audio signal sampled at 8KHz. We can see that the structures in the Hamming map are approximately reproduced in the similarity maps of the other measures except the correlation in which aligned structures parallel to the diagonal appear. This is explained by sensitivity of the correlation measure to the interferences due small phase differences which may cause low correlation values even when frames have similar sparse supports which is not the case for the other studied measures. Concretely, correlation in our case could be relevant when only using a unit hop size to select similar frames that are perfectly aligned, which would be computationally demanding and not necessary for the joint sparsity algorithm using a Fourier dictionary. Hence, the spectral cosine similarity happens to be the most appropriate measure and we select it for the experiments conducted in section V.

I MEAN INTERSECTION BETWEEN THE SETS OF FRAMES SELECTED BY THE REFERENCE METHOD AND THE PROPOSED SIMILARITY MEASURES, AS

V. EXPERIMENTAL RESULTS

We present the results of our approach based on the frame selection strategy combined with the joint-sparse optimization. In section V-A, we introduce the experimental setting, including the audio material, problem generation and framebased model parameters. In the section V-B, the tuning of two sensitive hyperparameters is described. Then, in section V-C, we show how the method can solve an audio inpainting problem for different rates of missing data1 . We compare the baseline OMP inpainting algorithm [START_REF] Adler | Audio inpainting[END_REF] and the proposed inpainting versions of the joint-sparse algorithms S-OMP, S-IHT and S-COSAMP, considering the single-channel case (C = 1) and the multichannel case (C = 2).

A. Experimental setting 1) Audio material:

To validate the non local frame selection process and tune hyperparameters, we use two audio signals of duration 4 s sampled at 8 kHz: a melody piano and a male speech composed of one sentence. The inpainting methods are evaluated over a larger set of other sounds from the SQAM dataset 2 . We have selected 26 sound excerpts that are classified into three categories, Speech, Music solo and Music group, whose main features are summarized in Table II 2) Problem generation and performance measures: the missing samples are generated randomly and uniformly according over the whole signal. The protocol consists in fixing the number of missing samples L miss . Then for each (a, b) ∈ N such that a × b = L miss , a holes with length b are generated randomly for each frame in the audio signal. The performance of the inpainting methods is assessed for a missing data rate ranging from 10% to 90%.

The audio inpainting performance is evaluated in terms of signal-to-noise-ratio averaged over the reconstructed frames as defined in [START_REF] Adler | Audio inpainting[END_REF], either on all the samples (SNR full ) or on the recovered samples only (SNR m ). The proposed algorithms are compared to the inpainting OMP algorithm [START_REF] Adler | Audio inpainting[END_REF], considered as a baseline since it relies on a similar sparse model without joint-sparsity aspects.

3) Frame-based model: for all the audio signals, we set the frame length to L = 256 samples and the hop size to h = L 4 . As a result, speech signals sampled at 8 kHz are segmented with a hop size of 8 ms to get around 900 frames with length 32 ms, while for music signals, the number of frames is about 2600 with a length of 16 ms and a hop size of 4 ms. The inpainting algorithms are compared using a redundant complex Fourier dictionary with a size 256 × 512.

B. Tuning hyperparameters

This section is dedicated to the tuning of the sparsity parameter T and the number of selected frames ζ. Those important parameters for the proposed approach are tuned using the piano and speech sounds previously mentioned. Beyond finding good values for those hyperparameters, the proposed 2 See https://tech.ebu.ch/publications/sqamcd. tuning experiments are also the opportunity to illustrate the behavior of the algorithms and to comment on them.

1) Sparsity T : one important hyperparameter is the number of selected atoms T for the sparse modeling. We question the relevance to fix it to a constant value, regardless of the missing data ratio, or to make it depend on this feature. Indeed, when the number of observations is reduced due to missing data, one cannot hope to retrieve the whole sparse support and must resort to more regularization with low T values. We study the optimal values of T for each algorithm and for various missing data ratios p. In order to sample the (p, T ) space adequately, the sparse optimization is carried out using values of T from a p-independent set 2 ; ∈ {3, . . . , 7} and from a p-dependent set

