Y Drouillas

T Lebourg

S Zerathe

Jean-Claude C Hippolyte

Raphaël Chochon

M Vidal

R Besso

Alpine deep-seated gravitational slope deformation and the Messinian Salinity Crisis

Keywords: Deep-seated gravitational slope deformation, Subalpine chains, Messinian Salinity Crisis, Gravitational slope evolution, Eustatic variation

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I-Introduction

For several decades, studies on gravitational phenomena have focused on the geomorphological characteristics and dynamic processes of large landslides to better understand the phenomenon and especially their evolution and their impact on the landscapes. The role played by landslides in mountain ranges is varied, but they are above all a vector of erosion and mass displacement. Our studied gravitational movements are deep-seated gravitational slope deformations (DSGSDs) (greater than 109 m3) (defined by Malgot 1977), and they can involve an entire hill slope. They are complex and require precise three-dimensional or even fourdimensional investigations with time considered. Yet these landslides are still less understood than compared with deep-seated landslides (DSLs) (106 to 107 m3) [START_REF] Pollet | Mouvements gravitaires rapides de grandes masses rocheuses: Apports des observations de terrain à la compréhension des processus de propagation et dépôt: Application aux cas de La Madeleine (Savoie, France)[END_REF]) and we still have to learn how certain DSGSD affect the overall geomorphological evolution of landscapes.

Several authors have linked the stability of these landslides to the long-term evolution of mountain ranges topography (e.g., rock uplift, exhumation rates, and river incision) [START_REF] Bovis | Uphill-facing (antislope) scarps in the Coast Mountains, southwest British Columbia[END_REF][START_REF] Crosta | Deep seated slope deformations: huge, extraordinary, enigmatic phenomena[END_REF][START_REF] Agliardi | Structural constraints on deep-seated slope deformation kinematics[END_REF]Ballantyne 2002a, b;Korupet al. 2007;[START_REF] Larroque | Aléa sismique dans une région intraplaque à sismicité modérée: la jonction Alpes-Bassin Ligure[END_REF][START_REF] Larsen | Landslide erosion coupled to tectonics and river incision[END_REF]Blöthe et al. 2007;[START_REF] Larroque | Aléa sismique dans une région intraplaque à sismicité modérée: la jonction Alpes-Bassin Ligure[END_REF][START_REF] Larsen | Landslide erosion coupled to tectonics and river incision[END_REF][START_REF] Blöthe | Large landslides lie low: excess topography in the Himalaya-Karakoram ranges[END_REF]. The localization of DSGSD is strongly controlled by the structural inheritance, the topographic constraints [START_REF] Dh | Gravitational creep of rock masses on slopes[END_REF][START_REF] Varnes | Measurement of ridge-spreading movements (Sackungen) at Bald Eagle Mountain[END_REF], and the geology [START_REF] Jomard | Morphological analysis of deep-seated gravitational slope deformation (DSGSD) in the western part of the Argentera massif. A morpho-tectonic control?[END_REF][START_REF] Bedoui | Deep-seated failure propagation in a fractured rock slope over 10,000 years: the La Clapière slope, the south-eastern French Alps[END_REF][START_REF] Zerathe | Evolution stages of large deep-seated landslides at the front of a subalpine meridional chain (Maritime-Alps, France)[END_REF]. It is also recognized that the seismic activity can control the destabilization or the reactivation of DSGSD (e.g., Beck 1968;[START_REF] Harp | Landslides triggered by the 1994 Northridge, California, earthquake[END_REF][START_REF] Mccalpin | Ridge-top spreading features and relationship to earthquakes, San Gabriel Mountains Region, Southern California: Part A. Distribution and description of ridge-top depressions (sackungen): Part B. Paleoseismic investigations of ridge-top depressions[END_REF][START_REF] Gutiérrez-Santolalla | Geomorphology and geochronology of sackung features (uphill-facing scarps) in the Central Spanish Pyrenees[END_REF][START_REF] Hippolyte | The recent fault scarps of the Western Alps (France): tectonic surface ruptures or gravitational sackung scarps? Combined mapping, geomorphic, levelling, and 10Be dating approach[END_REF][START_REF] Gutiérrez | Late Quaternary episodic displacement on a sackung scarp in the central Spanish Pyrenees. Secondary paleoseismic evidence?[END_REF].

Many DSGSDs in the Alps were triggered in the Holocene period [START_REF] Tibaldi | A giant deep-seated slope deformation in the Italian Alps studied by paleoseismological and morphometric techniques[END_REF][START_REF] Hippolyte | The recent fault scarps of the Western Alps (France): tectonic surface ruptures or gravitational sackung scarps? Combined mapping, geomorphic, levelling, and 10Be dating approach[END_REF][START_REF] Agliardi | Onset and timing of deep-seated gravitational slope deformations in the eastern Alps, Italy. Geomorphol, Dating, Trigger, Model Hazard Assess Large Landslides[END_REF][START_REF] Hippolyte | Cosmogenic 10Be dating of a sackung and its faulted rock glaciers, in the Alps of Savoy (France)[END_REF][START_REF] Pánek | Deep-seated gravitational slope deformations in the highest parts of the Czech Flysch Carpathians: evolutionary model based on kinematic analysis, electrical imaging and trenching[END_REF][START_REF] Hippolyte | 10Be ages reveal> 12ka of gravitational movement in a major sackung of the Western Alps (France)[END_REF][START_REF] Jomard | Morphological analysis of deep-seated gravitational slope deformation (DSGSD) in the western part of the Argentera massif. A morpho-tectonic control?[END_REF]) due to valley incision [START_REF] Bovis | Extensive deformations of rock slopes in southern Coast Mountains, southwest British Columbia, Canada[END_REF] and flank decompression related to glacier melting [START_REF] Agliardi | Structural constraints on deep-seated slope deformation kinematics[END_REF][START_REF] Hippolyte | The recent fault scarps of the Western Alps (France): tectonic surface ruptures or gravitational sackung scarps? Combined mapping, geomorphic, levelling, and 10Be dating approach[END_REF][START_REF] Hippolyte | Cosmogenic 10Be dating of a sackung and its faulted rock glaciers, in the Alps of Savoy (France)[END_REF][START_REF] Agliardi | Onset and timing of deep-seated gravitational slope deformations in the eastern Alps, Italy. Geomorphol, Dating, Trigger, Model Hazard Assess Large Landslides[END_REF][START_REF] Crosta | Deep seated gravitational slope deformations in the European Alps[END_REF]. Some of the largest examples of DSGSDs are in the Alps, like the Flims landslide (8.5 ka) (volume = 8.5-12 109 m3) [START_REF] Stead | A critical review of rock slope failure mechanisms: the importance of structural geology[END_REF], or the Sierre landslide (9.6 ka) (volume = 1.5 109 m3) [START_REF] Pedrazzini | From deep seated slope deformation to rock avalanche: destabilization and transportation models of the Sierre landslide (Switzerland)[END_REF]). In the central Italian Alps, [START_REF] Frattini | Activity and kinematic behaviour of deepseated landslides from PS-InSAR displacement rate measurements[END_REF], b) highlight by synthetic aperture radar (SAR) interferometry that a majority of the DSGSDs in the region are still active at present. Due to the glaciation/deglaciation cycles, it remains difficult to observe much older DSGSD in the Alps.

The glaciation/deglaciation cycles are not the only events that can trigger DSGSD. Indeed, at present time, [START_REF] Hou | Numerical study on deep-seated gravitational slope deformation in a shale-dominated dip slope due to river incision[END_REF] concluded that the primary destabilizing factors of DSGSDs of the Kii Valley in Western Japan are [START_REF] Bovis | Uphill-facing (antislope) scarps in the Coast Mountains, southwest British Columbia[END_REF] the degradation of rock masses and (2) the incision of the Yoshino River at the bottom of the slope. The incision alone is insufficient to trigger the slide. Furthermore, [START_REF] Tsou | Deep-seated gravitational deformation of mountain slopes caused by river incision in the Central Range, Taiwan: spatial distribution and geological characteristics[END_REF] found a relationship between the incision and the development of DSGSD in the mountains crossed by the Dahan River in Northern Taiwan. These observations are also present in the Mediterranean area; [START_REF] Buccolini | Late Quaternary geomorphological evolution and erosion rates in the clayey peri-Adriatic belt (Central Italy)[END_REF] and [START_REF] Gargani | Slope destabilization during the Messinian salinity crisis[END_REF] highlight the link between marine regressions and slope destabilization resulting from valley incision. This work demonstrates the importance of the valley incision factor in the establishment of DSGSDs.

