PhD Stanislas Rapacchi
email: stanislas.rapacchi@univ-amu.fr

Thomas Troalen

Zakarya Bentatou

Morgane Quemeneur

Maxime Guye

Monique Bernard

Alexis Jacquier

Frank Kober

Simultaneous multi-slice cardiac cine with Fourier-encoded self-calibration at 7 Tesla

Keywords: Cardiac function MRI (cine), Simultaneous Multi-Slice (SMS), 7 Tesla cardiac magnetic resonance (CMR), Fourier encoding, ultra-high field MRI

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Introduction

7 Tesla (7T) MRI promises increased signal-to-noise ratio (SNR), which in cardiac MRI translates to a potential increase in imaging resolution for refined dynamic cardiac MRI (cine).

Cine MRI is the fundamental of cardiac MRI that provides morphology, global and local function assessment, strain [START_REF] Haig | A Novel Method for Estimating Myocardial Strain: Assessment of Deformation Tracking Against Reference Magnetic Resonance Methods in Healthy Volunteers[END_REF] and potentially even tissue characterization [START_REF] Nordlund | Experimental validation of contrast-enhanced SSFP cine CMR for quantification of myocardium at risk in acute myocardial infarction[END_REF]. Cine imaging resolution being highly anisotropic, one benefit from 7T cardiac MRI is to acquire thinner short-axis slices.

However, thinner slices require more breath-holds to cover the entire ventricles. Numerous breath-holds would hamper a conventional MRI exam, as they are difficultly tolerated by patients and increase the possibility of misalignment of the stack of slices. To circumvent these issues, we propose to accelerate thin-slice cine MRI at 7T with a Simultaneous Multi-Slice (SMS) acquisition [START_REF] Barth | Simultaneous multislice (SMS) imaging techniques[END_REF][START_REF] Larkman | Use of multicoil arrays for separation of signal from multiple slices simultaneously excited[END_REF][START_REF] Breuer | Controlled aliasing in volumetric parallel imaging (2D CAIPIRINHA)[END_REF]. SMS acquisitions enable to reduce the number of breath holds by the SMS acceleration factor employed (SMS-3 reduces the number of breath-holds by 3-fold). SMS acceleration corresponds to the excitation of multiple slices at the same time, coupled with a parallel imaging reconstruction that un-alias super-imposed images using the information from multi-elements receiver coil arrays.

SMS has already been applied to cine MRI at 7T by Schmitter et al [START_REF] Schmitter | Simultaneous multislice imaging in dynamic cardiac MRI at 7T using parallel transmission[END_REF], using parallel transmission and investigating the impact of triggering single-band calibration datasets for SMS reconstruction. In their work, calibration datasets were acquired with cardiac gating in a separate breath-hold. The synchronization in cardiac time between the calibration dataset and the aliased imaging dataset proved to significantly reduce cross-talk (i.e. leakage) between slices acquired simultaneously. SMS-cine was also demonstrated with balanced steady-state free precession (bSSFP) readout [START_REF] Stäb | CAIPIRINHA accelerated SSFP imaging[END_REF]. The proposed SMS-cine technique allowed the acquisition of 2 slices simultaneously but the imposed shift in the frequency response was prone to artifacts for more than 2 slices. At 7T, due to larger static field inhomogeneity (B0) and SAR limitations, bSSFP is difficult to perform, thus spoiled gradient-echo (FLASH [START_REF] Haase | FLASH imaging: rapid NMR imaging using low flip-angle pulses[END_REF]) sequences are preferred for their robustness to B0 variations. As opposed to bSSFP, GRE sequences also impose less constraints on the conception of SMS strategies when more than two slices are to be acquired simultaneously. In this work, a custom SMS technique dedicated to high resolution GRE-cine imaging was implemented and evaluated at 7T in consideration of the application specificities but without parallel transmission.

First, SMS acquisitions require an excitation of multiple slices at the same time, which is achieved by multi-frequency bands excitation pulses. Since multi-band excitations deploy more power, they are necessarily limited by specific absorption rate (SAR) restrictions at 7T. Thus, the eventual cine image quality was evaluated as it depends on the achieved flip angle in the heart [START_REF] Tyler | Cardiac cine MR-imaging at 3T: FLASH vs SSFP[END_REF] and might therefore be impacted by SAR restrictions. Second, SMS reconstruction is conventionally calibrated from a separate non-aliased acquisition. Since cine acquisitions are performed under breath-hold, the calibration data have to be acquired either in a separate scan within the same breath-hold or with the same breath-hold position. Both would affect the quality and risk of corruption of the calibration data, the former due to low reproducibility across breathholds and the latter due to prolongation of the breath-hold, which increases the risk of diaphragm drift. Interestingly, the first applications of SMS to cardiac imaging have been using Hadamard encoding [START_REF] Müller | Simultaneous multislice imaging (SIMUSIM) for improved cardiac imaging[END_REF][START_REF] Souza | SIMA: simultaneous multislice acquisition of MR images by Hadamard-encoded excitation[END_REF] to boost image quality. The combination of multiple repetitions allowed obtaining each slice separately using Hadamard decoding. Following this concept, we propose here to exploit the redundancy in the cardiac temporal dimension to create an aliasing-free calibration dataset embedded in the imaging acquisition. Mimicking the Hadamard linear combination of multiple datasets, a cardiac-time Fourier encoding strategy was developed [START_REF] Zhu | Autocalibrating CAIPIRINHA: Reformulating CAIPIRINHA as a 3D Problem[END_REF][START_REF] Zahneisen | Three-dimensional Fourier Encoding of Simultaneously Excited Slices: Generalized Acquisition and Reconstruction Framework[END_REF]. The self-calibrated SMS cine acquisition was compared to the single-slice(SS) conventional cine. Finally, to alleviate the deteriorated image quality due to limited flip angle and noise amplification, a non-linear constrained image reconstruction was evaluated against conventional parallel imaging reconstruction.

Methods

Embedded calibration data using Fourier-encoding along the temporal dimension

Slice un-aliasing can be achieved using the CAIPIRINHA-SMS [START_REF] Breuer | Controlled aliasing in volumetric parallel imaging (2D CAIPIRINHA)[END_REF][START_REF] Breuer | Controlled aliasing in parallel imaging results in higher acceleration (CAIPIRINHA) for multi-slice imaging[END_REF] technique, which facilitates this process by shifting their field-of-view and thus increasing the distance between superimposed voxels. CAIPIRINHA imposes that consecutive k-space lines observe incremental excitation phase that varies between slices to produce a linear phase increment across k-space. However, each acquired cardiac phase is independent of the others and provides a degree of freedom for extra phase modulation across cardiac phases. Therefore, an extra Fourier excitation phase offset pattern was superimposed along the cardiac phase dimension (cardiac time dimension) for each k-space line to create a two-dimensional radiofrequency (RF) phase modulation. The complete RF excitation phase pattern is illustrated Figure 1 for 3 simultaneous slices (SMS-3). For SMS unwrapping, the reconstruction operates in three steps as follows: first, the Fourier phase offset decoding (i.e. Fourier transform) allows for combined cardiac phases to isolate k-spaces from each slice. For a SMS-N acceleration, the combination of N-phases is necessary. Multiple calibration datasets can then be embedded in the entire cine MRI dataset, with a total number of 𝑁 𝑟𝑒𝑓 = 𝑓𝑙𝑜𝑜𝑟(𝑁 𝑝ℎ𝑎𝑠𝑒 𝑁 𝑆𝑀𝑆 ⁄ ) calibration datasets with 𝑁 𝑝ℎ𝑎𝑠𝑒 the number of complete cardiac phases and 𝑁 𝑆𝑀𝑆 the SMS acceleration factor. In this work, the 𝑁 𝑟𝑒𝑓 calibration datasets are combined in a second step using singular value decomposition(SVD). As a third step, the first SVD eigenvector serves then for calibration of SMS reconstruction. In our case, Split-Slice-GeneRalized Autocalibrating Partial Parallel Acquisition (Split-Slice-GRAPPA, further noted SSG) [START_REF] Cauley | Interslice leakage artifact reduction technique for simultaneous multislice acquisitions[END_REF][START_REF] Setsompop | Blipped-controlled aliasing in parallel imaging for simultaneous multislice echo planar imaging with reduced gfactor penalty[END_REF] kernels (empirically optimized to a size of 3x3, see Supporting

Information Figure S1) were calibrated over the cropped k-space center (32x24) with a Tikhonov regularization of 10 -5 .

