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International audience; Current solutions for bacteria and viruses identification are based on time-consuming technics with complex preparation procedures. In the present work, we revealed label-free the presence of free viral particles and bacteria with a computational two-photon fluorescence (C-TPF) strategy. Six bacteria were tested: Escherichia coli, Staphylococcus epidermidis, Proteus vulgaris, Pseudomonas fluorescens, Bacillus subtilis and Clostridium perfringens. The two families of viral particles were the herpes virus with the cytomegalovirus (CMV, 300 nm of diameter) and the coronavirus with the SARS-CoV-2 (100 nm of diameter). The instrumental and computational pipeline FAMOUS optimized the produced 3D images. The origin of the fluorescence emission was discussed for bacteria regarding to their two-photon excitation spectra and attributed to the metabolic indicators (FAD and NADH). The optical and computational strategy constitute a new approach for imaging label-free viral particles and bacteria and paves the way to a new understanding of viral or bacterial ways of infection.

In this paper, we introduce a variational Bayesian algorithm (VBA) for image blind deconvolution. Our generic framework incorporates smoothness priors on the unknown blur/image and possible affine constraints (e.g., sum to one) on the blur kernel. One of our main contributions is the integration of VBA within a neural network paradigm, following an unrolling methodology. The proposed architecture is trained in a supervised fashion, which allows us to optimally set two key hyperparameters of the VBA model and lead to further improvements in terms of resulting visual quality. Various experiments involving grayscale/color images and diverse kernel shapes, are performed. The numerical examples illustrate the high performance of our approach when compared to state-of-the-art techniques based on optimization, Bayesian estimation, or deep learning., Comment: 13 pages

International audience; A wide class of problems involves the minimization of a coercive and differentiable function F on R N whose gradient cannot be evaluated in an exact manner. In such context, many existing convergence results from standard gradientbased optimization literature cannot be directly applied and robustness to errors in the gradient is not necessarily guaranteed. This work is dedicated to investigating the convergence of Majorization-Minimization (MM) schemes when stochastic errors affect the gradient terms. We introduce a general stochastic optimization framework, called SABRINA (StochAstic suBspace majoRIzation-miNimization Algorithm) that encompasses MM quadratic schemes possibly enhanced with a subspace acceleration strategy. New asymptotical results are built for the stochastic process generated by SABRINA. Two sets of numerical experiments in the field of machine learning and image processing are presented to support our theoretical results and illustrate the good performance of SABRINA with respect to state-of-the-art gradient-based stochastic optimization methods.

International audience; This work addresses the problem of hyperspectral image classification when the number of labeled samples is very small (few shot learning). Our work is based on the recently proposed framework of convolutional transform learning. In this work, we propose a semisupervised version of deep convolutional transform learning. We compare with four recent studies which are tailored for solving the few-shot learning problem in hyperspectral classification. Results show that our method can improve over the state-of-the-art.

International audience; Conventional Convolutional Neural Network (CNN) based clustering formulations are based on the encoder-decoder based framework, where the clustering loss is incorporated after the encoder network. The problem with this approach is that it requires training an additional decoder network; this, in turn, means learning additional weights which can lead to over-fitting in data constrained scenarios. This work introduces a Deep Convolutional Transform Learning (DCTL) based clustering framework. The advantage of our proposed formulation is that we do not require learning the additional decoder network. Therefore our formulation is less prone to over-fitting. Comparison with state-of-the-art deep learning based clustering solutions on benchmark image datasets shows that our proposed method improves over the rest in challenging scenarios where there are many clusters with limited samples.

International audience; State-space models (SSM) are central to describe time-varying complex systems in countless signal processing applications such as remote sensing, networks, biomedicine, and finance to name a few. Inference and prediction in SSMs are possible when the model parameters are known, which is rarely the case. The estimation of these parameters is crucial, not only for performing statistical analysis, but also for uncovering the underlying structure of complex phenomena. In this paper, we focus on the linear-Gaussian model, arguably the most celebrated SSM, and particularly in the challenging task of estimating the transition matrix that encodes the Markovian dependencies in the evolution of the multi-variate state. We introduce a novel perspective by relating this matrix to the adjacency matrix of a directed graph, also interpreted as the causal relationship among state dimensions in the Granger-causality sense. Under this perspective, we propose a new method called GraphEM based on the well sounded expectation-maximization (EM) methodology for inferring the transition matrix jointly with the smoothing/filtering of the observed data. We propose an advanced convex optimization solver relying on a consensus-based implementation of a proximal splitting strategy for solving the M-step. This approach enables an efficient and versatile processing of various sophisticated priors on the graph structure, such as parsimony constraints, while benefiting from convergence guarantees. We demonstrate the good performance and the interpretable results of GraphEM by means of two sets of numerical examples.

International audience; Optimization problems arising in signal and image processing involve an increasingly large number of variables. In addition to the curse of dimensionality, another difficulty to overcome is that the cost function usually reads as the sum of several loss/regularization terms, which are non-necessarily smooth and possibly composed with large-size linear operators. Proximal splitting approaches are fundamental tools to address such problems, with demonstrated efficiency in many applicative fields. In this paper, we present a new distributed algorithm for computing the proximity operator of a sum of non-necessarily smooth convex functions composed with arbitrary linear operators. Our algorithm relies on a primal-dual splitting strategy, and benefits from established convergence guaranties. Each involved function is associated with a node of a hypergraph, with the ability to communicate with neighboring nodes sharing the same hyperedge. Thanks to this structure, our method can be efficiently implemented on modern parallel computing architectures, distributing the computations on multiple nodes or machines, with controlled requirements for synchronization steps. Good numerical performance and scalability properties are demonstrated on a problem of video sequence denoising. Our code implemented in Julia is made available at \url{https://github.com/MarinENSTA/distributed_julia_denoising}.