Still in the Mediterranean area, the Messinian Salinity Crisis (MSC) represents the most relevant valley incision events that ever occur in the region [START_REF] Clauzon | Le canyon messinien de la Durance (Provence, France): Une preuve paléogéographique du bassin profond de dessiccation[END_REF][START_REF] Clauzon | Le canyon messinien du Rhone; une preuve decive du "desiccated deep-basin model"(Hsue, Cita and Ryan[END_REF][START_REF] Lofi | Erosional processes and paleo-environmental changes in the Western Gulf of Lions (SW France) during the Messinian Salinity Crisis[END_REF][START_REF] Maillard | Offshore evidence of polyphase erosion in the Valencia Basin (Northwestern Mediterranean): scenario for the Messinian Salinity Crisis[END_REF][START_REF] Bertoni | Major erosion at the end of the Messinian Salinity Crisis: evidence from the Levant Basin, Eastern Mediterranean[END_REF][START_REF] Cornée | Onshore to offshore reconstruction of the Messinian erosion surface in Western Sardinia, Italy: implications for the Messinian salinity crisis[END_REF]). This eustatic event was characterized by an almost complete desiccation of the Mediterranean Basin after its disconnection from the Atlantic Ocean at 5.97 Ma [START_REF] Krijgsman | Chronology, causes and progression of the Messinian salinity crisis[END_REF]. The Messinian Salinity Crisis (MSC) lasted from 5.97 to 5.46 Ma [START_REF] Gautier | Age et durée de la crise de salinité messinienne[END_REF]Clauzon et al. 1996a;[START_REF] Krijgsman | Chronology, causes and progression of the Messinian salinity crisis[END_REF][START_REF] Bache | A two-step process for the reflooding of the Mediterranean after the Messinian Salinity Crisis[END_REF][START_REF] Manzi | Age refinement of the Messinian salinity crisis onset in the Mediterranean[END_REF]) but the sea level drops down by about 1500 m compared with present levels (Gorini et al. 2005) only at 5.6 Ma (Clauzon et al. 1996a). Every river connected to the Mediterranean Sea underwent intense incisions from regressive erosion that penetrated inland in order to adjust to the new base level. Incision rates of up to 10 mm/year have been observed in certain parts of the Rhône [START_REF] Loget | Mesoscale fluvial erosion parameters deduced from modeling the Mediterranean sea level drop during the Messinian (late Miocene)[END_REF]. In France, we observe strong and steep incisions in the principal Mediterranean rivers, the Rhône (Gorini et al. 2005;[START_REF] Lofi | Erosional processes and paleo-environmental changes in the Western Gulf of Lions (SW France) during the Messinian Salinity Crisis[END_REF][START_REF] Mocochain | Réponses de l'endokarst ardéchois aux variations eustatiques générées par la crise de salinité messinienne[END_REF], the Durance [START_REF] Clauzon | Le canyon messinien de la Durance (Provence, France): Une preuve paléogéographique du bassin profond de dessiccation[END_REF][START_REF] Hippolyte | Messinian-Zanclean canyons in the Digne nappe (southwestern Alps): tectonic implications[END_REF], and the Var [START_REF] Clauzon | The Messinian Var canyon (Provence, Southern France) -paleogeographic implications[END_REF][START_REF] Savoye | The Messinian event on the margin of the Mediterranean Sea in the Nice area, southern France[END_REF]. The conditions encountered during the MSC are therefore suitable for the establishment of large-scale gravity deformations along the Messinian Canyons. The end of the MSC is marked by the flooding of the Mediterranean Sea which may have been very fast, ranging from a thousand years [START_REF] Hsü | The origin of the Mediterranean evaporite[END_REF] to only 36 years [START_REF] Blanc | The opening of the Plio-Quaternary Gibraltar Strait: assessing the size of a cataclysm[END_REF], or may also have occurred in several episodes with different filling speeds more spread over time [START_REF] Bache | A two-step process for the reflooding of the Mediterranean after the Messinian Salinity Crisis[END_REF]. During this flooding, the Messinian Canyons were transformed into deep rias that were filled by sediments prograding in Gilbert-type fan deltas [START_REF] Clauzon | Restitution de l'évolution géodynamique néogène du bassin du Roussillon et de l'unité adjacente des Corbières d'après les données écostratigraphiques et paléogéographiques[END_REF].

In this paper, we present a new case study, the Sinne Valley DSGSD in the lower Var Valley one of the largest mass movements (≈10.109 m3) but especially one of the oldest in the European Alps (5.6 Ma). The particularity of this Alpine DSGSD is that it has not been triggered by the glaciation/deglaciation cycles but by the creation of the Var Canyon during the MSC. With the help of topographic and geologic analyses, and field observations, we have identified several geological and geomorphological features linked to large-scale gravitational deformation related to alpine orogenesis and canyons creation during Messinian Salinity Crisis. Finally, we describe the complete evolution of an onshore Alpine DSGSD triggered by the MSC.

II-Geological setting

The study area is in the lower Var Valley in the southern Western Alps in the Alpes-Maritimes department (southeast France). The Var River is the largest river of the Alpes-Maritimes; it is 114 km long and its catchment area extends on about 2600 km2. The lower Var Valley is defined as the Var sedimentary basin composed of Pliocene conglomerate that filled the Var Messinian Canyon (Fig. 1 and Fig. 2) created during the MSC. This territory includes the southernmost mountain range of the French Alps resulting from two main thrusts: The Castellane arc to the West and the Nice arc to the East (Fig. 1). These two mountain ranges are the outcomes of the exhumation of the Argentera-Mercantour Massif (Fig. 1) during the Miocene and Pliocene [START_REF] Laurent | Modalités de la structuration d'un prisme de front de chaîne: L'exemple de l'arc de Castellane (Chaînes subalpines méridionales[END_REF] and are composed of Mesozoic to Cenozoic folded sedimentary rocks. The regional slope created during this exhumation allows the series to be detached from the crystalline basement via the Keuper level (Upper Triassic), a geological formation that acted as the "soap layer" [START_REF] Sanchez | Chronologies et évolution de la déformation de la croute moyenne à la surface dans un prisme collisionel en décrochement: impacts sur l'aléa sismogravitaire: exemple des Alpes Sud-occidentales[END_REF]. From bottom to top, this geological layer is composed of white dolomites interbed with varicolored marls and plastic clays, cargneules, large dolomites, and gypsum layers [START_REF] Dardeau | Le Jurassique des Alpes-Maritimes (France): stratigraphie, paléogéographie, évolution du contexte structural à la jonction des dispositifs dauphinois, briançonnais et provençal[END_REF]. The Keuper formation has weak mechanical properties that localize deformation (Young E modulus ≈ 40 GPa and compressive stresses σc ≈ 36 MPa, Fabre and Dayre 1982) (Fig. 2). The Castellane and Nice arcs did not evolve synchronously. The southern branch of the Castellane arc is essentially a Miocene structure [START_REF] Clauzon | The Messinian Var canyon (Provence, Southern France) -paleogeographic implications[END_REF][START_REF] Laurent | Modalité de la structuration miocène de la branche sud de l'arc de Castellande (chaîne subalpines méridionales)[END_REF] with a frontal thrust over the Tortonian formation (Miocene) [START_REF] Irr | Paléoenvironnements et évolution géodynamique néogènes et quaternaire de la bordure nord du bassin méditerranéen occidental: un système de pente de la paléo-marge liguro-provençal[END_REF]) (Fig. 2), while the Nice arc shows evidence of Late Neogene thrusting orogeny (Late Pliocene to Early Quaternary) [START_REF] Clauzon | The Messinian Var canyon (Provence, Southern France) -paleogeographic implications[END_REF]. Still both units underwent the same regional Quaternary uplift. This study focuses on the Carros and Gattières areas in the Castellane arc (Fig. 2) where we observed geomorphological and geological anomalies.

The main tectonic structures resulting from the thrusting of the Castellane arc are strike-slip fault, oriented N20-40° and dipping 80-90° toward the SE that moved with a sinistral horizontal sense (Fig. 2a). In the Alps, [START_REF] Ambrosi | Large sackung along major tectonic features in the Central Italian Alps[END_REF] demonstrated a relation between major structural features and DSGSDs. In the Marbrières Range of the Castellane arc (20 km eastward), [START_REF] Zerathe | Evolution stages of large deep-seated landslides at the front of a subalpine meridional chain (Maritime-Alps, France)[END_REF] observed abnormal vertical shifts and typical gravitational morpho structures on a major N20-40° fault, which suggest the presence of a general gravitational reactivation of the network of inherited faults, with reactivation evolving to scarps or trenches. The lower Var Valley runs through a Gilbert-type fan delta that includes marine bottomset and foreset beds [START_REF] Clauzon | Pliocene geodynamic and climatic evolutions in the French Mediterranean region[END_REF], named "conglomerate of the Var delta" [START_REF] Dubar | Les dépôts pliocènes et pléistocènes de la basse vallée du Var (Nice, Alpes-Maritimes): variations du niveau marin et néotectonique depuis 5 millions d'années[END_REF]) who filled most of the Messinian Var Canyon (Fig. 2). Seismic profiles show that the incision of the Var could be large, since the Messinian Erosional Surface is at 900 m depth near the present coast [START_REF] Savoye | The Messinian event on the margin of the Mediterranean Sea in the Nice area, southern France[END_REF]. To the north, the deep Messinian incision is still attested by 100-m-thick marine Pliocene conglomeratic foreset beds at Clans, more than 30 km upstream from the present coast [START_REF] Vernet | La phase d'édification post-miocène des alpes sur la transversale des Alpes-Maritimes[END_REF]Clauzon et al. 1996b).

The upper part of the western slope of the Var Valley, the Castellane arc, consists of subhorizontal Jurassic limestone (dip ≈ 5-20°) lying on deformed and thick (> 200 m) Triassic formation (Fig. 2c). The presence of the Keuper evaporate makes the leading edge of the Castellane thrust extremely favorable for large landslides (DSGSD, DSL) [START_REF] Zerathe | Origine et évolution des ruptures gravitaires de grande ampleur dans les chaînes subalpines méridionales à l'Holocène[END_REF]. Indeed, the Jurassic limestone is above plastic rocks, vulnerable to the dissolution because of the gypsum. The other outcropping main unit is thick (≈ 200 m) Miocene formation dated from middle Aquitanian to Burdigalian and composed of sandy and micaceous marls (Fig. 2). This formation is representative of a shallow sea depositional environment [START_REF] Ginsburg | The Late Messinian salinity crisis and Late Miocene tectonism: interaction and consequences on the physiography and post-rift evolution of the Gulf of Lions margin[END_REF].