7T Cardiac MRI experiments

All experiments were performed on a 7T investigative human MRI scanner (Magnetom-7T Step 2.3, Siemens Healthcare GmbH, Erlangen, Germany), using a 32 receive(Rx)/8 transmit(Tx) channels coil (MRITools GmbH, Berlin, Germany) with the 8 Tx channels combined as a single channel with a hardware phase setting optimized for cardiac imaging. Transmit voltage calibration was performed using a vendor-provided calibration sequence. Within the considerations of B1+ field inhomogeneity from the use of transmit surface coils, a global nominal flip angle is still referenced per sequence to compare the relative effective RF power of each sequence.

This study was approved by the local Institutional Review Board in accordance with the guidelines outlined in the Declaration of Helsinki. Twelve healthy volunteers were enrolled in this study (6 women, 23±3 years old) after written consent was obtained. Due to the poor RF penetration from the concomitant use of transmit surface coils and limited RF power supply (8kW), the subjects were recruited with a maximum body mass index (BMI) of 25 (avoiding overweight condition). SAR were limited to the initial level (Siemens "level 0") of established RF exposures.

A 2D FLASH-cine sequence with retrospective electrocardiogram gating was modified with CAIPIRINHA-SMS excitations [START_REF] Breuer | Controlled aliasing in volumetric parallel imaging (2D CAIPIRINHA)[END_REF] and the proposed cardiac time-Fourier RF phase cycling pattern. The radiofrequency (RF) pulses (1ms duration, time-bandwidth product 1.5) were then optimized for peak power using Wong's optimal phase offsets [START_REF] Wong | Optimized Phase Schedules for Minimizing Peak RF Power in Simultaneous Multi-Slice RF Excitation Pulses[END_REF]. Cine parameters were SMS-3

and GRAPPA-2 (24 auto-calibration lines), 1.8x1.8x4 mm 3 resolution reconstructed to 0.9x0.9x4 mm 3 , 192x168 acquisition matrix, TE/TR = 2.56/5.0 ms, 28 ms temporal resolution, 501 Hz/pixel bandwidth, 75/256 asymmetrical echo and 2-fold readout oversampling, flow compensation in slice and read direction, ~10s breath-hold/acquisition. SMS slice distance was fixed to 20 mm.

The same acquisitions were performed without SMS acceleration (noted single-slice or SS) for comparison. For both acquisitions, flip angles were maximized to fit within SAR restrictions and to obtain maximal FLASH-cine contrast-to-noise ratio [START_REF] Tyler | Cardiac cine MR-imaging at 3T: FLASH vs SSFP[END_REF]18). In order to strictly compare SS to SMS cine, additional SS acquisitions were matches to SMS in flip angle in four volunteers.

Image reconstruction

The image reconstruction was implemented in the Gadgetron (19) framework. A custom Matlab (Matlab R2017a, Mathworks, Natick, MA, USA) algorithm was designed as a "gadget" to perform our 3-steps SMS reconstruction: Fourier tranform, SVD and SSG. The in-plane reconstruction was then performed separately using gadgets available in the framework.

Conventional GRAPPA (20) reconstruction was implemented for online reconstruction, further noted SMS-G. A second reconstruction using SSG + cardiac time-regularized L1-SPIRiT [START_REF] Lustig | Sparse MRI: The application of compressed sensing for rapid MR imaging[END_REF][START_REF] Lustig | SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space[END_REF] was performed retrospectively for noise reduction, noted SMS-L. Asymmetrical echo and partial Fourier aspects were handled using a projection onto convex sets (POCS) reconstruction algorithm [START_REF] Xu | Partial Fourier imaging in multi-dimensions: A means to save a full factor of two in time[END_REF][START_REF] Peng | MR image reconstruction of sparsely sampled 3D kspace data by projection-onto-convex sets[END_REF]. Images were then interpolated with Gaussian k-space filtering. Eventually to facilitate visualization, a B1 filter was applied to the image series to correct for B1-gradient from the surface coil to the deep chest without affecting image contrast.

Image analysis

DICOM images were imported in Osirix for region-of-interest (ROI) based analysis. Signal-tonoise ratio (SNR) was evaluated as the mean-to-standard deviation ratio in a ROI drawn in the septum. SNR was measured at three levels: base, mid-ventricular and apex. Contrast-to-noise ratio (CNR) was evaluated as follows: the difference of mean intensity between the septum ROI and a ROI drawn over the left ventricle (LV) blood pool was then divided by the standard deviation of the septum ROI. The blood pool ROI was designed to avoid LV pillars. Slice leakage was evaluated by applying the corresponding SMS reconstruction (SMS-G) of the other two slices onto each of the three reconstructed slices [START_REF] Xu | Evaluation of slice accelerations using multiband echo planar imaging at 3 T[END_REF]. By crossing the SMS kernels of each slice onto the others allowed us to measure the residual signal that leaks between slices. The Split-Slice-GRAPPA reconstruction has been designed to minimize leakage at the kernel calibration level [START_REF] Cauley | Interslice leakage artifact reduction technique for simultaneous multislice acquisitions[END_REF], so that applying the SMS kernels of slices 2 and 3 onto slice 1 should output minimal signal. Thus, leakage was defined as the sum of the signals measured in the two "leaked" slices over the signal of the original reconstructed slice. Since leakage comes primarily from SSG processing, only SMS-G was evaluated, similar leakage values being expected from SMS-L. Leakage was then measured using an ellipsoid ROI over the left ventricle.

Eventually for visualization purposes, the stack of short-axis slices was imported in Matlab and interpolated to an isotropic resolution for long axis view rendering using a 3D linear interpolation.

To evaluate the capacity of SMS-cine images to assess cardiac function locally, one expert radiologist with more than 25 years of experience in cardiac MRI was asked to rate each AHA sector(26) from 0 (no visibility of both endo and epicardium) to 5 (perfect assessment of local myocardium and its contractility).

Statistical analysis

All results were reported in Excel sheets (Microsoft, Redmond, WA, USA). Data were then compiled in JMP (SAS, Cary, NC, USA) for a pair-wise analysis of variance with Bonferroni post hoc test for normally distributed data and Kruskal-Wallis test analysis with Dun-Bonferroni post hoc test for non-normally distributed data. A p-value inferior to 0.05 was considered statistically significant. The influence of flip angle on CNR was verified when comparing SS, SMS-G and SS using matched flip angle (further noted SSmatched), as observed in Figure 4. There was very little differences in SNR between SS, SSmatched and SMS-G (11.0±6.5, 9.6±2.5 and 8.4±1.6 respectively). However there was a notable decrease of CNR between SS and both SSmatched and SMS-G (14.5±7.9 compared to 6.6±2.1 and 6.2±2.2 respectively, p(SS/SSmatched)=0.08 and p(SS/SMS-G)=0.05). These differences demonstrated flip angle has little impact on SNR but a strong influence on FLASH-cine CNR, as demonstrated previously by Tyler et al.( 9)

Results

SAR limited multi-band excitations penalize image quality

Constrained reconstruction can reduce SMS noise amplification

Exploiting the sparsity in the spatio-temporal domain, SMS-L image reconstruction allowed to mitigate the noise amplification from SMS acquisition. Both SNR and CNR (Figures 3 and5)

were enhanced without compromising the morphological features and the peak systole analysis.

The SNR was improved by 23 ± 36% (SNR(SMS-G)=7.5 ± 2.8 vs SNR(SMS-L)=9.4 ± 5.0, p=0.004) and the CNR was improved as well by 45 ± 25 % (CNR(SMS-G)=5.6 ± 4.0 vs CNR(SMS-L)= 7.3 ± 6.0, p=0.008). However, areas of low intensity tended to be shadowed even further by the regularization, as observed in the posterior wall and the abdominal organs bellow (Figure 4).

