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With 15% of severe cases among hospitalized patients​, the SARS-COV-2 pandemic has put tremendous pressure on Intensive Care Units, and made the identification of early predictors of future severity a public health priority. We collected​ ​ clinical and biological data, as well as CT scan images and radiology reports from 1,003 coronavirus-infected patients from two French hospitals. Radiologists' manual CT annotations were also available. We first identified 11 clinical variables and 3 types of radiologist-reported features significantly associated with prognosis. Next, focusing on the CT images, we trained deep learning models to automatically segment the scans and reproduce radiologists' annotations. We also built CT image-based deep learning models that predicted future severity better than models based on the radiologists' scan reports. Finally, we showed that including CT scan features alongside the clinical and biological data yielded more accurate predictions than using clinical and biological data alone. These findings show that CT scans provide insightful early predictors of future severity.

Convolutional transform learning is an unsupervised framework we introduced recently, for feature generation based on learnt convolutions. In this work, we propose a supervised formulation for convolutional transform so as to address the multi-label classification problem. Unlike the simple multiclass classification, in multi-label problems, each sample can correspond to multiple classes simultaneously, making the problem quite challenging. We propose to make use of a label consistency penalty and develop a suitable minimization algorithm for the training step. We illustrate the performance of the developed formulation on the practical problem of nonintrusive load monitoring. Comparisons with popular techniques show that our proposed approach yields better results on benchmark datasets.

Three-dimensional (3D), in vivo and in live imaging of living samples with a sub-micrometer resolution is a current necessity for biomedical researches which corresponds to a hot topic for microscopy engineers. It is likely that the role of computational approaches is yet underestimated and underused in 3D-microscopy. This paper is an illustration of the fundamental role that could be played by such strategies. Usual imaging depths in biomedical microscopy reach few hundreds of micrometers in optimal conditions when multiphoton approaches are favored. However, light scattering and absorption still damage image quality, especially as imaging depth increases. Our approach rests on the multi-parametric 3D-PSF estimation of the true 3DGaussian model of the PSF along multi-millimeter depth. Image acquisition in MPM generates stacks of 2D images constituting an overall 3D-image. 3D-volumes of images containing a single object are selected and isolated all along the depth using automatic morphological tools. Finally, our computational 3DGaussian shape-fitting algorithm named FIGARO is applied on each individual PSF and quantify PSF full-width at half maximum (FWHM) in the 3 dimensions simultaneously with PSF tilt angles. FWHM evolution in the 3 dimensions along the 2 mm depth highlights a highly significant effect of spherical aberrations. Starting from standard values of PSF measured at sample top compared to what expected in MPM, we show an increase with a factor three of the PSF FWHM in axial plane when the sample bottom is reached, and no modification of PSF dimensions in lateral plane all along the depth. The main direction of the PSF shows a convergence toward a focal point that will be discussed

Objectifs Le but de cette etude est d’etudier les performances de l’analyse radiomique IRM dans le cadre du diagnostic des tumeurs des glandes parotides utilisant des methodes d’apprentissage automatique (machine learning). Nous evaluerons egalement l’impact des modeles de classification radiomique sur les interpretations de radiologues experimentes et d’internes suivant un cursus de formation dans cette specialite. Methodes Un total de 145 patients ont participe a cette etude monocentrique (Gustave Roussy cancer campus). Deux tâches de classification ont ete considerees : classification binaire benin/malin, et classification en 5 classes correspondant aux sous-types histologiques (adenome pleomorphe, tumeur de Warthin, lymphome, carcinome et autres types). Nous developpons plusieurs modeles d’apprentissage automatique en utilisant des features suivant le standard IBSI, extraites des sequences T1, T2 FLAIR, T1 gadolinium et diffusion de chaque patient. Ces modeles sont ensuite evalues a l’aide d’une procedure de validation croisee et des courbes ROC associees. Enfin, nous verifions la capacite du meilleur modele a aider les radiologues experts et internes a differencier les tumeurs. Resultats Les resultats et figures presentes ci-apres sont preliminaires : l’etude est en cours de developpement. Classification binaire benin/malin : Un modele de Random Forest donne une AUC moyenne de 0,663 ± 0,04 et une accuracy de 0,64 ± 0,06 ( Fig. 1 ). En utilisant une procedure de selection de features ayant recours a un test F ANOVA, nous obtenons une AUC moyenne de 0,691 ± 0,12 et une accuracy de 0,66 ± 0,11. Classification en sous-types histologiques : strategie One-vs-Rest. Adenome pleomorphe vs autres : AUC = 0,81 ± 0,05, accuracy = 0,76 ± 0,06. Tumeur de Warthin vs autres : AUC = 0,82 ± 0,12, accuracy = 0,80 ± 0,06. Lymphome vs autres : pas assez d’exemples dans le jeu d’entrainement, l’utilisation d’une methode de reechantillonnage est a prevoir. Carcinome vs autres : AUC = 0,63 ± 0,10, accuracy = 0,64 ± 0,04. Comparaison aux radiologues experts et internes : en cours de realisation. Conclusions Les resultats preliminaires de classification binaire indiquent qu’il est possible d’utiliser des algorithmes d’apprentissage automatique etablis sur des features radiomiques pour differencier la malignite des tumeurs de la glande parotide. Cependant, ces resultats pourraient etre ameliores grâce a un volume de donnees plus important. Il est a remarquer que cette tâche binaire est egalement complexe pour les radiologues : en effet, il n’existe pas de lien tangible entre les differents sous-types histologiques qui puisse expliquer la malignite ou non d’une tumeur. Concernant la classification multi-classe, il apparait que les adenomes pleomorphes et les tumeurs de Warthin sont les plus simples a categoriser. Or, il s’agit de tumeurs benignes : les carcinomes se revelent plus difficilement differentiables alors qu’ils sont malins. Toutefois, a l’heure ou ce document est ecrit, il reste plusieurs axes de recherche possibles que nous etudierons prochainement ( Fig. 2 ).