This last main sedimentary unit is the Carros breccia (late Miocene to early Pliocene in age) a consolidated breccia deposited all along the hill slope and described only in this area (Fig. 2). This breccia lies unconformably on Jurassic and Miocene formations (Fig. 2) [START_REF] Guglielmi | Hydrogéologie des aquifères plio-quaternaires de la basse vallée du Var (Alpes-Maritimes[END_REF][START_REF] Ginsburg | The Late Messinian salinity crisis and Late Miocene tectonism: interaction and consequences on the physiography and post-rift evolution of the Gulf of Lions margin[END_REF] and in the upper levels, microbreccias and marl interbeds have been found, revealing Pliocene marine microfauna [START_REF] Guebhardt | L'âge pliocène de la brèche du Broc[END_REF].

Finally, a large part of the area is covered with Quaternary scree deposits on steep slopes. Most of these slope deposits are consolidated and covered by vegetation [START_REF] Ginsburg | The Late Messinian salinity crisis and Late Miocene tectonism: interaction and consequences on the physiography and post-rift evolution of the Gulf of Lions margin[END_REF].

There is no glacial evidence in the southern part of the middle Var Valley. The nearest moraine deposits are located more than 20 km north of the study area (Fig. 2) [START_REF] Julian | Les alpes maritimes franco-italiennes. etude morphologique[END_REF][START_REF] Maisch | Die Gletscher der Schweizer Alpen: Gletscherhochstand 1850-Aktuelle Vergletscherung-Gletscherschwund-Szenarien 21. Jahrhundert, Schlussbericht NFP31 vdf Hochschulverlag[END_REF][START_REF] Jorda | Données nouvelles sur l'âge du dernier maximum glaciaire dans les Alpes méridionales françaises[END_REF][START_REF] Darnault | Timing of the last deglaciation revealed by receding glaciers at the Alpine-scale: impact on mountain geomorphology[END_REF]). The region presents several DSLs like the La Marbriére Landslide dated from 400 ka triggered by inherited geological anisotropy, and 6 dated from 4.2 ka, triggered by intense climatic events [START_REF] Zerathe | Origine et évolution des ruptures gravitaires de grande ampleur dans les chaînes subalpines méridionales à l'Holocène[END_REF]. In terms of regional seismicity, [START_REF] Larroque | Aléa sismique dans une région intraplaque à sismicité modérée: la jonction Alpes-Bassin Ligure[END_REF] shows that the faults of the area can produce earthquakes with magnitude up to 7. This magnitude is enough to trigger DSLs within a 100 km of the epicenter [START_REF] Keefer | The importance of earthquake-induced landslides to long-term slope erosion and slope-failure hazards in seismically active regions[END_REF][START_REF] Strak | L'évolution du relief le long des escarpements de faille normale active : observations, modélisations expérimentales et numériques (phdthesis)[END_REF][START_REF] Jibson | Landslides triggered by the 2002 Denali Fault, Alaska, earthquake and the inferred nature of the strong shaking[END_REF][START_REF] Jibson | Large rock avalanches triggered by the M 7.9 Denali Fault, Alaska, earthquake of 3[END_REF] and can have an impact on DSGSD [START_REF] Moro | The relationship between seismic deformation and deep-seated gravitational movements during the 1997 Umbria-Marche (Central Italy) earthquakes[END_REF].

III-Methods

We based our analysis on the combined use of GIS and field observations. Digital Terrain Model (DTM) and vectorized 1/ 50000 geological map (BD Charm-50 produced by the BRGM available at http://www.geocatalogue.fr/Detail.do?id=4156 (last accessed on 29/01/2019) analyses are used to perform large-scale geomorphological observations followed by more precise field surveys. The field surveys can confirm, disprove, or detail specific features with the help of GNSS locations, photos, and dip measurements.

The DTM used in this paper is provided by the Conseil departmental des Alpes-Maritimes (available at https: //trouver.datasud.fr/dataset/modeles-numeriques-de-terrain-go-06 (last accessed on 29/01/2020)) with a resolution of 5 m. DTM does not consider the vegetation and can cover the entire department; it allows a spatial 3D representation of the study area through 3D view and elevation profiles and allows many observations that are not possible in the field.

Slope, surface roughness, aspect, hill shades, and curvature are used to describe morphological features like major and minor scarps, ridges and cracks, and landslides boundaries [START_REF] Morelli | Kinematic reconstruction of a deep-seated gravitational slope deformation by geomorphic analyses[END_REF]). Slope, aspect, hill shades, and curvatures are estimated in ArcGIS 10.3 (Esri, Redlands, CA, USA) using the spatial Analyst extension, and the surface roughness is estimated at QGIS 2.18 (QGIS development Team 2019) using the Raster Terrain Analysis Plugin. Since slope and surface roughness present the best contrasts in the analysis of DTM data, particularly for escarpments, these two were performed on this study. According to [START_REF] Burrough | Principles of geographical information systems[END_REF], the slope is calculated at a given cell by comparing the altitude to its neighbors (3 × 3 cells), and it represents the maximal variation rate of altitude (from 0° to 90°). According to [START_REF] Riley | Index that quantifies topographic heterogeneity[END_REF], the surface roughness is estimated in each cell by calculating the sum change in the altitude of its neighbor (3×3 cells) (flat area has a value close to 0).

Elevation profiles are realized with the QGIS DTM surface plugin Profile tool (developed by Jurgiel et al.). 3D views of the area are realized with the QGIS plugin Qgis2threejs (developed by Akagi), who combine DTM data and images of other data like geology, orthophotos, or surface roughness. Finally, the r.volume model of GRASS plugin (Hinthorne 1988 updated to GRASS 7 by Landa) is used to calculate the volume of the DSGSD resulting from the DTM and the surface area of the DSGSD.

IV-Results

1) The Sinne Valley

The Sinne Valley is a deep valley (≈ 100 m) perched at 700 m high with no permanent watercourses. Its N20-40° orientation and the presence of a strike-slip fault (Fig. 2) point out to a tectonic origin. This family of strike-slip faults is linked to the thrusting of the Castellane arc and ceased their activity in late Miocene.

A set of different gaps or crevasses, 1 to 2 m wide and 1 to 3 m deep, all-oriented N20-40° and tracked on about 100 m was also observed in the Sinne Valley showing NW-SE extension (Fig. 3c).

The Sinne Valley is bordered by two plateaus, one to the east and the other to the west over a distance of ≈ 1.5 km (Fig. 2c, b and Fig. 3b). These two plateaus are composed of the same rocks, the Portlandian and Berriasian lithographic limestone (Fig. 2b, Fig. 3b).We measured bedding planes of the Jurassic formation. On the western plateau, they strike from 205 to 255° and dip from 5° to 20° (14 measurements) (Fig. 3e). They are consistent with those of [START_REF] Baggioni | Etude morphologique de la rive droite de la Basse Vallée du Var[END_REF] who described the formation of the summit as sub-horizontal including the plateaus. The bedding planes at the lower part of the Jurassic formation of the Carros/Gattières hill slope strike from 175° to 205° and dip from 25° to 40° (8 measurements) (Fig. 3e). These are consistent with those of Zerathe (2013) (Fig. 3a). Using the DTM and a stochastic approach that traces ten topographic profiles passing through the two plateaus (profiles ± NW-SE), it appears that the eastern plateau bordering the Sinne Valley has an average elevation of 925 ± 15 m, while the western plateau has an average altitude of 1015 ± 6 m, with a difference of approximately 90 ± 10 m (Fig. 3b). In addition, we perform an analysis on the geological map combine with the DTM and a 30 m stratigraphic offset is observed in the Portlandian-Berriasian (J7), Kimmeridgian (J6), and Sequanian (J5) layers (Fig. 3b). With an approximate 10° dip (Fig. 3b), the offset of the Jurassic series across the valley can be estimated at about 70-80 m, which is close to the 90 m offset between the two plateaus.

We infer that the shape of the Sinne Valley can be assimilated with a "double-crested ridge" (Fig. 3b), a geomorphological structure characteristic of DSGSDs [START_REF] Agliardi | Slow rock-slope deformation[END_REF].

2) The Carros breccia

Along the Var Valley, the Carros breccia is only present in the Carros/Gattières area and corresponds to a thick and highly consolidated slope formation. According to the Roquesteron Geological Map [START_REF] Ginsburg | The Late Messinian salinity crisis and Late Miocene tectonism: interaction and consequences on the physiography and post-rift evolution of the Gulf of Lions margin[END_REF]), the Carros breccia was deposited both at the front of the Castellane thrust and at the edge of the Var Messinian Canyon. [START_REF] Gèze | Notice explicative, carte géol[END_REF] described the breccia as synorogenic when the Castellane arc was emplaced. But [START_REF] Clauzon | The Messinian Var canyon (Provence, Southern France) -paleogeographic implications[END_REF] pointed out that at Le Broc borehole (from 98 to -12 m elevation) (Fig. 2b), the Carros breccia is at least 70 m thick (from -12 to 57 m elevation), and is overlain by Pliocene marls (from 57 to 68 m elevation) and Holocene alluvium (from 68 to 98 m elevation). He concluded that the breccia results from the Messinian incision of the Var River, and is not a syn-tectonic breccia because it postdates the emplacement of the Castellane arc. At Le Broc (Fig. 2), we observed northeast prograding subaqueous foreset beds of debris (Fig. 4a) with marine burrows on the limestone blocks (Fig. 4b) which confirms that the breccia continued to deposit after the flooding of the lower Var Valley at the end of the MSC. At present days, the outcropping surface of the Carros breccia is 3.8 km2, with an approximate thickness of 70 m (i.e., le Broc borehole) and it represents 2.7 × 108 m3. This volume is an underestimation since the Pliocene conglomerate of the Var delta and Holocene formation may cover it (i.e., le Broc borehole). Anyway, this formation indicates that the western slope of the Var Valley has been locally subject to high degradation during and after the Messinian incision.