Figure 6 summarizes SNR and CNR variations, as measured at the three levels of the heart. The SNR loss from noise amplification due to SMS acceleration was compensated by constrained image reconstruction. However, the loss of CNR using multi-band excitations remained a penalty despite a significant improvement using regularized image reconstruction. Basal slices, further distant from the coil, suffered from a significantly lower CNR in both SS-cine (compared to both apical(p=0.01) and middle slices(p=0.02)) and SMS-3 cine using SMS-L (compared to apical slices, p=0.01).

Cardiac SMS-3 cine has limited leakage

Slice leakage was limited below 20% in the left ventricle using SMS-3 cine. Figure 7 illustrates leakage measured in the three slices. Average leakage increased significantly from apex (7.4±6.1%) to mid-ventricle (9.3±4.6%, p=0.02) and from mid-ventricle to base (12.0±4.7%, p=0.02). Finally, the longitudinal spatial resolution can be appreciated by the reformat of the short-axis slices along the long axis of left ventricle, as demonstrated in Figure 8.

Evaluation of local cardiac function remains limited with SMS-cine

Figure 9 shows the mean ratings of local cardiac function and myocardium wall visualization for each of the 16 LV segments for the three techniques. Depending on the distance from the surface coil, the mid-ventricular and basal slices were difficult to assess, particularly for the posterior wall. The regularization from SMS-L significantly improved quality scores (from 3.6(SMS-G) to 3.9(SMS-L), p<0.001), despite not allowing full recovery of the contrast necessary for proper local myocardium evaluation that was obtained with SS-cine.

Discussion

This study demonstrates the feasibility and benefits of acquiring Simultaneous Multi-Slice dynamic cardiac MRI (SMS-cine) at 7 Tesla. The specificity of cardiac cine imaging was exploited to propose several improvements to SMS cine: first, the Fourier-encoding strategy allowed for embedded calibration data that circumvent issues with conventional separated singleslice calibration data; second, the sparsity along the cardiac time domain allowed for a constrained image reconstruction that mitigates the noise amplification from SMS acquisition.

As observed in this study, the benefits of extended spatial coverage from SMS acquisitions comes with the penalty of extra RF power that, in conjunction with strong SAR limitations at ultra-high field, directly impacts the ability to manipulate magnetization. In the context of cine, this drawback increases steady-state signal of static spins (i.e. myocardium) while decreasing signal of moving spins (i.e. flowing blood). The consequence is a partially recovered myocardium SNR and a severely decreased myocardium-blood CNR. Nonetheless, other applications such as phasecontrast MRI could benefit from SMS integration without penalization from the reduced RF power.

Two aspects of the proposed approach were not covered in this study: 1/ the benefits of integrating the calibration data into the imaging set rather than the conventional separate acquisition and 2/ the exploration of the multiple synchronous calibration datasets provided by the self-calibrating strategy. First, Figure 10 shows an acquisition when the separate calibration was acquired at the beginning of each breath-hold. In our experience, this strategy led to calibration data misregistered to the imaging dataset. Indeed, we found that, without specific instructions or extra delay, volunteers did not reach their breath-hold at the beginning of the acquisition, such that SMS acquisition with separate calibration could not be exploited. Second, the self-calibration strategy provided between 4 and 7 calibration datasets depending on the subject heart rate. However, these calibration datasets were noisy when taken individually. As a consequence, the use of synchronous calibration datasets did not permit to properly perform the SMS reconstruction, as shown in Supporting Information Figure S2. We opted for the SVD for combining these datasets, which significantly reduced the noise level of the eventual calibration dataset. Additionally, the combination of different cardiac phases can be tolerated for SMS unwrapping given that the distance between overlapping pixels remains greater than the deformation induced by cardiac motion. Indeed, while cardiac motion spans deformations on the order of 1cm, the overlapping pixels have a distance defined by the CAIPIRINHA shift (1/6 th of the phase FOV) and the slices gap (16mm). In this study, this distance is greater than 4cm, thus much larger than potential cardiac deformations.

Several aspects in the design of this study could be explored for further improvement. First, the benefits of SMS cine were explored with relatively thin slices (4mm thick) and a high in-plane resolution towards the purpose of high resolution cardiac MRI. In such severe conditions, the drawbacks of the proposed approach become blatant: strong noise amplification and loss of SNR and CNR are observed, and images loose diagnostic quality when heart's depth exceeded the penetration of the surface coil B1 fields (B1+ and B1-). Thicker slices could be acquired to provide sufficient signal from deep within the chest, and super-resolution techniques(28) could be integrated to achieve the sought high-resolution imaging. Second, image reconstruction was designed in a 2-step fashion, with SMS slice separation first (using split-slice GRAPPA) and phase-encode unwrapping second (GRAPPA or L1SPIRiT). An alternative would have been to perform a single-step image reconstruction [START_REF] Koopmans | Two-dimensional-NGC-SENSE-GRAPPA for fast, ghosting-robust reconstruction of in-plane and slice-accelerated blipped-CAIPI echo planar imaging[END_REF][START_REF] Zhu | Hybrid-Space SENSE Reconstruction for Simultaneous Multi-Slice MRI[END_REF], which could have helped better exploiting parallel imaging information in a 3D fashion. Adversely, the 2-step approach enables to balance between in-plane and through-plane noise amplification and residual artifact, and thus propose regularized algorithms such as L1-SPIRiT for phase-encode unwrapping. This ability to tune each reconstruction step can be critical to cardiac SMS-MRI as the coil arrangement is often not-aligned with the slice orientations, which undermines the coil sensitivity variations between overlapping pixels. Third, it would be relevant to evaluate RF transmission through B1+ mapping [START_REF] Nehrke | DREAM-a novel approach for robust, ultrafast, multislice B1 mapping[END_REF] instead of reporting a nominal flip angle. Mapping the local variations of transmitted RF power would unveil the inhomogeneity of the B1+ field for tailored RF design and personalized SAR management. Unfortunately, sequences for cardiac B1+ mapping at 7T were not available on our system at the time of this study. Fourth and last, this study evaluated only SMS-3 acceleration. As observed in Supporting Information Figure S3, lower acceleration (SMS-2) allowed for improved image quality while higher acceleration (SMS-4) suffered from remaining aliasing artifacts and a lower nominal flip angle, which directly impacted the image quality.

SMS-3 cine was chosen as a compromise between image quality and acceleration.

This study remains limited to a cohort of twelve healthy subjects for the purpose of demonstration. Additionally, the cardiac coil employed in this study was configured in a single transmit channel mode, despite presenting eight transmit channels. For simplicity, the eight channels were combined by a hardware pre-phaser, with a phase set optimized for cardiac imaging. While parallel transmit optimization (pTx) can certainly improve the B1+ field in the heart [START_REF] Lustig | SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space[END_REF], the difficulty to measure and customize B1+ for shimming in the heart was beyond the scale of the current study. To circumvent severe B1+ penetration limitations, subjects were screened prior to recruitment for a limited BMI (<25). Even without pTx, several improvements could benefit SMS-cine: improved RF pulse design for reduced peak power [START_REF] Xu | Partial Fourier imaging in multi-dimensions: A means to save a full factor of two in time[END_REF] and more accurate slice separation [START_REF] Peng | MR image reconstruction of sparsely sampled 3D kspace data by projection-onto-convex sets[END_REF] as well as variable-rate selective excitation (VERSE) pulse design [START_REF] Conolly | Variable-rate selective excitation[END_REF].

Finally, SMS-cine was explored in this study with thinner slices mainly for cardiac function imaging, but it could also benefit to cardiac UHF-MRI with thicker slices to reduce acquisition time dedicated to cine and allow more examination time for novel UHF contrasts that require elongated acquisition durations, in particular for cardiac applications.