In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is reliably estimated from the observations. As the posterior density of the unknown parameters is analytically intractable, the estimation problem is derived in a variational Bayesian framework where the goal is to provide a good approximation to the posterior distribution in order to compute posterior mean estimates. Moreover, a majorization technique is employed to circumvent the difficulties raised by the intricate forms of the non-Gaussian likelihood and of the prior density. We demonstrate the potential of the proposed approach through comparisons with state-of-the-art techniques that are specifically tailored to signal recovery in the presence of mixed Poisson-Gaussian noise. Results show that the proposed approach is efficient and achieves performance comparable with other methods where the regularization parameter is manually tuned from the ground truth.

International audience; Subspace clustering assumes that the data is separable into separate subspaces. Such a simple assumption, does not always hold. We assume that, even if the raw data is not separable into subspaces, one can learn a representation (transform coefficients) such that the learnt representation is separable into subspaces. To achieve the intended goal, we embed subspace clustering techniques (locally linear manifold clustering, sparse subspace clustering and low rank representation) into transform learning. The entire formulation is jointly learnt; giving rise to a new class of methods called transformed subspace clustering (TSC). In order to account for non-linearity, kernelized extensions of TSC are also proposed. To test the performance of the proposed techniques, benchmarking is performed on image clustering and document clustering datasets. Comparison with state-of-the-art clustering techniques shows that our formulation improves upon them.

Underdetermined or ill-posed inverse problems require additional information for sound solutions with tractable optimization algorithms. Sparsity yields consequent heuristics to that matter, with numerous applications in signal restoration, image recovery, or machine learning. Since the $\ell _0$ count measure is barely tractable, many statistical or learning approaches have invested in computable proxies, such as the $\ell _1$ norm. However, the latter does not exhibit the desirable property of scale invariance for sparse data. Extending the SOOT Euclidean/Taxicab $\ell _1$ -over- $\ell _2$ norm-ratio initially introduced for blind deconvolution, we propose SPOQ, a family of smoothed (approximately) scale-invariant penalty functions. It consists of a Lipschitz-differentiable surrogate for $\ell _p$ -over- $\ell _q$ quasi-norm/norm ratios with $p\in \,]0,2[$ and $q\geq 2$ . This surrogate is embedded into a novel majorize-minimize trust-region approach, generalizing the variable metric forward-backward algorithm. For naturally sparse mass-spectrometry signals, we show that SPOQ significantly outperforms $\ell _0$ , $\ell _1$ , Cauchy, Welsch, SCAD and $\mathrm{CEL}0$ penalties on several performance measures. Guidelines on SPOQ hyperparameters tuning are also provided, suggesting simple data-driven choices.

International audience; The proximal gradient algorithm is a popular iterative algorithm to deal with penalized least-squares minimization problems. Its simplicity and versatility allow one to embed non-smooth penalties efficiently. In the context of inverse problems arising in signal and image processing, a major concern lies in the computational burden when implementing minimization algorithms. For instance, in tomographic image reconstruction, a bottleneck is the cost for applying the forward linear operator and its adjoint. Consequently, it often happens that these operators are approximated numerically, so that the adjoint property is no longer fulfilled. In this paper, we focus on the proximal gradient algorithm stability properties when such an adjoint mismatch arises. By making use of tools from convex analysis and fixed point theory, we establish conditions under which the algorithm can still converge to a fixed point. We provide bounds on the error between this point and the solution to the minimization problem. We illustrate the applicability of our theoretical results through numerical examples in the context of computed tomography.

International audience; Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters, which can be estimated through computationally expensive and time-consuming methods. In contrast, deep learning offers very generic and efficient architectures, at the expense of explainability, since it is often used as a black-box, without any fine control over its output. Deep unfolding provides a convenient approach to combine variational-based and deep learning approaches. Starting from a variational formulation for image restoration, we develop iRestNet, a neural network architecture obtained by unfolding a proximal interior point algorithm. Hard constraints, encoding desirable properties for the restored image, are incorporated into the network thanks to a logarithmic barrier, while the barrier parameter, the stepsize, and the penalization weight are learned by the network. We derive explicit expressions for the gradient of the proximity operator for various choices of constraints, which allows training iRestNet with gradient descent and backpropagation. In addition, we provide theoretical results regarding the stability of the network for a common inverse problem example. Numerical experiments on image deblurring problems show that the proposed approach compares favorably with both state-of-the-art variational and machine learning methods in terms of image quality.