3) The DSLs

According to El [START_REF] Bedoui | Deep-seated failure propagation in a fractured rock slope over 10,000 years: the La Clapière slope, the south-eastern French Alps[END_REF]), Hradeck and Pánek (2008[START_REF] Jomard | Morphological analysis of deep-seated gravitational slope deformation (DSGSD) in the western part of the Argentera massif. A morpho-tectonic control?[END_REF], DSGSDs may induce rapid localized failure events like DSLs especially on the slope toe; this interaction can be explained by the long-term deformations of DSGSDs and the resulting steepening of the slopes. [START_REF] Zerathe | Origine et évolution des ruptures gravitaires de grande ampleur dans les chaînes subalpines méridionales à l'Holocène[END_REF] already documents a DSL in the area: the Gattières DSL (1 Fig. 2b,Fig. 3a). This DSL has an estimated volume of 1.5 × 106 m3 and a surface of 0.08 km2.

On a three-dimensional view of the roughness of the area (Fig. 3e), we can distinguish the presence of three triangular facets on the slope. According to [START_REF] Strak | L'évolution du relief le long des escarpements de faille normale active : observations, modélisations expérimentales et numériques (phdthesis)[END_REF], this geomorphological structure is representative of active normal faults, the southernmost triangular facet corresponding to Gattières DSL (Fig. 3a). This analysis was followed by field campaigns confirming the presence of a fault represented by a scarp that extends for about 2 km of length along the hill slope (Fig. 3e). This escarpment has many karstification indices with many concretions of speleothems covering the whole surface in some places and various evidences of deformation like NW-SE extensional crevasses of different sizes (Fig. 3d). Field campaigns, DTM analysis, and geological map analyses have enabled us to define that the Gattières DSL and two other DSLs are linked to the triangular facets and the socalled Gattières/Carros fault, the Ripert DSL (Fig. 2 and Fig. 3e with a volume estimated at 1.8 × 106 m3) and the Carros DSL (Fig. 2 and Fig. 3e with a volume estimated at 1 × 107 m3). Due to their lengths and shapes, the Gattières/Carros fault and the DSLs are very likely due to the DSGSD. DSGSD activity can create faults along the hill slope to accommodate the deformation, and the fault and the inward dip of the Jurassic formation contribute to fluid circulation to the Triassic gypsum formation whose dissolution leads to the subsidence of the massif and more unstable conditions.

According to [START_REF] Zerathe | Mid-Holocene cluster of large-scale landslides revealed in the Southwestern Alps by 36Cl dating. Insight on an Alpinescale landslide activity[END_REF], who performed cosmic ray exposure dating (CRE) on six DSLs of the region, including the Gattières DSL, their triggers are dated around 4 ka. These datings are correlated with the 4.2 ka climate events, an intense paleohydrological pulse in the Mediterranean area [START_REF] Zanchetta | The so-called "4.2 event" in the central Mediterranean and its climatic teleconnections[END_REF]). These datings correlate the triggering of the DSLs with intense and major climatic events, we will consider that in the absence of such events and of recent deformations observed in the field, the DSLs are considered dormant or suspended.

4) The Var River deviation

The most striking geomorphological structure of the area is the deviation of the Var River toward the east over 8 km north-south between the towns of Gattières and Carros, with a maximum shift of 1 to 2 km toward the east (Figs. 2b, c and3). Several authors agree that the Var took a much N-S straighter course in the lower Var Valley during the MSC [START_REF] Savoye | The Messinian event on the margin of the Mediterranean Sea in the Nice area, southern France[END_REF][START_REF] Clauzon | Preuves et implications de la régression endoréique messinienne au niveau des plaines abyssales: l'exemple du Midi méditerranéen français[END_REF][START_REF] Dubar | Les dépôts pliocènes et pléistocènes de la basse vallée du Var (Nice, Alpes-Maritimes): variations du niveau marin et néotectonique depuis 5 millions d'années[END_REF]. We propose that this deviation is related to the DSGSD of the Sinne Valley. This hypothesis is supported by the long-term evolution of the DSGSD and DSLs, which have continuously brought large quantities of gravity materials (i.e., Carros breccias, 2.7 × 108 m3) to the right bank slope of the Var Valley from the Messinian Canyon to its Pliocene infill.

5) Evolution of the Sinne Valley DSGSD

During the late Miocene period, the front of the Castellane arc overlapped the Miocene formations. The Keuper was overthickened because of thrusting and the Jurassic formations resting on the Triassic were titled northward by about 5-20° and acquired the present inward dip (Fig. 5A). The overlap phase formed a N20-40 strike-slip fault that contributes to the tectonic deformation in the region (Fig. 2, Fig. 5).

During the MSC when the canyon reached a certain depth (at present the canyon is approximately 300 m depth in the study area), slope-undermining phenomena and constraints applied to the right flank of the slope took advantage of the major tectonic fault in the Sinne Valley-a highly altered zone-thus triggering the DSGSD and the related normal faults to accommodate the deformation (Fig. 5B). The Keuper evaporites and clays may have played an important role in the setting up and dynamics of these landslides (DSGSD and DSLs). The counter dip of the Jurassic layers promotes fluid circulation inside the massif, while the normal faults are weakness areas that promoted deep water circulation [START_REF] Barton | Fluid flow along potentially active faults in crystalline rock[END_REF] within the Keuper evaporites. The fluid circulation could lead to the dissolution of the gypsum layers and the modification of the mechanical properties of the clay layers of the Keuper Formation, with both phenomena being related to the diminution of stability [START_REF] Baron | Structure and dynamics of deepseated slope failures in the Magura Flysch Nappe, outer Western Carpathians (Czech Republic)[END_REF][START_REF] Guerrero | Paleosubsidence and active subsidence due to evaporite dissolution in the Zaragoza area (Huerva River valley, NE Spain): processes, spatial distribution and protection measures for transport routes[END_REF][START_REF] Azañón | Late Quaternary large-scale rotational slides induced by river incision: the Arroyo de Gor area (Guadix basin, SE Spain)[END_REF][START_REF] Azañón | Regionalscale high-plasticity clay-bearing formation as controlling factor on landslides in Southeast Spain[END_REF][START_REF] Gutiérrez | Investigating gravitational grabens related to lateral spreading and evaporite dissolution subsidence by means of detailed mapping, trenching, and electrical resistivity tomography (Spanish Pyrenees)[END_REF].

The DSGSD may have proceeded at a very low speed over thousands of years, but the constraint applied to the hill slope was large enough to produce numerous DSL-type landslides, thus allowing the deposition of the Carros breccia during the late Messinian incision (Fig. 5B). Moreover, the crevasses in the Sinne Valley are the result of this activity and that demonstrates that the NW-SE extension was able to develop deep in the Jurassic formations.

These constraints continued during the marine flooding of the Var Valley at the end of the MSC when the Var Canyon was transformed to Ria. At the same time, the exhumation of the Argentera-Mercantour stopped, marking the end of the Castellane arc activity (Fig. 5C). The flooding of the lower Var Valley probably triggered a second phase of activity for the DSGSD and DSLs presented in Fig. 6 by increasing the pore water pressure and thus destabilizing the slopes. This effect may have been greatly accentuated when the water sea level reached the Keuper Formation (Fig. 5C) due to the clay and gypsum rocks being highly vulnerable to the presence of water.

In the Var Valley, the marine conglomeratic foreset beds indicate the elevation of the sea level during the Pliocene. Because the Alps and their foreland have been uplifted since the Pliocene, Pliocene marine deposits are present at various elevations. Despite Quaternary erosion, the Pliocene marine conglomerate at Carros is still present up to 350 m elevation, which is a minimum for the elevation of the Pliocene sea level at this place. At Aspremont, on the eastern flank of the Var Valley, marine conglomeratic foreset beds are present up to 650 m elevation. These elevations are partly due to local tectonic deformation, but they show that Pliocene flooding could have reached the elevation of the thrust detachment in the Keuper formation.

Thus, during the deposition of the Var conglomerate and the Pliocene high stand phase (Fig. 5C) in the lower Var Valley, we assume that the DSGSD and DSLs experienced sustained gravitational activity and brought large numbers of slope breccias to the foreset beds of the Pliocene Gilbert-type delta (Fig. 5C). With the progressive filling of the Messinian Canyon by Gilbert-type delta, the DSGSD had a more stable condition since the thick conglomerate acted as a buttress. We do not know when the DSGSD activity stopped, but we assume that the activity of geomorphological structures with deformations such as crevasses (Fig. 3) has ended before 1.7 Ma.

At present, the DSGSD in the Sinne Valley is still in place, due not only to its size but also to the post-Miocene uplift of about 280 m in the Castellane arc and the quaternary incision of the Var River. An estimation of the DSGSD's volume by the r.volume plugin gives 9.5 109 m3 from the Sinne Valley to the Miocene formations (Fig. 5D). The gravitational material resulted from the DSGSD and DSL activity represented by the Carros breccia (estimated at 2.7 108 m3 at present days) was an obstacle to the flowing of the Var River during the regional uplift (Fig. 5C) [START_REF] Clauzon | Limites de séquences et évolution géodynamique/Sequence boundaries and geodynamic evolution[END_REF][START_REF] Schroëtter | L'enregistrement sédimentaire de la déformation mio-plioquaternaire sur la bordure ouest de l'arc de Nice: analyse sédimento-morphostructurale[END_REF]. This hypothesis of a deviation of the Var River owing to the contribution of gravitational material from the slope is in agreement with the presence of the DSGSD and DSLs. There are no active evidences of deformations observe for the DSGSD and the crevasses on the Sinne Valley were most likely exhumed by erosion. There is also no evidence of active deformations for the three DSLs and the regional dynamics observed by [START_REF] Zerathe | Mid-Holocene cluster of large-scale landslides revealed in the Southwestern Alps by 36Cl dating. Insight on an Alpinescale landslide activity[END_REF] imply major climate events for their triggering so in the current state DSLs are considered dormant.