(1 -0.9 p) × 2 ; ∈ {5, 5.5, . . . , 8} , where [.] is the rounding operator and p is the ratio of missing data. The optimal value T opt is obtained from the best SNR m value for each algorithm and every ratio p, with ζ is set to 4. From left part of figure 4, we can see that T opt decreases approximately linearly with respect to p. It also shows that the joint sparse algorithms give similar T opt values for all ratios p. The right part of figure 4 give some preliminary SNR m performance values for each algorithm, showing how the performance decreases as a function of the ratio of missing data. It suggests that S-OMP and S-IHT inpainting algorithms may perform better then OMP and S-CoSamP inpainting algorithms, which needs to be confirmed on a separate and larger set of sounds, as proposed in section V-C. The retained T values are summarized in Table III 2) Number of similar frames ζ: another crucial parameter for the joint sparsity optimization is the size of S which corresponds to the number of similar frames ζ. In figure 5, the average SNR m , computed for the speech and piano sounds using S-OMP algorithm, is plotted as a function of the number of selected frames |S| for a particular case where p = 50% and holes duration is equal to 0.25 ms. The study shows that good SNR values are obtained for a size |S| equal to or greater than 4. When ζ = 1, the S-OMP inpainting performance is equivalent to that of OMP while ∀ ζ > 1 better performance is obtained, illustrating the improvement provided by multiple frame observations. For ζ 4, the SNR improvement may decrease since the additional selected frames may not be as similar as the first 4 selected frames. In addition, selecting a large set of frames may result in a large computational cost. Hence, for the rest of the experiments, we set |S| to 4.

This experiment gives also the opportunity to illustrate the origin of the selected frames. In particular, one may wonder whether the selected frames are neighboring frames located next to the target frame or whether they are very far away from the time of the target frame. Figure 6 illustrates the origin of the selected frames by counting the ratio of neighboring frames among the selected frames. On the absissa, a varying frame index radius is used as a threshold to separate the selected into neighboring frames and non-local frames. According to Figure 6, between 60 and 90% of the selected frames are located in the neighborhood of the target frames, depending on the ratio of missing data and the sound contents. It clearly appears that the more missing data, the more local selection. However, the number of non-local selected frames is significant, which demonstrates the utility to search for nonlocal similarities, as proposed in this paper.

Table IV

C. Inpainting results

Inpainting performance is reported for mono and stereo sounds separately in order to illustrate how the performance is impacted by the origin of the similar frames (neighboring and non-local vs. interchannel).

1) Mono sounds (C = 1): the evaluation of the inpainting results for single-channel sounds using the proposed algorithms is given in figures 7, 8 and 9. From all the figures, one can see that the inpainting algorithms based on the joint sparsity outperforms globally the inpainting OMP, specially in the reconstructed regions as illustrated by the SNR m values. For the speech sounds in figure 7, the three presented inpainting versions of S-OMP, S-IHT and S-CoSamP have a better average SNR m compared to the inpainting OMP, whatever the rate of missing data. However, when looking at the average SNR full for extremely low values of p (< 20%), they are less efficient: for instance, the S-CoSamP algorithm does not outperfom OMP until (p = 40%). This can be explained as follows: first, the number of observations is high enough so that OMP gives a good sparse decomposition. Second, generally, the joint sparse algorithms constrain the support of the selected frames to be equal, which may degrade the data fitting term (i.e., the reconstruction of the observations), especially with real data where supports are not exactly the same. In addition, the S-CoSamP algorithm is very sensitive to the pseudo-inverse. The stability of the latter depends on setting parameters like ν.

For music sounds in figures 8 and 9, we note the same behavior except that the improvement provided by the joint sparse algorithms is more important. This is reflected in a larger gap between the SNR values for S-OMP and S-IHT compared to OMP when p is comprised between 10% < p < 70%. The improvement in SNR values with the joint sparse methods reaches up to 5 dB for the average SNR full and SNR m values. Furthermore, we notice that the inpainting version of S-OMP is giving better performance than S-IHT, with music sounds, contrary to speech sounds for which the inpainting S-IHT outperforms the other algorithms. The difference in SNR between the two algorithms goes from 0 to 2 dB.

2) Stereo sounds (C = 2): in the following, we show how the performance may be additionally improved by taking into account the similarity between channels. The evaluation of the multichannel case is based on two hypotheses:

1) masks in each channel may be different; 2) similarity measures are computed channel-wise, as given by the sum over channels in eq. ( 8), ( 9) and [START_REF] Toumi | Sparse non-local similarity modeling for audio inpainting[END_REF]. In order to compare the mono case to the stereo case, the average SNR f ull and SNR m are computed using similar frames selected in two different ways:

• Mono case (solid lines): each channel is processed separately to select similar frames and apply a joint-sparse inpainting algorithm, and performance is averaged over channels.

• Stereo case (dashed lines): similar frames from both channel are selected jointly. The results are reported in figures 10, 11 and 12, where the SNR values are plotted as a function of the ratio of missing samples. For each algorithm, the average SNR between the two channels is represented.

Globally, the results show that an additional improvement is obtained by considering frames from both channels. For speech signals (see figure 10), the SNR m improvement brought by the use of a selection over the two channels is significant, reaching about 2 dB. Unlike for speech, the SNR improvement is not significant for music solo sounds (figure 11), and for music group sounds (figure 12), only the S-OMP inpainting algorithm shows some noticeable improvement of almost 1 dB.