This work proposes a supervised multi-channel time-series learning framework for financial stock trading. Although many deep learning models have recently been proposed in this domain, most of them treat the stock trading time-series data as 2-D image data, whereas its true nature is 1-D time-series data. Since the stock trading systems are multi-channel data, many existing techniques treating them as 1-D time-series data are not suggestive of any technique to effectively fusion the information carried by the multiple channels. To contribute towards both of these shortcomings, we propose an end-to-end supervised learning framework inspired by the previously established (unsupervised) convolution transform learning framework. Our approach consists of processing the data channels through separate 1-D convolution layers, then fusing the outputs with a series of fully-connected layers, and finally applying a softmax classification layer. The peculiarity of our framework - SuperDeConFuse (SDCF), is that we remove the nonlinear activation located between the multi-channel convolution layers and the fully-connected layers, as well as the one located between the latter and the output layer. We compensate for this removal by introducing a suitable regularization on the aforementioned layer outputs and filters during the training phase. Specifically, we apply a logarithm determinant regularization on the layer filters to break symmetry and force diversity in the learnt transforms, whereas we enforce the non-negativity constraint on the layer outputs to mitigate the issue of dead neurons. This results in the effective learning of a richer set of features and filters with respect to a standard convolutional neural network. Numerical experiments confirm that the proposed model yields considerably better results than state-of-the-art deep learning techniques for real-world problem of stock trading., Comment: Accepted in Elsevier Expert Systems With Applications 2020

International audience; Purpose: The second edition of the artificial intelligence (AI) data challenge was organized by the French Society of Radiology with the aim to: (i), work on relevant public health issues; (ii), build large, mul-ticentre, high quality databases; and (iii), include three-dimensional (3D) information and prognostic questions. Materials and methods: Relevant clinical questions were proposed by French subspecialty colleges of radiology. Their feasibility was assessed by experts in the field of AI. A dedicated platform was set up for inclusion centers to safely upload their anonymized examinations in compliance with general data protection regulation. The quality of the database was checked by experts weekly with annotations performed by radiologists. Multidisciplinary teams competed between September 11 th and October 13 th 2019. Results: Three questions were selected using different imaging and evaluation modalities, including: pulmonary nodule detection and classification from 3D computed tomography (CT), prediction of expanded disability status scale in multiple sclerosis using 3D magnetic resonance imaging (MRI) and segmentation of muscular surface for sarcopenia estimation from two-dimensional CT. A total of 4347 examinations were gathered of which only 6% were excluded. Three independent databases from 24 individual centers were created. A total of 143 participants were split into 20 multidisciplinary teams. Conclusion: Three data challenges with over 1200 general data protection regulation compliant CT or MRI examinations each were organized. Future challenges should be made with more complex situations combining histopathological or genetic information to resemble real life situations faced by radiologists in routine practice.

Latent factor models have been used widely in collaborative filtering based recommender systems. In recent years, deep learning has been successful in solving a wide variety of machine learning problems. Motivated by the success of deep learning, we propose a deeper version of latent factor model. Experiments on benchmark datasets shows that our proposed technique significantly outperforms all state-of-the-art collaborative filtering techniques., Comment: This is an initial draft of the accepted paper at Elsevier Signal Processing

International audience; Joint deconvolution and segmentation of ultrasound images is a challenging problem in medical imaging. By adopt- ing a hierarchical Bayesian model, we propose an accelerated Markov chain Monte Carlo scheme where the tissue reflectivity function is sampled thanks to a recently introduced proximal unadjusted Langevin algorithm. This new approach is combined with a forward-backward step and a preconditioning strategy to accelerate the convergence, and with a method based on the majorization-minimization principle to solve the inner noncon- vex minimization problems. As demonstrated in numerical ex- periments conducted on both simulated and in vivo ultrasound images, the proposed method provides high-quality restoration and segmentation results and is up to six times faster than an existing Hamiltonian Monte Carlo method.

International audience; Image restoration is frequently addressed by resorting to variational methods which account for some prior knowledge about the solution. The success of these methods, however, heavily depends on the estimation of a set of hyperparameters. Deep learning architectures are, on the contrary, very generic and efficient, but they offer limited control over their output. In this paper, we present iRestNet, a neural network architecture which combines the benefits of both approaches. iRestNet is obtained by unfolding a proximal interior point algorithm. This enables enforcing hard constraints on the pixel range of the restored image thanks to a logarithmic barrier strategy, without requiring any parameter setting. Explicit expressions for the involved proximity operator, and its differential, are derived, which allows training iRestNet with gradient descent and backpropagation. Numerical experiments on image deblurring show that the proposed approach provides good image quality results compared to state-of-the-art variational and machine learning methods.

International audience; Recently, methods based on Data Augmentation (DA) strategies have shown their efficiency for dealing with high-dimensional Gaussian sampling within Gibbs samplers compared to iterative-based sampling (e.g., Perturbation-Optimization). However, they are limited by the feasibility of the direct sampling of the auxiliary variable. This paper reviews DA sampling algorithms for Gaussian sampling and proposes a DA method which is especially useful when direct sampling of the auxiliary variable is not straightforward from a computational viewpoint. Experiments in two vibration analysis applications show the good performance of the proposed algorithm.