Since there is no evidence of any deformations link to the DSGSD or the three DSLs, we did not perform any activity measurement in the area. The combination of 5 m resolution DTM analysis and field checking seems to be suitable in particular for the detection of escarpments, which are highlighted by roughness measurements especially over an area of more than 20 km2. This technique could easily be applied to the entire front of the Castellane arc to highlight escarpments that could be linked to DSLs. Moreover, due to the unfavorable topography and the land use on the overall slope, it was not possible to set up geophysical profiles such as electrical resistivity tomography (ERT) profiles or seismic reflection profiles. Those techniques would have allowed us to confirm or disproved, and visualized, the presence of the gravity faults highlighted in this paper instead of just relying on the DTM analyses.

IV-Conclusion

In this study, we highlight that the lower Var Valley records gravitational deformations since 5.6 Ma. We provided several arguments in favor of the presence of a DSGSD of about 10 billion m3, the largest and the oldest landslide in the front of the Castellane arc and in the Alpes-Maritimes department.

This DSGSD results from a gravitational process that occurred during the MSC when the Mediterranean Sea level dropped of about 1500 m (compared with present levels) and induced the incision of the Messinian Var Canyon that later was filled by conglomerates during the Pliocene (Fig. 5).

This deformation affected the entire massif and allowed the establishment of DSLs (Carros, Gattières, and Ripert) which actively participated in the creation of the Carros breccia.

The proposed evolution of the DSGSD follows the events that influenced the lower Var Valley over millions of years and explains in a coherent way the various observations and geomorphological characteristics found at present including the Sinne Valley, the Carros breccia, and the Var River deviation.

Landslides and collapse processes are used to be studied in recent times with active signs of deformations but at present days, there is no evidence of DSGSD or DSLs activities in the area. However, in this work, we show that it is possible to observe very old stigmas of collapse protected from erosion by their size with a dynamic driven by tectonic and gravitational events. [START_REF] Sanchez | Chronologies et évolution de la déformation de la croute moyenne à la surface dans un prisme collisionel en décrochement: impacts sur l'aléa sismogravitaire: exemple des Alpes Sud-occidentales[END_REF] and recent fault systems (in bold, proposed Holocene activity) [START_REF] Sanchez | The active fault system of SW Alps[END_REF]. (b) Cross-section A-B: Simplified North-South section across the Western South Alps [START_REF] Sanchez | Chronologies et évolution de la déformation de la croute moyenne à la surface dans un prisme collisionel en décrochement: impacts sur l'aléa sismogravitaire: exemple des Alpes Sud-occidentales[END_REF], modified from [START_REF] Laurent | Modalités de la structuration d'un prisme de front de chaîne: L'exemple de l'arc de Castellane (Chaînes subalpines méridionales[END_REF].

Fig. 1 :

 1 Fig. 1: (a) Structural map of the Western South Alps[START_REF] Sanchez | Chronologies et évolution de la déformation de la croute moyenne à la surface dans un prisme collisionel en décrochement: impacts sur l'aléa sismogravitaire: exemple des Alpes Sud-occidentales[END_REF] and recent fault systems (in bold, proposed Holocene activity)[START_REF] Sanchez | The active fault system of SW Alps[END_REF]. (b) Cross-section A-B: Simplified North-South section across the Western South Alps[START_REF] Sanchez | Chronologies et évolution de la déformation de la croute moyenne à la surface dans un prisme collisionel en décrochement: impacts sur l'aléa sismogravitaire: exemple des Alpes Sud-occidentales[END_REF], modified from[START_REF] Laurent | Modalités de la structuration d'un prisme de front de chaîne: L'exemple de l'arc de Castellane (Chaînes subalpines méridionales[END_REF].

Fig. 2 :

 2 Fig. 2: (a) Geological map of the lower Var Valley at 1/5000000 (modified from Ginsburg et al. 1980). (b) Zoom on the Carros/Gattières area (1) Gattières DSL, (2) Ripert DSL, and (3) Carros DSL. (c) Geological section A-B Fig. 2b.

Fig. 3 :

 3 Fig. 3: 3D view of the area. (a) Cross-section M-N (Fig.3e) Gattières DSL (modified from[START_REF] Zerathe | Origine et évolution des ruptures gravitaires de grande ampleur dans les chaînes subalpines méridionales à l'Holocène[END_REF]. (b) Average offset between the two plateaus and the Jurassic limestone formations between the two banks of the Sinne valley without formations dip (up) with formations dip (down). (c) Crevasse toward N20-40° in the limestone formations of the Sinne Valley (up to 2 m wide and 100 m long). (d)Gattières/Carros fault markers, crevasses in NW-SE extension. (e) 3D view of the Gattières/Carros side, geological map (up) roughness map(down)

Fig. 6 :

 6 Fig. 6: Schematic interpretation of the processes that triggered the landslides in the case of the Gulf of Lion landslide (A-C) (~ 1.108 m3), the Nile valley landslide (D-F) (~ 2.108 m3), and the Alboran landslide (G-I). The river erosion increased the slope gradient along the side slopes of valleys and the apparent relief H. The flooding of the Mediterranean Sea and incised valleys by seawater increased the pore pressure along the Messinian incised valleys[START_REF] Gargani | Slope destabilization during the Messinian salinity crisis[END_REF]).

Fig. 5 :

 5 Fig. 5: Interpretations of geological events on the right bank of the Var at Carros from the Messinian (5.5 Ma). (A) Late Miocene. (B) Messinian crisis. (C) Pliocene. (D) Current. Geological layer and section position Fig. 2.

Acknowledgments:

We thank all the regions that make up this program. We also thank Loïc Santino for his support.

Funding information : This study was financially supported by the Interreg-Alcotra-AD-VITAM project.


Keywords: Machine Learning, Deep Learning, Neural Networks, Wavelets, Denoising, Image restoration

Sparsity based methods, such as wavelets, have been state-of-the-art for more than 20 years for inverse problems before being overtaken by neural networks. In particular, U-nets have proven to be extremely effective. Their main ingredients are a highly non-linear processing, a massive learning made possible by the flourishing of optimization algorithms with the power of computers (GPU) and the use of large available data sets for training. While the many stages of non-linearity are intrinsic to deep learning, the usage of learning with training data could also be exploited by sparsity based approaches. The aim of our study is to push the limits of sparsity with learning, and comparing the results with U-nets. We present a new network architecture, which conserves the properties of sparsity based methods such as exact reconstruction and good generalization properties, while fostering the power of neural networks for learning and fast calculation. We evaluate the model on image denoising tasks and show it is competitive with learning-based models.

I. INTRODUCTION

The U-net was introduced by [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] to perform biomedical image segmentation. It has since then been used in a wide variety of image-to-image problems, not just segmentation, either as a strong baseline or as the building block for a more complex model. In particular, the U-nets have had success in image-to-image translation [START_REF] Isola | Image-to-image translation with conditional adversarial networks[END_REF], image reconstruction (in CT [START_REF] Adler | Learned primal-dual reconstruction[END_REF] or MRI [START_REF] Zbontar | fastMRI: An open dataset and benchmarks for accelerated MRI[END_REF][START_REF] Minh Quan | Compressed sensing MRI reconstruction using a generative adversarial network with a cyclic loss[END_REF][START_REF] Chul Ye | Deep convolutional framelets: A general deep learning framework for inverse problems[END_REF]) and denoising [START_REF] Chul Ye | Deep convolutional framelets: A general deep learning framework for inverse problems[END_REF].

However, like many other deep learning approaches, the reason for its success is not well understood. The ideas of the U-net come from [START_REF] Long | Fully convolutional networks for semantic segmentation[END_REF] in part. In this work, the base choices that make a U-net are grounded with intuitive explanations. To be able to distinguish between critical and legacy parts in the U-net design, it is important to understand its mechanisms.

On the other hand, wavelets-based approaches are not stateof-the-art anymore for denoising but are theoretically grounded (see for example [START_REF] David | De-noising by soft-thresholding[END_REF]). For applications where guarantees are needed -such as medical applications -this makes them ideal candidates.

Similarly to wavelets, U-nets present a multi-scale approach, which analyse the signal at different resolutions. Their main difference is the application of non-linearity. Indeed, where wavelets apply only one non-linearity when applied to denoising -a method called wavelet shrinkage -the U-net architecture relies on several ReLUs and max-poolings. These chained non-linearities make the analysis of the denoising in U-nets very complicated. In particular it is difficult to see how a network trained on one type of noise can be applied to other types of noises. Some works [START_REF] Nina | The troublesome kernel: why deep learning for inverse problems is typically unstable[END_REF] even show that classical neural networks can fail to recover elements that classical methods do, suggesting a trade-off between quality and stability.

The idea of this work was therefore to build a network which made use of one of the strongest advantages of neural networks, learning via gradient descent to enhance the expressive power of wavelets, while keeping some of the understanding we have of wavelets, in particular the denoising process. We term this network 'Learnlets'. We chose to test this network on a denoising problem, a task where wavelets have historically well-performed but are now overtaken by deep learning approaches.