Conclusion

A novel SMS technique was proposed for SMS-cine acquisition at 7T. Exploiting cardiac cine specificity, Fourier encoded self-calibration and regularized image reconstruction allowed us to 13 acquire three slices simultaneously while maintaining SNR level. Nevertheless, due to SAR restrictions, the excitation flip angle had to be reduced from optimal values leading to significant CNR decrease using SMS-3 cine in the current experimental setting. This study therefore demonstrates general feasibility of SMS-cine but also illustrates its limitations, especially at ultrahigh field. Consequently, the contrast between blood and myocardium decreases with the flip angle. Embedding the calibration data within the imaging dataset solves this issue.

Figure 2

 2 Figure2shows an example of a SMS-3 short-axis cine-FLASH acquisition compared with single slice acquisitions from the same locations. Conventional SS-cine provides excellent image quality for a 7T scan with homogeneous intensity over the heart except for a small B1+ void close to the anterior junction. The homogeneity of the heart's intensity is maintained using SMS-3 cine. Using 1ms 3-band excitations, specific absorption rate (SAR) restrictions required us to reduce the flip angle for SMS-3 cine by 38 ± 7% compared to single-band cine, i.e. from 36-69 to 20-50 degrees. We note that in both cases, the actual flip angle in the heart is likely to be lower than this nominal flip angle due to the inhomogeneous B1+ field. Additionally, SMS-3 images have increased noise, as measured by the difference of SNR in the septum from SS acquisitions to SMS acquisition (SNR(SS) = 9.9 ± 6.4 vs SNR(SMS-G) = 7.4 ± 2.8, p = 0.03). SNR decreased from apex to base due an increased distance from the transmit/receive surface coil, although differences were not significant.

Figure 3

 3 Figure3illustrates a case of exacerbated signal variations due to the SAR-limited flip angle of multi-band excitations in one of the larger subjects of this study, and the benefits from regularized image reconstruction. With SMS, the LV wall of the basal slice was difficult to separate from the blood pool due to low effective flip angle and high noise level. The apical and mid-ventricular slices were closer to the surface coil and did not suffer from signal loss as much as the basal slice, distant from the coil. CNR decreased when using SMS acquisitions as shown in Figures2 and 3. The CNR between the LV blood pool and the septum was significantly decreased from SS cine: CNR(SS)= 14.3 ± 7.7 to CNR(SMS-G)=5.6 ± 3.6 (p<0.001) for SMS-3cine. Several effects participate in this image quality degradation: first, the limited SMS nominal flip angle reduced signal saturation difference between myocardium and fresh spins from flowing blood, in particular as the myocardium T1 is elongated at 7T[START_REF] Rodgers | Inversion recovery at 7 T in the human myocardium: measurement of T(1), inversion efficiency and B(1) (+)[END_REF]; and second, noise was amplified by the SMS acceleration.

Figure 1 :

 1 Figure 1: SMS-3-cine custom design of phase shifts encoding combining CAIPIRINHA phase shifts and Fourier encoded phase shifts along the cardiac phase dimensions. Proposed SMS-cine encoding provides embedded reference data for SMS calibration to perform slice separation.

Figure 2 :

 2 Figure 2: Examples of diastole images and y-t profiles from SMS-3 short-axis cine-FLASH compared with single slice acquisitions. The increased acceleration from SMS combined to the decreased flip angle due to SAR restrictions induced a loss of SNR and CNR between SS cine and accelerated SMS-3 cine. Losses increased from apex to base due to a greater distance from the surface coil. SMS-3 images were reconstructed with SMS-G.

Figure 3 :

 3 Figure 3: In the case of the heart being morphologically further away from the surface coil, a severe loss of SNR and CNR was observed between SS-cine and SMS-3-cine. Constrained image reconstruction (SMS-L) reduced noise amplification compared to SMS-G. Nominal flip angle instructions were 69° for SS and 40° for SMS-3. Dark spots in SMS-3-cine images are exacerbated B1+ losses.

Figure 4 :

 4 Figure 4: Comparison between SS and SMS-G at maximum SAR levels and SS with matched flip angle (SSmatched) with SMS. By decreasing the flip angle, the steady-state signal of static spins (myocardium) increases while the transient signal from flowing spins (blood) decreases.

Figure 5 :

 5 Figure 5: After split-slice GRAPPA (SSG), L1-SPIRiT non-linear regularized image reconstruction (SMS-L) improved the SNR and CNR compared to the conventional GRAPPA (SMS-G) reconstruction.

Figure 6 :

 6 Figure 6: Bar graphs of SNR and CNR measurements at the three ventricle levels: apex, mid and base. Statistically significant differences (p<0.05) are noted with a *.

Figure 7 :

 7 Figure 7: SMS slice leakage measured at the three levels of the ventricle showed increased leakage from apex to base. Leakage maps were masked for visualization. Average slice leakage measured in the left ventricle is reported in the graph below for all volunteers.

Figure 8 :

 8 Figure 8: Short axis slices and horizontal long axis (HLA) reformat of the entire stack from the single-slice cine and the SMS-3-cine with SMS-L image reconstruction. Note that SMS-3 cine covers the lower part of the atria as well due to the fixed slice gap in this study.

Figure 9 :

 9 Figure 9: Bullseye plots of quality assessment of myocardium wall visualization and contractile function for the 16 left ventricle segments. Even with SS, the posterior segments of the basal slice were sometimes difficult to observe throughout the cardiac cycle. SMS-G and SMS-L suffered from severe loss of signal and contrast particularly at the basal level.

Figure 10 :

 10 Figure 10: Comparison of SS and SMS-G with separate calibration or with proposed embedded Fourier-encoded calibration. The separate calibration data were acquired too early in the breathhold, leading to mis-registration with the imaging data, thus the SMS reconstruction fails.

Acknowledgements

This work was performed by a laboratory member of France Life Imaging network (grant ANR-11-INBS-0006), on the platform 7T-AMI, a French "Investissements d'Avenir" programme" (grant ANR-11-EQPX-0001).

The project leading to this publication has received funding from the following institutions:

Excellence Initiative of Aix-Marseille University -A*MIDEX (grant ANR-11-IDEX-0001-02), a

French "Investissements d'Avenir" programme"; Agence Nationale de la Recherche (grant ANR-14-CE17-0016); Fondation de la Recherche Médicale (grant FRM DBS20140930772).

Last but not least, the authors would like to thank Sebastian Schmitter and Giulio Ferrazzi for very insightful discussions.

Supporting Information Figure

 S1: SMS-G reconstruction using increasing SSG kernel sizes from 3x3 to 7x7. Aliasing artifacts can be observed when the kernel size increases (red ellipses).

The more conservative kernel size of 3x3 was chosen for this study to limit these artifacts. S2: Comparison of the SMS reconstruction either using the combination of the multiple calibration datasets with singular value decomposition (SVD) or using calibration synchronous to the imaging datasets (phase-resolved). For the phase-resolved SMS calibration, each imaging cardiac phase is reconstructed using the nearest calibration dataset in cardiac time. This approach limits the influence of cardiac motion into the SMS reconstruction.

Supporting Information Figure

However, in our study design, the individual calibration datasets were too noisy to robustly calibrate the SMS reconstruction. S3: Example of results from SMS-2, SMS-3 and SMS-4 cine. SAR restrictions limited the increasing RF power of the SMS excitation pulses such that nominal flip angles (FA) decreased dramatically with increasing number of slices. As a consequence, SNR dropped severely for SMS-4 and image reconstruction (SMS-L) retained aliasing artifacts.

Supporting Information Figure


Stéphane Abide

Stéphane Viazzo

Isabelle Raspo

Anthony Randriamampianina

Gabriel Meletti

Uwe Harlander

Andreas Krebs

High-Order Compact scheme for High-Performance Computing of stratified rotating flows

To take advantage of modern generation computing hardware, a scalable numerical method, based on high-order compact scheme, was developed to solve rotating stratified flows in cylindrical annular domains.