International audience; Fitting Gaussian functions to empirical data is a crucial task in a variety of scientific applications, especially in image processing. However, most of the existing approaches for performing such fitting are restricted to two dimensions and they cannot be easily extended to higher dimensions. Moreover, they are usually based on alternating minimization schemes which benefit from few theoretical guarantees in the underlying nonconvex setting. In this paper , we provide a novel variational formulation of the multi-variate Gaussian fitting problem, which is applicable to any dimension and accounts for possible non-zero background and noise in the input data. The block multiconvexity of our objective function leads us to propose a proximal alternating method to minimize it in order to estimate the Gaus-sian shape parameters. The resulting FIGARO algorithm is shown to converge to a critical point under mild assumptions. The algorithm shows a good robustness when tested on synthetic datasets. To demonstrate the versatility of FIGARO, we also illustrate its excellent performance in the fitting of the Point Spread Functions of experimental raw data from a two-photon fluorescence microscope.

International audience; Purpose : New-onset pituitary gland lesions are observed in up to 18% of cancer patients undergoing treatment with immune checkpoint blockers (ICB). We aimed to develop and validate an imaging-based decision-making algorithm for use by the clinician that helps differentiate pituitary metastasis (PM) from ICB-induced autoimmune hypophysitis (HP). Materials and methods : A systematic search was performed in the MEDLINE and EMBASE databases up to October 2018 to identify studies concerning PM and HP in patients treated with cytotoxic T–lymphocyte–associated protein 4 and programmed cell death (ligand) 1. The reference standard for diagnosis was confirmation by histology or response on follow-up imaging. Patients from included studies were randomly assigned to the training set or the validation set. Using machine learning (random forest tree algorithm) with the most-described six imaging and three clinical features, a multivariable prediction model (the signature) was developed and validated for diagnosing PM. Signature performance was evaluated using area under a receiver operating characteristic curves (AUCs).Results : Out of 3174 screened articles, 65 were included totalising 122 patients (HP: 60 pts, PM: 62 pts). Complete radiological data were available in 82 pts (Training: 62 pts, Validation: 20 pts). The signature reached an AUC = 0.91 (0.82, 1.00), P < 10−8 in the training set and AUC = 0.94 (0.80, 1.00), P = 0.001 in the validation set. The signature predicted PM in lesions either ≥ 2 cm in size or < 2 cm if associated with heterogeneous contrast enhancement and cavernous extension.Conclusion : An image-based signature was developed with machine learning and validated for differentiating PM from HP. This tool could be used by clinicians for enhanced decision-making in cancer patients undergoing ICB treatment with new-onset, concerning lesions of the pituitary gland.

International audience; In drug target interaction (DTI) the interactions of some (a subset) drugs on some (a subset) targets are known. The goal is to predict the interactions of all drugs on all targets. One approach is to formulate this as a matrix completion problem, where the matrix of interactions having drugs along the rows and targets along the columns is partially filled. So far standard matrix completion approaches such as nuclear norm minimization and matrix factorization have been used to address the problem. In this work, we propose a deep matrix factorization approach to improve the prediction results. Experiments have been performed on benchmark databases and comparison carried out with some state-of-the-art algorithms. Empirically our proposed deep method, outperforms all the techniques compared against.

International audience; Population Monte Carlo (PMC) algorithms are a family of adaptive importance sampling (AIS) methods for approximating integrals in Bayesian inference. In this paper, we propose a novel PMC algorithm that combines recent advances in the AIS and the optimization literatures. In such a way, the proposal densities are adapted according to the past weighted samples via a local resampling that preserves the diversity, but we also exploit the geometry of the targeted distribution. A scaled Langevin strategy with Newton-based scaling metric is retained for this purpose, allowing to adapt jointly the means and the covariances of the proposals, without needing to tune any extra parameter. The performance of the proposed technique is clearly superior in two numerical examples at the cost of a reasonable computational complexity increment.

International audience; Reducing acquisition time is a crucial issue in MRI especially in the high resolution context. Compressed sensing has faced this problem for a decade. However, to maintain a high signal-to-noise ratio (SNR), CS must be combined with parallel imaging. This leads to harder reconstruction problems that usually require the knowledge of coil sensitivity profiles. In this work, we introduce a calibra-tionless image reconstruction approach that no longer requires this knowledge. The originality of this work lies in using for reconstruction a group sparsity structure (called OSCAR) across channels that handles SNR inhomogeneities across receivers. We compare this reconstruction with other calibrationless approaches based on group-LASSO and its sparse variation as well as with the auto-calibrated method called 1-ESPIRiT. We demonstrate that OSCAR outper-forms its competitors and provides similar results to 1-ESPIRiT. This suggests that the sensitivity maps are no longer required to perform combined CS and parallel imaging reconstruction.