The full implementation of our method is open source in Python 1 .

II. RELATED WORK

Different studies have attempted to work at the intersection of wavelets and neural networks. In [START_REF] Recoskie | Learning filters for the 2D wavelet transform[END_REF], the authors cast the wavelet transform as an auto-encoder where the latent representation has to be sparse and learn the filters in this architecture and only a simply high-pass and low-pass filter pair is learned. Observing U-nets two parts are very similar to synthesis and analysis concepts in wavelet decompositions, [START_REF] Chul Ye | Deep convolutional framelets: A general deep learning framework for inverse problems[END_REF] proposed to use the wavelet transform to perform a better pooling/unpooling than simply max-pooling/bilinear upsampling. [START_REF] Fan | Soft-Autoencoder and Its Wavelet Shrinkage Interpretation[END_REF] inspired themselves from the cascading wavelet shrinkage systems to enhance denoising autoencoders. In brief, they proved that using a soft thresholding non-linearity provided more power to the denoising autoencoders than other nonlinearities.

In these related papers, non-linearities (namely ReLU) are in majority applied to the low frequencies rather than the high frequencies, contrarily to what is common in the wavelet framework. In this work, we don't try to modify U-nets by importing wavelet ingredients, but rather try to push the limits of sparsity based approach by using learning while keeping sparsity concept unchanged. This allows us to recover the classical properties of wavelets i.e. decomposition with exact reconstruction, thresholding and reconstruction, while using a learning based approach. III. LEARNLETS, THE MODEL Let x ∈ R n×n be an image. Let x = x + be the version of this image corrupted by an additive white Gaussian noise ∼ N (0, σ 2 ) whose variance σ 2 is assumed known. Let Σ be a compact set of possible values for σ, we chose to have σ ∼ U(Σ). For a given number of scales m and a given set of parameters θ = (θ S , θ t , θ A ) ∈ Θ m , we defined the learnlets as function f θ from (R n×n × Σ) to R n×n :

f θ (x, σ) = S θ S (T θ T (A θ A (x) , σ)) (1)
where we have: 1) A θ A , the analysis function defined in III-A.

2) T θ T , the thresholding function defined in III-B.

3) S θ S , the synthesis function defined in III-C. An illustration of the learnlets is given in Figure 1.

x F θ (1) A * g * h * F θ (2) A * g * h * Aθ A ST (., .) ST (., .) σ Tθ T F θ (2) S * F θ (1) S * + + u u x Sθ S Figure 1
. Schematic representation of the learnlets model, with m = 2 scales. The red nodes are inputs/outputs. The lightly green nodes correspond to functions whose parameters can be learned. Note that the standard deviation of the noise before thresholding is not learned but rather estimated, and is omitted in this diagram for clarity.

A. Analysis

Intuitively, one can see the analysis linear function as the equivalent of the wavelet transform with some learned filters. It is important to note that the analysis function is linear. The analysis function is defined as:

A θ A (x) = F θ (i) A * g hi-1 (x) m i=1 , hm (x) (2)
where we have:

• F θ (i) A
, the filter bank at scale i. The convolutions are done without bias. θ (i)

A are the J i convolution kernels all of the same square size (k A , k A ) (for now J i = J m ).

• h = ū • h, the low-pass filtering (h) followed by a decimation (ū). The decimation is performed by taking one line out of 2 and one row out of 2, in line with the way it's done in wavelet transforms. • g the high-pass filtering defined as: g(y) = yu( h(y)), with u the upsampling operation performed with a bicubic interpolator.

For ease of manipulation we rewrite

A θ A (x) = ((d i ) m i=1 , c), with d i ∈ R n 2 i-1 × n 2 i-1
×Ji the detail coefficients and c the coarse coefficients.

B. Thresholding

The non-linearity function used for wavelet shrinkage is typically either a hard-thresholding or a soft-thresholding [START_REF] David | De-noising by soft-thresholding[END_REF]. The soft-thresholding offers more stability and therefore we made this choice for our architecture. The thresholding function, in the case of a white Gaussian noise of variance σ 2 , is defined as:

T θ T (((d i ) m i=1 , c) , σ) = (t ij (d ij , σ)) Ji i=1 m i=1 , c (3)
where

t ij (d, σ) = σij ST 1 σij d ij , θ (ij)
T σ , with:

• d ij ∈ R n 2 i-1 × n 2 i-1
the output of the j-th filter of i-th scale.

• σij the estimated standard deviation of d ij when the input of the transform is set to be a white Gaussian noise of variance 1. This ensures the noise coming just before the thresholding is of variance approximately σ. The threshold is therefore truly θ

(ij) T σ. • θ (ij) T
is the thresholding level applied at scale i on the j-th analysis filter.

C. Synthesis

Intuitively, one can see the synthesis function as the equivalent of the wavelet reconstruction operator, with learned filters. It is important to note that the synthesis function is linear. The synthesis function is defined recurrently as:

S θS ((d i ) m i=1 , c) = S θ (m-1) S (d i ) m-1 i=1 , u(c) + F θ (m) S * d m (4)
where S ∅ (∅, c) = c and:

• F θ (i)

S

, the filter bank at scale i, used for regrouping. The convolutions are done without bias and added all together. θ (i) S are the J i convolution kernels all of the same square size (k S , k S ).

• u, the upsampling operation performed with a bicubic interpolator.

D. Constraints

Some constraints are used on the parameters of the learnlets to make them as close as possible to the wavelets and therefore make them understandable:

• The analysis filters are forced to have a unit norm.

• The thresholding levels are in [0, 5].

E. Learning

The optimization problem is given as:

argmin θ∈Θ E x,σ [L f (θ)] (5)
where

L f (θ) = x -f θ (x, σ) 2 2
and the expected value is computed empirically, via the empirical mean over a batch.

F. Learnlets with exact reconstruction

Exact reconstruction guarantees that if no noise is present, the signal will be reconstructed as is. This can be achieved using the analysis filter previously fixed as identity. In particular, let's consider a single scale i, after the application of the g filter. The operation carried out by the network, without thresholding can be written as:

x (i) out = N j=1 F θ (i,j) S * F θ (i,j) A * x in ( 6
)
where N is the number of filters at that scale. Since we have F θ (i,1)

A

= Id, we can also fix the corresponding synthesis filter F θ (i,1)

S = Id - N j=2 F θ (i,j) S * F θ (i,j) A
. This trivially gives without thresholding, x out = x in . We implemented this constraint in the network, allowing to learn a different thresholding level for this filter. We compare in the next section the performance against a network which didn't feature this forced exact reconstruction.

IV. DATA AND EXPERIMENTS

The implementation was done in Python 3.6, using the TensorFlow 2.1 framework [START_REF] Abadi | TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems[END_REF] for model design. The training was done on a computer equipped with a single GPU Quadro P5000 with 16GB of RAM.

A. Data

The data used was the BSD500 dataset [START_REF] Arbelaez | Contour Detection and Hierarchical Image Segmentation[END_REF]. This data consists of natural images of sizes 481 × 321 and 321 × 481. The train and tests subsets of BSD500 were used as the training dataset. The validation subset of BSD500, containing the BSD68 [START_REF] Martin | A Database of Human Segmented Natural Images and its Application to Evaluating Segmentation Algorithms and Measuring Ecological Statistics[END_REF] images was left out. We used BSD68 as the test dataset. This choice is motivated by the fact that many other denoising studies [START_REF] Zhang | Beyond a Gaussian denoiser: Residual learning of deep CNN for image denoising[END_REF], [START_REF] Lefkimmiatis | Universal denoising networks: a novel CNN architecture for image denoising[END_REF] use this dataset for comparison.

B. Pre-processing

For training, patches of size 256 × 256 were randomly extracted on-the-fly. The images were then linearly mapped from [0, 255] to the [-0.5, 0.5] interval and converted from RGB to grayscale using the function provided by TensorFlow2 . oise was then added by first drawing uniformly at random in the specified interval Σ a noise level σ, then generating a 256 × 256 white Gaussian noise patch with this standard deviation. It is to note that during training, a single batch can feature different noise standard deviations.

At test time, the images were mirror-padded to a 352 × 512 size (or 512 × 352), in order to avoid shape mismatches when downsampling and upsampling, and the image quality metric was computed only on the original image shape. The test images were also corrupted by an additive white Gaussian noise for various standard deviations σ: {0.0001, 5, 15, 20, 25, 30, 50, 55, 60, 75}. This allowed us to test the performance of our method in different noise level settings.

C. Model and training

1) Models design: We compare the learnets with the Unet for the task of denoising. For the U-net, we used the architecture described in [START_REF] Chul Ye | Deep convolutional framelets: A general deep learning framework for inverse problems[END_REF]Fig.10.(a)] which contains 31 million parameters.

Unless specified otherwise, the learnlets parameters were chosen as:

• m = 5 scales.

• 256 learnable analysis filters + 1 fixed analysis filters being just the identity, F θ (i)

A

, of size 11 × 11.

• 257 learnable synthesis filters, F θ (i)

S

, of size 13 × 13.

• the thresholding levels only depend on the scale, θ

(ij) T = θ (i)
T . This amounts to 372k trainable parameters, only one hundredth of the size of the U-net.