The azimuthal direction has been discretized using Fourier series expansion to benefit from the natural periodicity of the cylindrical geometry, and the favorable complexity algorithms for computing Fast Fourier Transforms. The space discretization in the two wall-bounded directions relies on the fourth-order compact scheme approximations. The code parallelization strategy combines two approaches. The first one is the 2d-pencil decomposition to address the parallel solution of the implicit viscous terms and the pressure-like equations based on the diagonalization method. The second strategy of parallelization consists in the calculation of the compact derivatives/interpolations, using the approximate tridiagonal solver named reduced Partial Diagonal Dominant (rPDD) algorithm [START_REF] Abide | An efficient parallel high-order compact scheme for the 3D incompressible Navier-Stokes equations[END_REF].The developed technique is validated with respect to analytical solutions, using the method of manufactured solutions, and available data for two specific configurations of rotating stratified flows : the Taylor-Couette setup under an axial thermal stratification and the baroclinic cavity. The purpose is to demonstrate its ability to correctly capture the flow characteristics in strato-rotational instability and in baroclinic instability with associated small-scale features. Moreover, this code is found to drastically reduce the huge execution times that often prevent detailed numerical investigations of these complex phenomena.

Figure 1 shows a strong scaling test carried out to assess the performance for up to 1024 cores using grid up to 128 × 568 × 568 in radial, axial and azimuthal directions. Figure 2 shows instantaneous isocontours in the (θ, z) plane of the horizontal velocity divergence ∇ h .u along the inner cold wall and along the outer hot cylinder in the baroclinic configuration. This variable is introduced to exhibit the occurrence of small-scale features simultaneously with the large-scale baroclinic waves. In the first plot, the small-scale structures, developing towards the bottom wall, have been identified as inertia gravity waves (IGWs) by different authors in similar water-filled cavities. The present observed features recall such IGWs reported by these authors. Recently, for the same present configuration, [START_REF] Von Larcher | Instabilities and small-scale waves within the Stewartson layers of a thermally rotating annulus[END_REF] mentioned the presence of ripples resulting from hydrodynamical instability along the outer hot cylinder. We also capture the same phenomenon, as illustrated by the isocontours of the horizontal divergence.

Figure 1 :

 1 Figure 1: Baroclinic configuration -Strong scaling test a) temporal iteration b) solution of Poisson equation c) convective terms.

Figure 2 :

 2 Figure 2: Baroclinic configuration -Instantaneous isocontours in (θ, z) plane of the horizontal divergence of the velocity: at radius close to inner wall (a), at radius close to outer wall (b).

Acknowledgements

This work was granted access to the HPC resources of CALMIP supercomputing center under the allocation 2017P17027 and to the HPC resources of Aix-Marseille Université financed by the project Equip@Meso (ANR-10-EQPX-29-01) of the program "Investissements d'Avenir" supervised by the "Agence Nationale de la Recherche". The authors acknowledge financial support from "Ministère des Affaires Étrangères", France, in the framework of a PROCOPE project (PHC 28369XH and 35299PM).


Gabriel Meletti

Uwe Harlander

Torsten Seelig

Stéphane Viazzo

Stéphane Abide

Andreas Krebs

Anthony Randriamampianina

Isabelle Raspo

Torsten

Experimental Confirmation of Linear Stability Results on Stratified Taylor-Couette Flows

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Understanding the mechanisms that can result in an outward transport of angular momentum is a central problem regarding astrophysical objects formation, particularly in the theory of accretion, on which turbulence might explain this phenomenon in accretion discs [START_REF] Armitage | Astrophysics of Planet Formation[END_REF]. Among other candidates, the Strato Rotational Instability (SRI) has attracted attention in recent years as a possible instability leading to turbulent motion in these systems. The SRI is a purely hydrodynamic instability consisting of a classical Taylor-Couette (TC) system with stable density stratification due to, for example, salinity or a vertical temperature gradient.

Many information about the SRI can be obtained from numerical simulations and particularly designed laboratory experiments of axially-stratified TC setups, as the one in the laboratory of Aerodynamics and Fluid Mechanics (LAS) of the Brandenburg University of Technology (BTU) Cottbus-Senftenberg. For obtaining a stable density stratification along the cylinder axis, the bottom lid of the setup is cooled, and its top part is heated, establishing an axial linear temperature gradient between 3K and 5K per 0.7m.

Numerical simulations using the same configuration as the BTU experiment have been performed at the M2P2 laboratory at the Aix-Marseille University (AMU), and at the LAMPS laboratory at the University of Perpignan, with the temperature difference set as 4K between the bottom and top parts of the cylinder.

The inner and outer cylinders on the experimental setup rotate independently, each one driven by a DC motor unit controlled by servo amplifiers. The experimental results presented were obtained at a fixed rotation ratio of µ = Ω out /Ω in = 0.35, where Ω is the angular velocity of the cylinder. The velocity profiles shown are obtained from Particle Image Velocimetry (PIV), with the camera co-rotating with the outer cylinder. The PIV measurements absolute error is of less than 2%, and all experiments were repeated at least 2 times at different days, so that the result's reproducibility could be guaranteed.

The experimental results obtained with PIV are in agreement with the linear stability curves presented in [START_REF] Rüdiger | The stratorotational instability of Taylor-Couette flows with moderate Reynolds numbers[END_REF] for constant values of Rn, a stratification related Reynolds number. The linear stability curve for Rn=250 (adapted from [START_REF] Rüdiger | The stratorotational instability of Taylor-Couette flows with moderate Reynolds numbers[END_REF]) is shown as a black solid line in figure 1, where some of the experimental results obtained during this work are also represented along the vertical red line of constant µ = 0.35.

The red triangles represent unstable flows obtained for Re = 400, Re = 600, and Re = 800, while the blue circle represents the stable case when µ = 0.35, Rn = 250, and Re = 1000. As it can be seen in fig. 1, the stable case is just outside the marginal linear stability line. All the other experiments are inside the unstable regions. The instability can be observed in the Hovmöller plots (figure 2), as well as in the analysis of the Reynolds stress tensor components (e.g., -ρu v ), since it is zero for the stable case, and non-zero when the flow is SRI unstable.

Comparisons of the experimental results with numerical simulations using the codes described in [START_REF] Harlander | Stratorotational instability in a thermally stratified Taylor-Couette flow[END_REF] and [START_REF] Abide | An efficient parallel high-order compact scheme for the 3D incompressible Navier-Stokes equations[END_REF] did show a good agreement regarding the SRI frequencies and the mean velocity profiles obtained. New high-performance numerical simulations considering all the same input parameters as the experiments shown in this abstract are now being performed for further comparison with linear stability analysis.

Figure 1 :

 1 Figure 1: Linear stability map for Rn=250. The solid red vertical line refers to the constant rotation ratio (µ = 0.35) of the performed experiments. The red triangles are unstable cases, and the blue circle represents stable cases.

Figure 2 :

 2 Figure 2: Hovmöller plot showing the azimuthal velocity as function of radius at constant angle and time. Parameters: Re=600, µ = 0.35, ∆T ≈ 5K, N=0.320, F r ≈ 1.2

Acknowledgements

The authors thank the Deutsche Forschungsgemeinschaft (DFG) for financial support.


Dominique Morvan
email: dominique.morvan@univ-amu.fr

Wildfires physics and modelling

The behavior of wildfires is governing by various physical mechanisms, at different scales in space (and time), ranged between less than 1mm (the flame) to larger than 100km (the plume). Many of these physical mechanisms, such as the decomposition of the vegetation into combustible gas and solid, the chemical reaction inside the flame and its interaction with the atmosphere, are nonlinear, which constitutes an additional difficulty for their predictions using numerical models. For all these reasons, the numerical simulation of wildfires is a high challenging multiscale problem. Despite these difficulties, the resolution of some problems in fire safety engineering such as the propagation of a fire front through a wildland urban interface (WUI), needs to describe a fire at a relative local scale (few hundred meters), with a relatively high level of details. It is in this context, that a new class of fire models, referred in the literature as "fully physical models", has been proposed at the end of 90's [START_REF]Mathematical Modelling of Forest Fires and New Methods of Fighting them[END_REF][START_REF] Morvan | Multiphase formulation applied to the modeling of fire spread through a forest fuel bed[END_REF][START_REF] Linn | A transport model for prediction of wildfire behaviour[END_REF][START_REF] Sullivan | Wildland surface fire spread modelling 1990-2007: 1 physical and quasiphysical models[END_REF]. Before developing such kind of models, it is capital to identify all scales (in space and time) associated to the physical mechanisms contributing to the ignition and the propagation of a fire through a vegetation stratum.