Le glioblastome est le type de tumeur cerebrale primaire la plus agressive chez l’adulte avec un mauvais pronostic. L’anti angiogenique avec le bevacizumab, est actuellement le traitement le plus utilise pour la prise en charge des glioblastomes recurrents. Cependant, la reponse therapeutique reste tres heterogene selon les patients. L’objectif de l’etude porte sur l’identification de biomarqueur pouvant predire la survie chez des patients atteints de glioblastome et ayant recu le traitement au bevacizumab en tant que traitement de seconde ligne. A partir d’une cohorte de 158 patients, nous avons utilise des donnees radiomiques issues de la segmentation des tumeurs, avant debut du traitement, sur des images IRM T2 Flair et avec injection de gadolinium, ainsi que des donnees cliniques. Plusieurs techniques de machine learning ont ete testees afin de predire la survie des patients, ainsi que pour la classification selon 3 differents modeles binaire : survie a plus ou moins de 9 mois, plus ou moins de 12 mois et plus ou moins de 15 mois. Resultats Le meilleur resultat pour la regression a ete obtenu par un algorithme de gradient boosting avec un C-index de 0,61 sur le test (0,83 sur le train). L’AUC obtenu par une regression logistique sur la classification a plus ou moins 9 mois etait de 0,77 (0,81 sur le train), 0,72 (0,77) pour plus ou moins 12 mois et 0,72 (0,72) pour plus ou moins 15 moins. Les scores sur la regression et la classification atteinte ici semble montrer le potentiel des radiomiques combines avec des donnees diagnostiques sur la prediction de survie des patients atteints de glioblastomes et traites au bevacizumab. De plus, la recurrence de certains parametres parmi les modeles suggere la possibilite d’etablir une signature radiomique et diagnostique ( Fig. 1 , Fig. 2 ).

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often estimated from training sets, which may lead to poor out-of-sample performance. In this work, we bring new insights in this problem by using the framework which has been developed in quantitative finance for risk measures. We show that the original min-max problem can be recast as a convex minimization problem under suitable assumptions. We discuss several important examples of robust formulations, in particular by defining ambiguity sets based on \begin{document}$ \varphi $\end{document} -divergences and the Wasserstein metric. We also propose an efficient algorithm for solving the corresponding convex optimization problems involving complex convex constraints. Through simulation examples, we demonstrate that this algorithm scales well on real data sets.

International audience; This work proposes a new representation learning technique called convolutional transform learning. In standard transform learning, a dense basis is learned that analyses the image to generate the representation from the image. Here, we learn a set of independent convolutional filters that operate on the images to produce representations (one corresponding to each filter). The major advantage of our proposed approach is that it is completely unsupervised; unlike CNNs where labeled images are required for training. Moreover, it relies on a well-sounded minimization technique with established convergence guarantees. We have compared the proposed method with dictionary learning and transform learning on standard image classification datasets. Results show that our method improves over the rest by a considerable margin.

In this paper, we propose a probabilistic optimization method, named probabilistic incremental proximal gradient (PIPG) method, by developing a probabilistic interpretation of the incremental proximal gradient algorithm. We explicitly model the update rules of the incremental proximal gradient method and develop a systematic approach to propagate the uncertainty of the solution estimate over iterations. The PIPG algorithm takes the form of Bayesian filtering updates for a state-space model constructed by using the cost function. Our framework makes it possible to utilize well-known exact or approximate Bayesian filters, such as Kalman or extended Kalman filters, to solve large-scale regularized optimization problems., 5 pages, includes an extra numerical experiment

International audience; The dimension and the complexity of inference problems have dramatically increased in statistical signal processing. It thus becomes mandatory to design improved proposal schemes in Metropolis-Hastings algorithms, providing large proposal transitions that are accepted with high probability. The proposal density should ideally provide an accurate approximation of the target density with a low computational cost. In this paper, we derive a novel Metropolis-Hastings proposal, inspired from Langevin dynamics, where the drift term is preconditioned by an adaptive matrix constructed through a Majorization-Minimization strategy. We propose several variants of low-complexity curvature metrics applicable to large scale problems. We demonstrate the geometric ergodicity of the resulting chain for the class of super-exponential distributions. The proposed method is shown to exhibit a good performance in two signal recovery examples.

International audience; In this paper, we present a new distributed algorithm for minimizing a sum of non-necessarily differentiable convex functions composed with arbitrary linear operators. The overall cost function is assumed strongly convex. Each involved function is associated with a node of a hypergraph having the ability to communicate with neighboring nodes sharing the same hyperedge. Our algorithm relies on a primal-dual splitting strategy with established convergence guarantees. We show how it can be efficiently implemented to take full advantage of a multicore architecture. The good numerical performance of the proposed approach is illustrated in a problem of video sequence denoising, where a significant speedup is achieved.

International audience; The geometry-texture decomposition of images produced by X-Ray Computed Tomography (CT) is a challenging inverse problem which is usually performed in two steps: reconstruction and decomposition. Decomposition can be used for instance to produce an approximate segmentation of the image, but this one can be compromised by artifacts and noise arising from the acquisition and reconstruction processes. We propose a geometry-texture decomposition based on a TV-Laplacian model, well-suited for segmentation and edge detection. The corresponding joint reconstruction and decomposition task from CT data is then formulated as a convex constrained minimization problem. We use our recently introduced proximal interior point method to solve this inverse problem in a reliable manner. Numerical experiments on realistic images of material samples illustrate the practical efficiency of the proposed approach. Our algorithm indeed compares favorably with a state-of-the-art method.