2) Training parameters: The networks were both trained on the mean squared error in line with [START_REF] Minh Quan | Compressed sensing MRI reconstruction using a generative adversarial network with a cyclic loss[END_REF]. Each epoch consisted of 200 batches of 8 extracted patches, and their respective noise level in the case of the learnlets. The training noise standard deviation range was chosen as Σ = [0; 55]. The networks were trained with an Adam optimizer [START_REF] Diederik | Adam: A Method for Stochastic Optimization[END_REF]. The learning rate was set at 10 -3 , then decreased by half every 25 epochs, until it reached a minimum of 10 -5 . The trainings took about 1 day for 500 epochs each.

D. Evaluation 1) Evaluation metric:

For the evaluation of the performance of the different models we used the Peak Signal to Noise Ratio (PSNR). It is defined image-wise as the following (with images taken in the [-0.5; 0.5] range):

P SN R(x, x) = -10 log 10 x -x 2 2 (7)
For each test noise standard deviation σ, we compute the mean of the PSNR of the denoised images, for all BSD68 images.

2) Testing: In addition, the networks were compared to wavelets denoising [START_REF] Mallat | A wavelet tour of signal processing[END_REF] and BM3D [START_REF] Dabov | Image denoising with block-matching and 3D filtering[END_REF]. We used the code of PySAP [START_REF] Farrens | PySAP: Python Sparse Data Analysis Package for Multidisciplinary Image Processing[END_REF] to implement the wavelets denoising. The wavelets family was the Biorthogonal 7.9, 5 scales were used, a hard thresholding was used with a thresholding level of 3 (except for the first scale where it was 4). The results for BM3D were taken from various sources [START_REF] Zhang | Beyond a Gaussian denoiser: Residual learning of deep CNN for image denoising[END_REF][START_REF] Zhang | FFDNet: Toward a fast and flexible solution for CNN-Based image denoising[END_REF][START_REF] Lefkimmiatis | Universal denoising networks: a novel CNN architecture for image denoising[END_REF] while the qualitative results were generated using the code provided by the authors of [START_REF] Dabov | Image denoising with block-matching and 3D filtering[END_REF] 3 . Table I Runtimes of the different models for the denoising of one image. Parameters used are the same as Figure 2.

V. RESULTS

A. Quantitative results

1) Comparison with other methods:

We compared the Unet and the learnlets against algorithms not involving learning, namely BM3D and wavelets shrinkage, and another neural network that was for long state of the art in image denoising, DnCNN [START_REF] Zhang | Beyond a Gaussian denoiser: Residual learning of deep CNN for image denoising[END_REF]. Figure 2 shows that for a large part of the band, [5; 55] where they have been trained, the learnlets are competitive compared to BM3D PSNR-wise. Keeping the same formula as the wavelets, we manage to reach the performance of state-of-the-art classical methods that are relatively complex. In this same band, the wavelets have performance that are degraded compared to the learnlets. Using learning, the learnlets enhance their decomposition power compare to the original wavelet model with no learning. For small noise level, both learning methods gets degraded performances compared with wavelet and BM3D. In this setting, the denoiser must act as the identity. For the learnlets this can be fixed by forcing exact reconstruction as can be seen in the next section. Finally, we can see that for unseen test noise levels (i.e. 70), the performances of DnCNN drop significantly while the learnlets keep relatively good performances. This suggests that the learnlets generalise much better on unseen noise levels than U-nets.

In addition, we can see in Table V-A1 that the learnlets benefit from their GPU implementation and run much faster than the wavelets and BM3D.

2) Learnlet with exact reconstruction: We saw in Figure 2 that the learnlets without exact reconstruction compete with classical methods on small noise standard deviations. Figure 3 shows that the performance of the network with forced exact reconstruction is almost the same as the one without forced exact reconstruction (we only lose 0.1dB at σ = 30 for example) on the majority of the test noise standard deviations. However, for low noise standard deviations, the network with forced exact reconstruction completely overpowers the other one. This is due to the fact that, at low noise standard deviations, for the i-th scale, the term x (i) out is practically the same as its thresholded version, because the thresholds θ (ij) T σ are going to be low. Therefore, it is compensated in the corresponding synthesis filter used for exact reconstruction at that scale, F θ (i,1)

A

. This allows to guarantee, in this case, no loss of information in the signal if it is clearly present.

B. Qualitative results

The Figure 4 shows that the learnlets suffer from some of the drawbacks of the wavelets like the creation of artifacts in the high frequency parts of the image. However the results are less blurred in comparison. Compared to the U-net or BM3D, the learnlets are clearly suffering visually from a loss of contrast. This is a known effect of the soft thresholding which inherently biases the results. This could be improved by the use of reweighting to further approach the hard thresholding, which doesn't bias the results.

VI. CONCLUSIONS

Pushing the limits of sparsity using massive learning and training data, we have proposed a novel neural network architecture -named learnlet -with the following properties:

• Despite very simple used concepts (linear filters and soft thresholding), it allows performances similar to relatively complex sparsity based methods like BM3D. • Although its performances are inferior to DnCNN, learnlets generalize better than DnCNN on noise levels that were not present in the training data and in the exact reconstruction domain. • Learnlets benefit from a fast implementation lacking for both wavelets and BM3D. • Learnlets can be forced to guarantee exact reconstruction when no thresholding is applied. This allows an embedding of the learnlets in applications where there is a need for guarantees of retrieval like in medical imaging. Learnlets therefore bridge the gap between parsimony and neural networks, by combining massive learning and the computing power of GPUs as in neural networks, but keeping a perfect understanding of how results are obtained, with all the theoretical guarantees existing in the area of parsimony.

The future directions of this work are to try to adapt what has been successful in the wavelets domain to this network For example, reweighting [START_REF] Emmanuel | Enhancing sparsity by reweighted l1 minimization[END_REF] could help us to get rid of the loss of contrast. Curvelet filters [START_REF] Starck | The curvelet transform for image denoising[END_REF] could also be used as a good initialisation or as complementary filters for the analysis. Finally, just like with the wavelets, many different types of noise -such as Poisson or spatially non-uniform white Gaussian noise -could be taken into account with a single model when implemented in an undecimated way, by adapting the thresholding function to the noise.

  • ST (d, s) is the soft-thresholding function applied point-wise on d with threshold s: ST (d, s) = sign(d) max(|d|s, 0).

Figure 2 .

 2 Figure 2. Ratio of the denoised image PSNR compared to the original noisy image PSNR for different standard deviations of the noise added to the test images for all considered models. The train noise standard deviation range was [0; 55].

Figure 3 .

 3 Figure 3. Ratio of the denoised image PSNR compared to the original noisy image PSNR for different standard deviations of the noise added to the test images for learnlets with and without forcing exact reconstruction. The train noise standard deviation range was [0; 55]. The number of filters used was 64.

  Image denoised BM3D: Image denoised Learnlets: Image denoised U-net: Image denoised

Figure 4 .

 4 Figure 4. Denoising results for a specific image in the BSD68 dataset. The noise standard deviation used was of 30. Parameters used for the methods are the same as for Figure 2.

https://github.com/zaccharieramzi/understanding-unets

https://www.tensorflow.org/api docs/python/tf/image/rgb to grayscale; TensorFlow Documentation for RGB to grayscale

http://www.cs.tut.fi/ ∼ foi/GCF-BM3D/


Fabienne Gourand
email: gourand@cyceron.fr.

Delphine Patin

Axelle Henry

Meźiane Ibazizenè

Martine Dhilly

Fabien Fillesoye

Olivier Tirel

Mihaela-Liliana Tintas

Cyril Papamicael

Vincent Levacher
email: vincent.levacher@insa-rouen.fr.

Meźiane Ibazizeǹe

Louisa Barré

Chemical Delivery System of MIBG to the Central Nervous System: Synthesis, 11 C-Radiosynthesis, and in Vivo Evaluation

Keywords: Central nervous system, norepinephrine transporter, MIBG, radiosynthesis, redox chemical delivery system, 1, 4-dihydroquinolines carriers 50 depression, anxiety, attention deficit hyperactivity disorders

T he in vivo expression of norepinephrine transporter (NET) is mostly established in the central and peripheral sympathetic nervous system. Several different radiotracers for clinical imaging of NET expression were developed.