To avoid the complete description of the vegetation, impossible task if we consider the fractal nature of the interface between all the elements (leaves twigs . . . ) constituting a plant, it is represented as an equivalent porous media, characterized by a set of local physical properties such as the density, the volume fraction, the composition. Then the problem is formulated from the balance equations (mass, momentum, energy . . . ) of the coupled system formed by the vegetation and the surrounding atmosphere. This approach is often referred in the literature as a multiphase formulation.

The objective of this lecture, will be to identify all the physical phenomenon and the associated scales, contributing to the dynamics of a forest fire, followed by a short presentation of what is a fully physical wildfires model and a presentation of some results obtained with this kind of approach.

Figure 1 :

 1 Figure 1: Example of numerical simulation of a surface fire propagating in a grassland (from Frangieh et al Fire Safety Journal 2018, in press)


Glenn Herrou
email: glenn.herrou@b-com.com

Wassim Hamidouche
email: wassim.hamidouche@insa-rennes.fr

Luce Morin
email: luce.morin@insa-rennes.fr

LOW-COMPLEXITY SCALABLE ENCODER BASED ON LOCAL ADAPTATION OF THE SPATIAL RESOLUTION

Keywords: Video compression, spatial scalability, lowcomplexity, adaptive spatial resolution, SHVC

A two-layer low-complexity scalable encoding scheme based on local Adaptive Spatial Resolution (ASR) is proposed. This scheme relies on a block-level spatial resolution adaptation in the enhancement layer encoder. For each block, the optimal resolution is either obtained via a rate-distortion optimization followed by a decision refinement process or by a prediction via motion compensation exploiting the base layer motion vectors. The proposed architecture has been integrated over of the High Efficiency Video Coding (HEVC) reference software (HM16.12) which is used as a base layer encoder. Compared to SHVC, the scalable extension of HEVC, experimental results show bitrate savings of 0.76 % as well as encoding complexity reductions of 47 % for the whole scalable encoder and 96 % for the enhancement layer encoder.

INTRODUCTION

The deployment of the latest Ultra High Definition TV (UHDTV) [START_REF] Itu-R | Recommendation BT.2020-1: Parameters Values of Ultra-High Definition Television Systems for Production and International Programme Exchange[END_REF] systems aims to increase the user's Quality of Experience (QoE) by introducing to the existing High Definition TV (HDTV) system [START_REF] Itu-R | Recommendation BT.709-5: Parameter Values for the HDTV Standards for Production and International Programme Exchange[END_REF] new features such as higher spatial resolution, High Dynamic Range (HDR), wider color gamut and High Frame-Rate (HFR) [START_REF] Nilsson | Ultra high definition video formats and standardisation[END_REF][START_REF] Sugawara | UHDTV Image Format for Better Visual Experience[END_REF]. The introduction of these new features is driven by the will to provide a more realistic and immersive experience to the consumer. These new formats require a very large amount of data to be encoded before transmission to the end-user. In addition, the heterogeneity of the user's requirements, in terms of available bandwidth, display, computing and energy capabilities, drastically increases the storage and bandwidth resources required to encode and deliver the video.

The scalable extension of the High Efficiency Video Coding (HEVC) standard, SHVC [START_REF] Boyce | Overview of SHVC: scalable extensions of the High Efficiency Video Coding Standard[END_REF], enables to encode the video in several formats, depending on the chosen type of scalability, within a single layered bitstream. However, with its architecture comprising one HEVC encoder instance per layer, SHVC becomes unsuitable for the coding of new immersive video formats and their increased resolutions due to its high complexity [START_REF] Hamidouche | 4k real-time and parallel software video decoder for multilayer hevc extensions[END_REF].

Despite the current trend of increasing the capture and display devices spatial resolutions further and further, such resolutions are not necessarily required to represent the critical information of the signal. A well-known strategy consists in downsampling the video prior to encoding and upsampling back to the original resolution after decoding, in an effort to reduce the bitrate and/or the coding complexity for a similar reconstructed output quality [START_REF] Alfred M Bruckstein | Downscaling for better transform compression[END_REF][START_REF] Afonso | Low complexity video coding based on spatial resolution adaptation[END_REF][START_REF] Lin | Adaptive downsampling to improve image compression at low bit rates[END_REF][START_REF] Nguyen | Adaptive downsampling/upsampling for better video compression at low bit rate[END_REF][START_REF] Afonso | Video compression based on spatio-temporal resolution adaptation[END_REF][START_REF] Shen | Down-sampling based video coding using super-resolution technique[END_REF][START_REF] Wang | Adaptive downsampling video coding with spatially scalable ratedistortion modeling[END_REF][START_REF] Dong | Adaptive downsampling for highdefinition video coding[END_REF][START_REF] Li | Convolutional neural network-based block up-sampling for intra frame coding[END_REF]. Several studies have considered applying the down/up-sampling at an image level, showing that coding at a lower resolution performs better, especially at low bitrate [START_REF] Alfred M Bruckstein | Downscaling for better transform compression[END_REF][START_REF] Afonso | Low complexity video coding based on spatial resolution adaptation[END_REF]. Since the spatial frequency components are highly variable within different areas comprised in a single natural image, several investigations have been carried out on coding based on local Adaptive Spatial Resolution (ASR), where the down/upsampling is performed at a block level [START_REF] Lin | Adaptive downsampling to improve image compression at low bit rates[END_REF][START_REF] Nguyen | Adaptive downsampling/upsampling for better video compression at low bit rate[END_REF], showing promising results.

Based on the recent advances in the active field of single image Super Resolution (SR) [START_REF] Dong | Image super-resolution using deep convolutional networks[END_REF][START_REF] Kim | Deeplyrecursive convolutional network for image super-resolution[END_REF], several studies have used SR upsampling for ASR-based coding showing increased gains compared to common upsampling filter-banks [START_REF] Afonso | Video compression based on spatio-temporal resolution adaptation[END_REF][START_REF] Shen | Down-sampling based video coding using super-resolution technique[END_REF][START_REF] Wang | Adaptive downsampling video coding with spatially scalable ratedistortion modeling[END_REF][START_REF] Dong | Adaptive downsampling for highdefinition video coding[END_REF][START_REF] Li | Convolutional neural network-based block up-sampling for intra frame coding[END_REF]. However, these gains come at the expense of a significant increase in processing complexity, making SR unsuitable for low-complexity encoding/decoding.

Inspired by the above mentioned previous works, we propose, in this paper, a two-layer low-complexity scalable encoding scheme, which uses a standard Base Layer (BL) encoder and an Enhancement Layer (EL) encoder based on local adaptation of the spatial resolution.

The main contributions of this paper include:

• the design of a low-complexity block-level ASR-based EL encoder that determines the optimal spatial resolution among a list of several sampling-rates through a Rate Distortion Optimization (RDO) stage and a decision refinement process.

• the prediction of the block-level EL spatial resolution thanks to a derivation process based on the re-utilization of BL encoder Motion Vector(s) (MV).

• the implementation of this low-complexity EL encoder over the HEVC reference software (HM16.12) as base layer.

The remainder of this paper is organized as follows. Section 2 describes the proposed low-complexity scalable architectures, first the ASR-based encoder and then its extension with resolution prediction via motion compensation. Section 3 presents the test methodology and provides an analysis of the experimental results. Section 4 concludes this paper.