Multiphoton microscopy (MPM) is a relatively recent tool involved in biological imaging. Its resolution is somewhat limited due to its physical principles, resulting experimentally in a deteriorated planar resolution of about few tenths of micrometers and a reduced axial resolution of a few micrometers. In this communication, we present a numerical approach taking the form of a processing pipeline for image restoration going from the raw images of 0.2 μm diameter fluorescent microbeads to the reconstructed ones. The strategy consists in estimating 3D Point-Spread Function (PSF) shapes in automatically selected volumes of interest, considering a 3D Gaussian profile of intensity. An automatic crop procedure selects areas of a few dozens of individual beads. Our algorithms, based on a variational approach for multivariate Gaussian fitting, allows us to identify evolutions of PSF dimensions along the 3 dimensions of the volume. A proximal alternating optimization method called FIGARO is employed to minimize a cost function serving to quantify the optimality of the process. The difficulty overcome thanks to this novel variational approach for multivariate Gaussian fitting lies in its ability to estimate parametrically Gaussian shapes in a 3D space, which leads to accurate models of the PSF. Thanks to our technique, the PSF measurements show a dimension in (X,Y,Z) of (0.21, 0.27, 1.49) μm. It is the first time to our knowledge that such a direct 3D measurement has been made possible. This process paves the way to a significant improvement of the resolution, perfectly suited to MPM.

Interior point methods have been known for decades to be useful for the resolution of small to medium size constrained optimization problems. These approaches have the benefit of ensuring feasibility of the iterates through a logarithmic barrier. We propose to incorporate a proximal forward-backward step in the resolution of the barrier subproblem to account for non-necessarily differentiable terms arising in the objective function. The combination of this scheme with a novel line-search strategy gives rise to the so-called Proximal Interior Point Algorithm (PIPA) suitable for the minimization of the sum of a smooth convex function and a non-smooth convex one under general convex constraints. The convergence of PIPA is secured under mild assumptions. As demonstrated by numerical experiments carried out on a large-scale hyperspectral image unmixing application, the proposed method outperforms the state-of-the-art.

The l1/l2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the blind context. However, the l1/l2 function raises some difficulties when solving the nonconvex and nonsmooth minimization problems resulting from the use of such a penalty term in current restoration methods. In this paper, we propose a new penalty based on a smooth approximation to the l1/l2 function. In addition, we develop a proximal-based algorithm to solve variational problems involving this function and we derive theoretical convergence results. We demonstrate the effectiveness of our method through a comparison with a recent alternating optimization strategy dealing with the exact l1/l2 term, on an application to seismic data blind deconvolution.

International audience; The Poisson-Gaussian model can accurately describe the noise present in a number of imaging systems. However most existing restoration methods rely on approximations of the Poisson-Gaussian noise statistics. We propose a convex optimization strategy for the reconstruction of images degraded by a linear operator and corrupted with a mixed Poisson-Gaussian noise. The originality of our approach consists of considering the exact, mixed continuous-discrete model corresponding to the data statistics. After establishing the Lipschitz differentiability and convexity of the Poisson-Gaussian neg-log-likelihood, we derive a primal-dual iterative scheme for minimizing the associated penalized criterion. The proposed method is applicable to a large choice of convex penalty terms. The robustness of our scheme allows us to handle computational difficulties due to infinite sums arising from the computation of the gradient of the criterion. We propose finite bounds for these sums, that are dependent on the current image estimate, and thus adapted to each iteration of our algorithm. The proposed approach is validated on image restoration examples. Then, the exact data fidelity term is used as a reference for studying some of its various approximations. We show that in a variational framework the Shifted Poisson and Exponential approximations lead to very good restoration results.

International audience; Hyperspectral data unmixing aims at identifying the components (endmembers) of an observed surface and at determining their fractional abundances inside each pixel area. Assuming that the spectral signatures of the surface components have been previously determined by an endmember extraction algorithm, or to be part of an available spectral library, the main problem is reduced to the estimation of the fractional abundances. For large hyperspectral image data sets, the estimation of the abundance maps requires the resolution of a large-scale optimization problem subject to linear constraints such as non-negativity and sum less or equal to one. This paper proposes a primal-dual interior-point optimization algorithm allowing a constrained least squares estimation approach. In comparison with existing methods, the proposed algorithm is more flexible since it can handle any linear equality and/or inequality constraint and has the advantage of a reduced computational cost. It also presents an algorithmic structure suitable for a parallel implementation on modern intensive computing devices such as Graphics Processing Units (GPU). The implementation issues are discussed and the applicability of the proposed approach is illustrated with the help of examples on synthetic and real hyperspectral data.