Among them, meta-iodobenzylguanidine (MIBG) is structurally similar to the neurotransmitter norepinephrine, and [ 123 I]MIBG single photon emission computed tomography (SPECT) imaging studies are the most accurate method for detection of catecholamine-secreting tumors including neuroendocrine tumors such as pheochromocytoma and neuroblastoma. [1][2][3] Moreover, MIBG was also radiolabeled with iodine-131 for radiotherapy to treat neuroendocrine tumors. Positron emission tomography (PET) is more accurate and has the potential to be more sensitive and to provide better image resolution. In this context, efforts to develop MIBG analogs labeled with a positron emitter remain of great interest, and several [START_REF] Benoit | Facile synthesis of annelated NADH model precursors[END_REF] F-labeled benzylguanidine analogs have already been developed for PET imaging of NET expression. Recently, the radiotracer meta-[ 18 F]Fluorobenzylguanidine ([ 18 F]MFBG) has shown to be a very promising PET candidate leading to successful clinical investigations. [START_REF] Neuenschwander | Current strategy for the imaging of neuro-305 blastoma[END_REF][START_REF] Zhang | Imaging the Norepinephrine Transporter in Neuroblastoma: A Comparison of [18F]-MFBG and 123I-MIBG[END_REF][START_REF] Hu | A Practical, Automated Synthesis of meta-[18F]Fluorobenzylguanidine for Clinical Use[END_REF][START_REF] Pandit-Taskar | Biodistribution and Dosimetry of 18F-Meta-Fluorobenzylguanidine: A First-in-Human PET/CT Imaging Study of Patients with Neuroendocrine Malignancies[END_REF] Dysregulation of NET is implicated in various neuropsychiatric disorders such as hydrolysis releases the active compound, which can then act directly on the target into the CNS. By using this approach, Bodor et al. have targeted many drugs to the CNS. [START_REF] Bodor | Improved delivery through biological membranes. XLI. Brain-enhanced delivery of chlorambucil[END_REF][START_REF] Wu | Brain-specific chemical delivery systems for beta-lactam antibiotics. In vitro and in vivo studies of some dihydropyridine and dihydroisoquinoline derivatives of benzylpenicillin in rats[END_REF][START_REF] Pop | Chemical systems for delivery of antiepileptic drugs to the central nervous system[END_REF][START_REF] Bodor | Soft Drugs in Retrometabolic Drug Design and Targeting[END_REF] Later, Levacher et al. have solved many drawbacks related to this CDS by means of 1,4-dihydroquinolines instead of 1,4dihydropyridines. However, although mainly drugs were successfully targeted using this strategy, very few reports deal with the use of this CDS to target radiotracers into the brain. A survey of the literature indicated that, aside from our previous work on MIBG, [START_REF] Gourand | Chemical delivery system of Metaiodobenzylguanidine (MIBG) to the central nervous system[END_REF][START_REF] Gourand | Delivering FLT to the Central Nervous System by Means of a Promising Targeting System: Synthesis, [ 11 C]Radiosynthesis and in Vivo Evaluation[END_REF] only a single research article [START_REF] Tedjamulia | Evaluation of the brain-specific delivery of radioiodinated (Iodophenyl) alkylsubstituted amines coupled to a dihydropyridine carrier[END_REF] explored the potential of this appealing CDS approach to deliver a radiolabeled agent into the CNS. As far as our preliminary research work on MIBG is concerned, our initial work focused on the radiolabeling with carbon-11 of the CDS in order to validate the concept described previously. The results of the in vivo studies were highly encouraging, supporting our working hypothesis that the dihydroquinoline system may possibly be a promising CDS to target MIBG to brain tissues. Indeed, after in vivo injection into rats of [ 11 C]CDS-MIBG ([ 11 C]1a), the passage of [ 11 C]1a through the BBB has been demonstrated as well as the presence of MIBG in the brain. However, this chemical delivery system has some limitations: (1) a moderate brain penetration has been measured, and (2) the oxidation kinetics of [ 11 C]1a was quite slow since more than 50% was still present in rat brain at 45 min post injection. For these reasons, this CDS still needed to be optimized before being applied to radioiodinated MIBG. This Letter will focus on the preparation and in vivo evaluation of new 1,4-dihydroquinoline-MIBG systems [ 11 C]1b,c bearing methoxy groups to tune the redox potential of the CDS. The preparation and in vivo evaluation of a 1,4-dihydroquinoline [ 11 C]1d having a selfimmolative linker between the CDS and MIBG will be also reported (Figure 1).

To perform the radiosynthesis and in vivo study of our systems, it was first necessary to synthesize the precursors for radiolabeling and references that will be used to identify compounds in radio-HPLC. We have previously described the synthesis of the targeting system 1a starting from quinoline 4a s1 (Scheme 1). [START_REF] Gourand | Chemical delivery system of Metaiodobenzylguanidine (MIBG) to the central nervous system[END_REF] We decided to adopt the same approach to prepare 1b,c. Thus, a coupling reaction from quinolines 4b,c [START_REF] Benoit | Facile synthesis of annelated NADH model precursors[END_REF][START_REF] Charpentier | An efficient synthesis of 3cyanoquinoline derivatives[END_REF] and MIBG using CDI led to the corresponding quinolines 5b,c in moderate yields (36% and 30%, respectively). Alternatively, quinoline 5c could be prepared We next turned our attention to the synthesis of a CDS 121 having a γ-aminobutyric acid (GABA) self-immolative linker 122 group. [START_REF] Zhang | An autoimmolative spacer allows first-time incorporation of a unique solid-state fluorophore into a detection probe for acyl hydrolases[END_REF][START_REF] Dewit | synthesis, and cyclization of 4-aminobutyric acid derivatives: potential candidates as selfimmolative spacers[END_REF][23] We envisaged the synthesis of quinoline 9 from 123 s2 GABA derivative 6a (Scheme 2, route A). So, neutralization of 124 hydrochloride amine salt 6a and subsequent coupling reaction 125 with carboxylic acid 4a using BOP reagent led to quinoline 7a 126 (79% yield). The methyl ester functional group was hydrolyzed 127 by LiOH to give carboxylic acid 7b (96% yield). The latter was 128 subsequently involved in a coupling reaction with MIBG using 129 BOP to give 9 in a very low yield (4% yield). We also 130 investigated other activation strategies of carboxylic acid 7b by 131 means of CDI, ClCOOEt, (COCl), NBI, or NHS/DCC. 132 Unfortunately, we failed to obtain 9 by using these reagents. 133 Alternatively, N-protected GABA 6b and MIBG were reacted 134 in the presence of BOP reagent to furnish the coupling product 135 8a in 25% yield (Scheme 2, route B). Then, N-Boc 136 deprotection was carried out by using either acetyl chloride/ 137 MeOH or TFA to lead, respectively, to the desired ammonium 138 salts 8b and 8b′ (95% and 98% yields). One may note that 20 139 equiv of acetyl chloride/MeOH or TFA were required during 140 the course of the N-Boc deprotection to prevent from the 141 formation of the undesired γ-lactam ring resulting from the 142 cyclization reaction of the self-immolative linker. Thereafter, 143 ammonium 8b was neutralized back to pH 7 with sodium 144 hydroxide before being converted into the desired amide 9 in 145 25% yield by means of a coupling reaction between 4a and 146 BOP reagent. The quaternization reaction of 9 with methyl 147 triflate afforded a mixture of 2d,e (44% and 23%, respectively, 148 estimated by 1 H NMR). We then proceeded to a classical 149 reduction of the mixture of quinolinium salts 2d,e with BNAH. 150 However, LC/MS analysis of the crude reaction medium 151 revealed the presence of both 1,4-dihydroquinolines 1d,e and quinolinium salts 2d,e, which turned out to be extremely difficult to separate. Given this result, we decided to explore another route to obtain exclusively 1,4-dihydroquinoline 1d.

To overcome the alkylation reaction leading to undesirable compound 2e, quinoline 4e was first quaternized with methyl s3 triflate to give the key intermediate 10 in 96% yield (Scheme s3 3). The resulting NHS-activated quinolinium 10 24 was smoothly reacted with linker-MIBG derivative 8b′ to yield compound 2d (58%). Finally, a classical reduction reaction with BNAH led to the desired MIBG-targeting system 1d (77% determined by 1 H NMR).

Radiosyntheses of [ 11 C]1b,c were carried out as depicted in s4 Scheme 4 according to a two-step synthetic procedure. [START_REF] Gourand | Chemical delivery system of Metaiodobenzylguanidine (MIBG) to the central nervous system[END_REF][START_REF] Gourand | Delivering FLT to the Central Nervous System by Means of a Promising Targeting System: Synthesis, [ 11 C]Radiosynthesis and in Vivo Evaluation[END_REF]25 The structures of the [START_REF] Bodor | Improved delivery through biological membranes. XLI. Brain-enhanced delivery of chlorambucil[END_REF]

ACS Medicinal Chemistry Letters

  112 by reacting MIBG with the activated enol ester 20 4d (76%), 113 the latter having been obtained by reacting 4c with NBI (74%). 114 Then, quinolines 5b,c were easily transformed into their 115 corresponding quinolinium salts 2b,c (60% and 81%, 116 respectively) in the presence of methyl triflate. Finally, the 117 desired CDS-MIBG 1b,c were successfully obtained after 118 regioselective reduction of quinolinium salts 2b,c by means of 119 BNAH (32% and 70%, respectively).

  120

Figure 1 .

 1 Figure 1. Development of a 11 C-chemical delivery system of MIBG into the CNS. Scheme 1. Synthesis of the Redox CDS-MIBG 1a-c a

  Scheme 2. Initial Routes To Synthesize the Targeting System 1d a

Scheme 3 .

 3 Scheme 3. Alternative Route to the Redox CDS-MIBG 1d a

Letter DOI: 10

 10 .1021/acsmedchemlett.8b00642 ACS Med. Chem. Lett. XXXX, XXX, XXX-XXX C 198 were also interested (both in brain and plasma) in the 199 oxidation rates of [ 11 C]1b-d into the corresponding quinolinium salts [ 11 C]2b-d, which subsequently led to the cleavage of MIBG from the carrier through hydrolysis. The results will be compared to those already obtained from [ 11 C]

  Scheme 4. Radiosyntheses of [ 11 C]1b-d a

Figure 2 .

 2 Figure 2. Ex vivo biodistribution of the radioactivity in rat brain at different time intervals following tail vein injection of [ 11 C]1a-d (5, 10, 30, and 45 min for [ 11 C]1a-c; 5 and 10 min for [ 11 C]1d). Results are expressed in percent of injected dose per gram (%ID/g, mean, n = 2 for each point). [ 11 C]1a* results are from ref 15.

Figure 3 .

 3 Figure 3. Percentage of the expected [ 11 C]radioactive species in brain after injection into rat of (a) [ 11 C]1a, (b) [ 11 C]1b, (c) [ 11 C]1c, and (d) [ 11 C]1d (mean, n = 2 for each time point). [ 11 C]1a* results are from ref 15.

DOI: 10.1021/acsmedchemlett.8b00642 ACS Med. Chem. Lett. XXXX, XXX, XXX-XXX B

Author Contributions

276

The manuscript was written through contributions of all