By comparing the performance obtained in the mono and stereo cases, the results suggest that depending on the sound contents, the improvement obtained by the proposed jointsparse approach may originate differently: for speech sounds, the global SNR m improvement is about 2.5 dB and comes both from the frame selection in time and between channels, while for music sounds, the global improvement is up to 5 dB and is mainly due to the selection of neighboring and non-local frames, rather than from the interchannel observations. This may be due to the fact that music sounds can be composed of very similar occurrences of some patterns while speech contents may vary a lot in excerpts that last a few seconds.

Finally, one may retain that the S-OMP inpainting algorithm seems to give the best performance compared to the other joint-sparse inpainting algorithms S-IHT and S-CoSamP.

VI. CONCLUSION

In this paper, a new framework for audio inpainting using joint-sparsity is presented based on two steps: first, in the audio signal, similar sparse structures are selected using a similarity measure called spectral cosine similarity which proved to be suitable for the joint-sparse decomposition using a redundant Fourier dictionary. Second, a joint-sparse algorithm, using frame-dependent dictionaries, is applied to recover the missing samples. All the inpainting versions of the studied joint-sparse algorithms S-OMP, S-IHT and S-CoSamP give better results compared to the standard sparse inpainting OMP algorithm. This result in the evidence that the inpainting performance improves thanks to the selection of a few similar frames.

This principle may naturally extends to other algorithms, including those for an analysis model or for convex problem formulations, and to other inpainting settings like declipping.

Fig. 3 .

 3 Fig. 3. Similarity matrices for the reference frame selection method (Hamming similarity, top left) and the proposed measures.

Fig. 4 .

 4 Fig. 4. Selection of Topt for the sparse optimization algorithms according to the best SNR computed over the missing samples.

Fig. 5 .

 5 Fig. 5. Average SNRm as a function of the number of selected frames for the joint sparse algorithms (ζ).

Fig. 6 .

 6 Fig.[START_REF] Siedenburg | Audio declipping with social sparsity[END_REF]. Percentage of selected frames in neighborhood as a function of neighborhood radius; each curve is related to a ratio of missing data.

Fig. 7 .Fig. 8 .Fig. 9 .

 789 Fig. 7. Average SNR full (left) and SNRm (right) as a function of the percentage (p) of missing samples for single-channel speech sounds.

Fig. 10 .Fig. 11 .Fig. 12 .

 101112 Fig. 10. Comparison of the average SNR full (left) and SNRm (right) as a function of the percentage (p) of missing samples for speech sounds in the multi channel case.

  Fig. 2. Diagram of the method for the selection of the best similarity measure.

		Segmentation
	𝒔	to overlapped
		frames
		Random Holes Generation	{𝒔 " }			𝜞 3455 𝜞 6 𝜞 78		𝓢 𝒄𝒐𝒓𝒓 𝓢 𝒎 𝓢 𝑰𝑺
		{𝒚 " }			Similarity measures		Select the 𝜻 largest values	Intersection between the
			OMP	{𝒙 " }	Hamming similarity ( 𝜸𝒉𝒂𝒎 𝒋 )	𝜞 9:6	Select the 𝜻 largest values	𝓢 𝒉𝒂𝒎	sets of indices
								Select the best
								measure

( 𝜸𝒄𝒐𝒓𝒓 𝒋 , 𝜸𝒎 𝒋 , 𝜸𝑰𝑺 𝒋 )

TABLE

  .

	Category Number	Content	Sampling	Mean
		of sounds		frequency	duration
	Speech	6	Male & female	8 kHz	7 s
			sentences
	Music	9	Single	16 kHz	10 s
	solo		instruments &
			vocals
	Music	11	Pop music &	16 kHz	11 s
	group		Vocal with
			Orchestra

TABLE II CONTENTS

 II OF THE DATASET USED FOR THE INPAINTING EVALUATION.

  .

	Missing data (%)	20	40 60 80
	OMP	102 64 32 16
	S-OMP	102 77 51 26
	S-IHT	128 77 32 26
	S-CoSamP	128 77 51 26

TABLE III T

 III VALUES RETAINED FOR THE DIFFERENT INPAINTING ALGORITHMS.

  finally summarizes the retained parameters.

	Parameter	Value
	Frame length (L)	32 ms @ 8 kHz and 16 ms @ 16 KHz
	Hop size (h)	L 4
	Dictionary size	Ω = 2 × L = 512
	T	see Table (III)
	ζ	4
	Block duration	0.25 ms @ 8 kHz and 0.125 ms @ 16 kHz
	ν	0.25
	Iterations number (imax)	500
		TABLE IV
	SUMMARY OF PARAMETER SETTINGS.

For reproducibility, the code and data are available at https://mad.lis-lab.fr/.