In this paper, we develop a novel second-order method for training feed-forward neural nets. At each iteration, we construct a quadratic approximation to the cost function in a low-dimensional subspace. We minimize this approximation inside a trust region through a two-stage procedure: first inside the embedded positive curvature subspace, followed by a gradient descent step. This approach leads to a fast objective function decay, prevents convergence to saddle points, and alleviates the need for manually tuning parameters. We show the good performance of the proposed algorithm on benchmark datasets., EUSIPCO 2017

International audience; This paper presents a fast approach for penalized least squares (LS) regression problems using a 2D Gaussian Markov random field (GMRF) prior. More precisely, the computation of the proximity operator of the LS criterion regularized by different GMRF potentials is formulated as solving a Sylvester-like matrix equation. By exploiting the structural properties of GMRFs, this matrix equation is solved column-wise in an analytical way. The proposed algorithm can be embedded into a wide range of proximal algorithms to solve LS regression problems including a convex penalty. Experiments carried out in the case of a constrained LS regression problem arising in a multichannel image processing application, provide evidence that an alternating direction method of multipliers performs quite efficiently in this context.

International audience; Optimization methods play a central role in the solution of a wide array of problems encountered in various application fields, such as signal and image processing. Especially when the problems are highly dimensional, proximal methods have shown their efficiency through their capability to deal with composite, possibly nonsmooth objective functions. The cornerstone of these approaches is the proximity operator, which has become a quite popular tool in optimization. In this work, we propose new dual forward-backward formulations for computing the proximity operator of a sum of convex functions involving linear operators. The proposed algorithms are accelerated thanks to the introduction of a block-coordinate strategy combined with a preconditioning technique. Numerical simulations emphasize the good performance of our approach for the problem of jointly deconvoluting and deinterlacing video sequences.

NMR is a tool of choice for the measure of diffusion coefficients of species in solution. The DOSY experiment, a 2D implementation of this measure, has proven to be particularly useful for the study of complex mixtures, molecular interactions, polymers, etc. However, DOSY data analysis requires to resort to inverse Laplace transform, in particular for polydisperse samples. This is a known difficult numerical task, for which we present here a novel approach. A new algorithm based on a splitting scheme and on the use of proximity operators is introduced. Used in conjunction with a Maximum Entropy and $\ell_1$ hybrid regularisation, this algorithm converges rapidly and produces results robust against experimental noise. This method has been called PALMA. It is able to reproduce faithfully monodisperse as well as polydisperse systems, and numerous simulated and experimental examples are presented. It has been implemented on the server http://palma.labo.igbmc.fr where users can have their datasets processed automatically., Comment: 23 pages, 9 figures revised version, with new examples

International audience; Various recent iterative optimization methods require to compute the proximity operator of a sum of functions.We address this problem by proposing a new distributed algorithm for a sum of non-necessarily smooth convex functionscomposed with arbitrary linear operators. In our approach, each function is associated with a node of a graph, whichcommunicates with its neighbors. Our algorithm relies on a primal-dual splitting strategy that avoids to invert any linearoperator, thus making it suitable for processing high-dimensional datasets. The proposed algorithm has a wide array of applicationsin signal/image processing and machine learning and its convergence is established.

The solution of many applied problems relies on finding the minimizer of a sum of smooth and/or nonsmooth convex functions possibly involving linear operators. In the last years, primal-dual methods have shown their efficiency to solve such minimization problems, their main advantage being their ability to deal with linear operators with no need to invert them. However, when the problem size becomes increasingly large, the implementation of these algorithms can be complicated, due to memory limitation issues. A simple way to overcome this difficulty consists of splitting the original numerous variables into blocks of smaller dimension, corresponding to the available memory, and to process them separately. In this paper we propose a random block-coordinate primal-dual algorithm, converging almost surely to a solution to the considered minimization problem. Moreover, an application to large-size 3D mesh denoising is provided to show the numerical efficiency of our method.

Inverse problems encountered in video processing often require to minimize criteria involving a high number of variables. Among available optimization techniques, proximal methods have shown their efficiency in solving large-scale possibly nonsmooth problems. When some of the proximity operators involved in these methods do not have closed form expressions, they may constitute a bottleneck in terms of computational complexity and memory requirements. In this paper, we address this problem and propose accelerated techniques for solving it. A new dual block-coordinate forward-backward algorithm computing the proximity operator of a sum of convex functions composed with linear operators is proposed and theoretically analyzed. The numerical performance of the approach is assessed through an application to deconvolution and super-resolution of interlaced video sequences.

International audience

Primal-dual proximal optimization methods have recently gained much interest for dealing with very large-scale data sets encoutered in many application fields such as machine learning, computer vision and inverse problems [1–3]. In this work, we propose a novel random block-coordinate version of such algorithms allowing us to solve a wide array of convex variational problems. One of the main advantages of the proposed algorithm is its ability to solve composite problems involving large-size matrices without requiring any inversion. In addition, the almost sure convergence to an optimal solution to the problem is guaranteed. We illustrate the good performance of our method on a mesh denoising application.