PROPOSED METHOD

Scalable coding scheme

The proposed scalable architecture, based on the one used in SHVC [START_REF] Boyce | Overview of SHVC: scalable extensions of the High Efficiency Video Coding Standard[END_REF], is depicted in Fig. 1. On one hand, the input Ultra High Definition (UHD) (3840x2160 pixels) video is first downsampled to High Definition (HD) (1920x1080 pixels) resolution with the filter bank detailed in [START_REF] Chen | Shvc test model 9 (shm 9) introduction and encoder description[END_REF] before being fed to the base-layer encoder, a standard HEVC encoder. On the other hand, the input UHD video is fed to the enhancement layer encoder whose architecture is described in the next section. Both bitstreams are then transmitted and processed by the decoder of their respective layer, the EL bitstream only being decoded if the desired output is the higher resolution video, e.g. UHD in the chosen use-case.

To facilitate the processing of the UHD input video, inter-layer communications are enabled in this scalable coding scheme, with several encoding decisions made by the BL encoder (partitioning, prediction mode etc.) transmitted to the EL encoder, in addition to the decoded BL video.

ASR-based enhancement layer encoder

The local adaptation of the spatial resolution is at the heart of the proposed low-complexity EL encoder. Indeed, since natural images/videos comprise locally variant spatial frequency components, it can be beneficial to adjust the sampling rate at a block level to perform a down/upsampling based encoding [START_REF] Lin | Adaptive downsampling to improve image compression at low bit rates[END_REF][START_REF] Nguyen | Adaptive downsampling/upsampling for better video compression at low bit rate[END_REF]. The proposed EL encoder allows for different combinations of horizontal and vertical sampling rates of 1 and 1/2, achieved by successive 1D downsamplings of the EL input block. This leads to the set of possible resolution modes L = {2N×2N, N×2N, 2N×N, N×N }, with N the width of the square block in BL resolution, and W×H referring to an EL block coding spatial resolution of width W and height H.

Fig. 2 depicts the proposed EL encoder architecture for a selection of the spatial resolution based on Rate-Distortion (R-D) optimization. For each EL block, whose size has been directly derived from the decision made by the BL encoder for its co-located BL block, the spatial resolution selection process is as follows.

The block is first successively encoded using each possible resolution mode to obtain the different R-D costs, computed as:

J(m) = D(m) + λ • R(m), (1)
with J the R-D cost, D the distortion and R the bit cost associated to resolution mode m. The derivation of Lagrangian weighting factor λ from the Quantization Parameter (QP) has been carefully optimized for the resolution mode selection problem following the method presented in [START_REF] Gary | Rate-distortion optimization for video compression[END_REF]. Since the selection of the resolution with the lowest R-D cost would result in a highly variable coding spatial resolution, even in areas with homogeneous spatial features, a resolution refinement process has been designed. Indeed, excessively frequent resolution transitions, especially at higher QP values, would tend to lower the visual quality of the reconstructed output. Thus, a list L best of resolution modes having an associated R-D cost close to the optimal one, Jmin, is first computed by Equation [START_REF] Itu-R | Recommendation BT.709-5: Parameter Values for the HDTV Standards for Production and International Programme Exchange[END_REF].

m ∈ L best if J(m) ∈ [Jmin, Jmin + α • WB] , (2)
where WB is the width of the block B under consideration in input EL resolution, α is a parameter defining the strength of the resolution refinement process. Then, two different tests are carried out depending on the optimal resolution mode candidates comprised in the L best list. First, if one of the candidates is a rectangular resolution, i.e. either 2N×N or N×2N , the input EL block is analysed to assess the presence of strong directional edges. Sobel-based gradients are thus computed along vertical and horizontal directions, and the rectangular resolution under consideration is selected as the final coding spatial resolution if the inequality expressed in Equation ( 3) is verified.

S B,d 2N > TG • S B,d N , (3)
with S B,d 2N and S B,d N the average Sobel-based gradient, along axes with higher and lower resolution, respectively, for the image block B. TG is a threshold used to adjust the edge detection process. Secondly, if the previous condition does not yield to the final resolution choice, the top and left neighboring blocks are subsequently analysed and compared to the current block under consideration. If the neighboring block coding spatial resolution is comprised in L best , a list Q of similarity metrics is computed from the Sobelbased gradients of the current EL block and its considered neighbor. Then, if the criterion defined in Equation ( 4) is satisfied, the selected final coding resolution is the resolution of the neighboring block.

∀q ∈ Q : q ∈ 1 TC , TC , (4)
with

Q = W B W H , S B,h S H,h , S B,v S H,v , S B,h •S H,v S B,v •S H,h
, B the current block, H the neighboring block under test, Wi the width of block i and S i,d the average Sobel-based gradient of block i along direction d. TC is a parameter defining the similarity threshold between two considered blocks. TG and TC have been optimized to give the best performance results on a subset of the test sequences used in Section 3.

Otherwise, the final choice is set to the resolution mode resulting in the lowest R-D cost. Fig. 3 shows the resolution mode decisions after refinement for a sample of the CatRobot sequence. Fig. 4: EL encoder architecture for resolution mode derivation via motion compensation.

Once the final spatial resolution has been selected, the EL block (resp. corresponding decoded BL block) is downsampled (resp. upsampled) to the coding resolution, using the same filter banks as the SHVC reference software [START_REF] Chen | Shvc test model 9 (shm 9) introduction and encoder description[END_REF], to generate the prediction residuals. Then, these residuals are transformed, quantized and entropy coded using the same tools as HEVC [START_REF] Gary J Sullivan | Overview of the High Efficiency Video Coding (HEVC) standard[END_REF]. The only difference is the addition of two context-coded bins to the Context-Adaptive Binary Arithmetic Coding (CABAC) engine in order to signal, in the bitstream, the chosen resolution among the four possible ones.

Resolution derivation via motion compensation

To further leverage the decisions made by the base layer encoder, the BL motion vectors, when available, are used to derive the resolution mode from previously encoded EL frames. Fig. 4 depicts the EL encoder architecture for this case of resolution mode prediction through motion compensation.

The RDO and resolution refinement steps are thus replaced by a resolution prediction stage for EL blocks with a corresponding intercoded block in the BL. For such an EL block, the MVs and reference frame are first extracted from the base layer. Then, after a proper scaling of the MVs to match the input EL resolution, the EL reference block is obtained to perform the resolution mode prediction. Since it is possible for the reference block to overlap several coding blocks of the reference frame, thus comprising pixels that have been encoded using different resolutions, a derivation process has been designed as follows:

r =    2N×2N if P(m = 2N×2N ) > p T h arg max s∈L P(m = s) otherwise (5)
with r the derived resolution from the set of possible resolutions L = {2N×2N, N×2N, 2N×N, N×N } and P(m) the probability corresponding to the relative frequency of pixels in the EL reference block in resolution mode m, with m ∈ L. The probability threshold p T h for the selection of the 2N×2N resolution has been introduced to avoid losing important details when the majority of the reference block has not been coded in the EL input resolution. The value of 0.3 has been selected to give the best performance results on a subset of the test sequences used in Section 3. In the case of bi-predictions, the derivation process remains the same, with the probabilities computed across both reference blocks. It should be noted that to reuse BL decisions during the EL encoding process, the EL encoder has to follow the same Group of Pictures (GOP) structure and keep the same reference frame buffer management as the BL encoder. With this resolution mode prediction process, the signalling of the chosen spatial resolution is not required, for each block, in the generated EL bitstream since the prediction can also be performed at the decoder side. Thus, in addition to the added temporal coherence brought by the motion compensated resolution prediction, the signalling cost of the ASR technique is considerably reduced when MVs are available in the base layer.

EXPERIMENTAL RESULTS

Test methodology

In this section, the proposed scalable encoder architecture is evaluated and compared to SHVC both in terms of coding performance and encoding complexity. Two different studies are carried out, one comparing the proposed ASR-based encoder depicted in Fig. 2 with SHVC, and the other comparing the proposed scalable encoder with resolution prediction via motion compensation, as shown in Fig. 4, with SHVC.