International audience; Primal-dual interior-point methods are used in image processing to solve inversion problems that can be reduced to constrained convex minimization. Such iterative methods require the solution of a sequence of positive definite symmetric linear systems which are used to derive descent directions. This approach is very consuming in terms of computing time and memory usage for large-scale problems, unless the normal matrices have a specific structure. This is the case in the spectral unmixing problem where the normal matrices are block-diagonal when no spatial regularization is considered. Here, we consider the spatially regularized case and we propose to tackle the linear system solving using a majorization-minimization (MM) approach based on separable quadratic majorant functions. The resulting systems have the same structure as in the non-regularized case and can thereby be solved efficiently. The interior-point algorithm is speeded-up while remaining convergent. An example of spectral unmixing is proposed to illustrate the efficiency of this approach

International audience; Many inverse problems require to minimize a criterion being the sum of a non necessarily smooth function and a Lipschitz differentiable function. Such an optimization problem can be solved with the Forward-Backward algorithm which can be accelerated thanks to the use of variable metrics derived from the Majorize-Minimize principle. The convergence of this approach is guaranteed provided that the criterion satisfies some additional technical conditions. Combining this method with an alternating minimization strategy will be shown to allow us to address a broad class of optimization problems involving large-size signals. An application example to a nonconvex spectral unmixing problem will be presented.

Complex-valued data play a prominent role in a number of signal and image processing applications. The aim of this paper is to establish some theoretical results concerning the Cramer-Rao bound for estimating a sparse complex-valued vector. Instead of considering a countable dictionary of vectors, we address the more challenging case of an uncountable set of vectors parameterized by a real variable. We also present a proximal forward-backward algorithm to minimize an l 0 penalized cost, which allows us to approach the derived bounds. These results are illustrated on a spectrum analysis problem in the case of irregularly sampled observations.

Complex-valued data are encountered in many application areas of signal and image processing. In the context of the optimization of functions of real variables, subspace algorithms have recently attracted much interest, owing to their efficiency for solving large-size problems while simultaneously offering theoretical convergence guarantees. The goal of this paper is to show how some of these methods can be successfully extended to the complex case. More precisely, we investigate the properties of the proposed complex-valued Majorize-Minimize Memory Gradient (3MG) algorithm. Important practical applications of these results arise in inverse problems. Here, we focus on image reconstruction in Parallel Magnetic Resonance Imaging (PMRI). The linear operator involved in the observation model then includes a subsampling operator over the k-space (2D Fourier domain) the choice of which is analyzed through our numerical results. In addition, sensitivity matrices associated with the multiple channel coils come into play. Comparisons with existing optimization methods confirm the better performance of the proposed algorithm. HighlightsAn extension of the Majorize-Minimize Memory Gradient algorithm for minimizing functions of complex variables is proposed.The convergence of the algorithm is proved under weak assumptions.A novel application of the algorithm to parallel Magnetic Resonance Imaging reconstruction is proposed.Through simulations on real data, the algorithm is shown to outperform recent optimization strategies in terms of convergence speed.The algorithm can handle various subsampling schemes, both convex and nonconvex penalization functions and different possibly redundant frame representations.

International audience; In multichannel imaging, several observations of the same scene acquired in different spectral ranges are available. Very often, the spectral components are degraded by a blur modelled by a linear operator and an additive noise. In this paper, we address the problem of recovering the image components in a wavelet domain by adopting a variational approach. Our contribution is twofold. First, an appropriate multivariate penalty function is derived from a novel joint prior model of the probability distribution of the wavelet coefficients located at the same spatial position in a given subband through all the channels. Secondly, we address the challenging issue of computing the Maximum A Posteriori estimate by using a Majorize-Minimize optimization strategy. Simulation tests carried out on multispectral satellite images show that the proposed method outperforms conventional techniques.

The estimation of abundance maps in hyperspectral imaging requires the resolution of an optimization problem under nonnegativity and sum to one constraints. Assuming that the spectral signatures of the image components have been previously determined by an endmember extraction algorithm, we propose here a primal-dual interior point algorithm for the estimation of their fractional abundances. In comparison with the reference method FCLS, our algorithm has the advantage of a reduced computational cost, especially in the context of large scale images and allows to deal with a penalized criterion favoring the spatial smoothness of abundance maps. The performances of the proposed approach are discussed with the help of synthetic and real examples.

International audience; This paper proposes accelerated subspace optimization methods in the context of image restoration. Subspace optimization methods belong to the class of iterative descent algorithms for unconstrained optimization. At each iteration of such methods, a stepsize vector allowing the best combination of several search directions is computed through a multidimensional search. It is usually obtained by an inner iterative second-order method ruled by a stopping criterion that guarantees the convergence of the outer algorithm. As an alternative, we propose an original multidimensional search strategy based on the majorize-minimize principle. It leads to a closed-form stepsize formula that ensures the convergence of the subspace algorithm whatever the number of inner iterations. The practical efficiency of the proposed scheme is illustrated in the context of edge-preserving image restoration.

National audience; Cet article s'intéresse au développement d'algorithmes itératifs pour la reconstruction d'images. La particularité de ces problèmes réside dans la taille élevée des images et la quantité importante de données générée par le processus de mesure. Outre le fait de surmonter la difficulté liée à la grande taille du problème, les algorithmes proposés se fondent sur des résultats de convergence théoriquement établis. Nous illustrons ces développements à l'aide de trois modalités d'imagerie distinctes : la tomographie par émission de positrons (TEP), l'imagerie par résonance magnétiques nucléaire (IRM) parallèle et la résonance magnétique nucléaire bidimentionnelle (RMN 2D).