Encodings have been performed with the SHVC reference software SHM9.0 [START_REF]SHVC reference software version 9.0[END_REF]. Both the proposed encoder and the reference SHVC encoder use the same base layer, respectively encoded in All Intra (AI) or Random Access (RA) configuration for the first and second studies. The considered RA configuration uses a GOP size of 16 images with an intra-period of approximately one second.

Considering the EL encoders, for both studies, the SHM software has been limited to use either intra prediction modes or interprediction modes with the upsampled decoded base layer as reference (PBL only) for fair comparison purposes. Fixed-QP configuration has been used for every encodings carried out in both studies. The parameters used to define the strength of the resolution refinement process have been set to α = 2.56, TG = 2 and TC = 1.5. These values have been carefully optimized to offer the best results in terms of R-D performance and resolution choice homogeneity. Coding performance has been assessed in terms of rate-distortion using the Bjøntegaard delta metric (BD-Rate) [START_REF] Bjøntegaard | Improvements of the BD-PSNR model[END_REF], representing the average bit-rate gain/loss (-/+) for equal Peak Signal-to-Noise Ratio (PSNR) values. In order to evaluate the proposed scalable coding chain over a wide range of bit-rates, QPs ranging from 22 to 37 with a step of one have been used for each of the six UHD video test sequences.

Results and analysis

The first study focuses on the performance of the proposed lowcomplexity ASR-based scalable encoder with only the R-D optimized resolution selection process. BD-rate results are summarized in Table 1, positive values corresponding to a bitrate overhead for the proposed scalable encoder compared to SHVC for the same EL output PSNR value.

The average bitrate overhead of the proposed scheme is 5.13 % compared to SHVC. The per-sequence results are fairly homogeneous, around 4 ∼ 6 % bitrate overhead for equal PSNR-YUV values, the variations mainly depending on the content of the video, i.e. the ability of the resolution selection process to locally reduce the resolution whenever possible. For example, Fig. 5a depicts the per-QP resolution mode distribution for the Tango and Drums sequences. As can be observed, the ASR algorithm decisions lead to a majority of blocks coded at reduced resolutions even at low QP values for the Tango sequence, while the majority resolution transition from 2N×2N to N×N happens at a much higher QP for the Drums sequence. This correlates with the lower (resp. higher) than average bitrate overhead for the Tango (resp. Drums) sequence. The measured performance gain if the resolution mode signalling cost is not taken into account reaches, on average, 3.5 % of the total bitrate. Hence the interesting coding potential of the adaptive spatial resolution scheme if the signalling cost can be reduced, which is the purpose of the following experiment. Table 2 summarizes the BD-rate results for the proposed encoder compared to SHVC. Overall, the proposed ASR-based encoder with resolution mode derivation enabled achieves average bitrate savings of 0.76 % compared to SHVC. The performance of both U and V chroma channels are better than the results obtained for the luma channel, with respectively -4.1 %, -3.5 % and -0.1 % average BD-rate values. As can be observed, the proposed encoder performs better than the RDO-based version of the ASR algorithm on sequences that benefit from the changes in spatial resolution, and shows equivalent losses on the other sequences with high spatial details. In particular, performance of chroma components is highly variable depending on the sequence, with BD-rate values ranging from 16.4 % bitrate savings to 3.7 % bitrate overhead for Day-lightRoad and CatRobot sequences, respectively.

Fig. 5b shows the mean bit per block signalling cost, averaged over all sequences, with each tested QP value for the proposed encoder with and without the resolution mode derivation enabled. As can be expected from the BD-rate results, the signalling cost is at least divided by six for every QP when the derivation is enabled. The cost is gradually decreasing when the quantization parameter in- creases due to the overall lower amount of intra coded blocks in the base layer, at lower bitrates. Fig. 5c depicts the per-sequence portion of the EL bitrate taken by the resolution mode signalling, averaged over all QP values. The cost reduction factor is nearly constant for all sequences, with an average value of 17.5.

Concerning the codec complexity, the proposed ASR-based scalable coding scheme achieves a 72 % encoding time reduction compared to the SHVC reference software, as reported in Table 3. If only the EL layer is considered, the proposed architecture is 8.5 times faster than SHM at the encoder side. This complexity gain is mostly due to the low computational demand of the few modes to test during the RDO stage and the derived EL partitioning. For the proposed encoder with motion compensated resolution prediction, the EL encoder only represents 4 % of the EL SHM encoding time. The lower computation time compared to the previously presented version of the ASR-based encoder is due to the skip of the RDO stage when MVs are available. Considering the overall complexity, the reduction reaches 47 % compared to the SHM. This high difference between the EL-only and overall results can be explained by the increased complexity related to the inter-picture predictions in the BL encoder.

CONCLUSION AND FUTURE WORK

This paper proposes a two-layer low-complexity scalable encoding scheme based on local adaptations of the spatial resolution in the enhancement layer encoder. This EL encoder, which heavily re-uses the BL encoder decisions, allocates the spatial resolution at a blocklevel, either by performing a RDO stage followed by a carefully designed decision refinement process to select the resolution among a list of several sampling rates or by predicting the spatial resolution via motion compensation. This framework has been implemented over the HM16.12 reference software used as BL encoder. Experimental results show that the proposed framework achieves 0.76 % bitrate savings compared to SHVC. Complexity-wise, encoding time reductions of 47 %, for the dual-layer architecture, and 96 %, if only the EL is taken into account, are observed. Future work will include the integration of inter-predictions in the ASR-based EL encoder and real-time implementation of the proposed solution.

Fig. 1 :

 1 Fig. 1: Block diagram of the proposed scalable coding chain.

Fig. 2 :

 2 Fig. 2: Proposed EL encoder for R-D optimized resolution selection. Upsampling factors 4, 2 and 1 and downsampling factors 1, 2 and 4 correspond to resolution 2N×2N , N×2N or 2N×N and N×N , respectively.

Fig. 3 :

 3 Fig. 3: Example of resolution mode decisions for rate-distortion optimized resolution selection. (yellow: 2N×2N , green: N×2N , purple: 2N×N , white: N×N )

  Per-QP resolution mode distribution for the Tango and Drums sequences.

  Per-QP signalling cost (bits per block), averaged over all sequences. Per-sequence signalling cost (% of EL bitrate) averaged over all QP values.

Fig. 5 :

 5 Fig. 5: Example of resolution mode distribution and signalling costs with and without motion compensated resolution prediction.

Table 1 :

 1 BD-Rate results (%) for proposed ASR-based scalable encoder compared to SHVC. BL in AI config, EL in PBL config.

	Sequence	PSNR-Y	PSNR-U	PSNR-V	PSNR-YUV
	S1. DaylightRoad S2. CatRobot S3. Drums S4. Tango S5. RollerCoaster S6. FoodMarket2	4.43 3.16 5.15 3.63 4.0 5.08	2.11 9.71 9.33 3.67 10.65 7.92	-1.49 12.98 7.67 4.55 7.81 8.26	3.67 5.4 6.03 4.22 5.38 6.06
	Average	4.24	7.23	6.63	5.13
	Without resolution signalling cost	0.67	3.8	3.26	1.62

Table 2 :

 2 BD-Rate results (%) for proposed scalable encoder with mode derivation compared to SHVC. BL in RA config, EL in PBL config.

	Sequence	PSNR-Y	PSNR-U	PSNR-V	PSNR-YUV
	S1. DaylightRoad S2. CatRobot S3. Drums S4. Tango S5. RollerCoaster S6. FoodMarket2	-0.31 -1.48 4.16 -2.58 -0.36 0.22	-15.3 -4.42 0.86 -5.96 -0.03 0.29	-16.41 3.71 0.49 -7.63 -1.26 0.12	-3.98 -0.85 3.81 -3.7 -0.2 0.39
	Average	-0.1	-4.09	-3.50	-0.76

Table 3 :

 3 Encoding time (% of SHVC) of the proposed scalable encoder compared to SHVC.

		Enhancement Layer	Overall (EL + BL)
	Without inter-predicted BL	12 %	28 %
	With inter-predicted BL	4 %	53 %

The authors acknowledge funding from the French government through the National Research Agency (ANR) investment ANR-A0-AIRT-07.