International audience; In interventional radiology, 3D reconstruction of devices such as needles can increase the precision of procedures. Doing so with CBCT is time-consuming and increases the X-ray dose. Needles being sparse, a compressed-sensing reconstruction approach seems viable. In this paper, we thus investigate the benefits of directional total variation as an adequate prior for anisotropic devices. We introduce a decomposition method that allows several a priori directions to be considered at once as well as excludes the anatomical background that is not sparse. The capacity of the method is illustrated in simulations of limited-angle acquisitions. It allows good reconstruction of the needles from a small angular coverage, even if it cannot recover the anatomical background.

International audience; This article introduces a new Penalized Majorization-Minimization Subspace algorithm (P-MMS) for solving smooth, constrained optimization problems. In short, our approach consists of embedding a subspace algorithm in an inexact exterior penalty procedure. The subspace strategy, combined with a Majoration-Minimization step-size search, takes great advantage of the smoothness of the penalized cost function, while the penalty method allows to handle a wide range of constraints. The main drawback of exterior penalty approaches, namely ill-conditioning for large values of the penalty parameter, is overcome by using a trust-regionlike technique. The convergence of the resulting algorithm is analyzed. Numerical experiments carried out on two large-scale image recovery applications demonstrate that, compared with state-of-the-art algorithms, the proposed method performs well in terms of computational time.

Most optimization problems arising in imaging science involve high-dimensional linear operators and their adjoints. In the implementations of these operators, approximations may be introduced for various practical considerations (e.g., memory limitation, computational cost, convergence speed), leading to an adjoint mismatch. This occurs for the X-ray tomographic inverse problems found in Computed Tomography (CT), where the adjoint of the measurement operator (called projector) is often replaced by a surrogate operator. The resulting adjoint mismatch can jeopardize the convergence properties of iterative schemes used for image recovery. In this paper, we study the theoretical behavior of a panel of primal-dual proximal algorithms, which rely on forward-backward-(forward) splitting schemes, when an adjoint mismatch occurs. We analyze these algorithms by focusing on the resolution of possibly non-smooth convex penalized minimization problems in an infinite-dimensional setting. By using tools from fixed point theory, we show that they can solve monotone inclusions that go beyond minimization problems. Such findings indicate these algorithms can be seen as a generalization of classical primal-dual formulations. The applicability of our findings are also demonstrated through two numerical experiments in the context of CT image reconstruction.

International audience; In a medical use, ultrastructure of muscle is currently revealed by images of resected samples achieved thanks to Electron Microscopy (EM), requiring freezing and paraffin sections, with a set of histological, molecular and biochemical analyses. The resection, slicing and labelling steps cause an alteration of the phenotypic and volumetric information compared to their initial integrity. Starting from this statement, we have developed an original pipeline resting on the imbrication of an optical and computational strategy for imaging 3D biomedical structures without resorting to slicing, freezing and labelling steps. The assembly of myosin of a whole muscle is revealed thanks to the second harmonic generation (SHG) recorded with a multiphoton microscope, all along the entire 180 µm of thickness of the Extensor digitorum longus (EDL) of a wild mouse. During the SHG recording, the Point-Spread-Function (PSF) of the multiphoton microscope is recorded all along the imaging depth. This step highlights an axial broadening of the PSF while maintaining a constant planar PSF throughout the whole depth of the recordings. Then, a fitting algorithm estimated a mathematical model of the PSF, highlighting its variability into the whole image depth. Finally, a computational image restauration is led thanks to the fast image deblurring algorithm BD3MG accounting for the depth variant PSF. The non-stationary distortions all along the recorded image is employed thus correcting accurately the image distortion. The axial organization of the myosin is revealed for the first time, highlighting tubular organization of myosin into the myofibrils.

In this work, we propose an asynchronous Majorization-Minimization (MM) algorithm for solving large scale differentiable non-convex optimization problems. The proposed algorithm runs efficient MM memory gradient updates on blocks of coordinates, in a parallel and possibly asynchronous manner. We establish the convergence of the resulting sequence of iterates under mild assumptions. The performance of the algorithm is illustrated on the restoration of 3D images degraded by depth-variant 3D blur, arising in multiphoton microscopy. Significant computational time reduction, scalability and robustness are observed on synthetic data, when compared to state-of-the-art methods. Experiments on the restoration of real acquisitions of a muscle structure illustrate the qualitative performance of our approach and its practical applicability.

Nous présentons une nouvelle stratégie instrumentale et computationnelle appelée FAMOUS (pour fast algorithm for three-dimensional (3D) multiphoton microscopy of biomedical structures) basée sur une approche de microscopie multiphotonique assistée par calcul. Le but est l’amélioration visuelle des images d'échantillons biologiques épais offrant ainsi un nouveau point de vue sur les structures biologiques. L'approche de post-traitement repose sur un algorithme de restauration d'image régularisé, alimenté par une estimation 3D précise de la fonction d'étalement du point (Point Spread Function en anglais, PSF) de l'instrument sur toute la profondeur des structures. Cette dernière étape revient à mesurer, grâce à un algorithme d'ajustement de modèle avancé, les distorsions variant en profondeur de l'image résultant de la combinaison entre la contribution instrumentale et les hétérogénéités du milieu. Les performances du pipeline FAMOUS sont évaluées pour un milieu hétérogène constitué d’un muscle entier de souris. La génération de seconde harmonique (SHG), émise par l'assemblage des chaines de myosine du muscle est enregistrée. Les artefacts optiques issus de la chaîne d'acquisition incluant des hétérogénéités dans les 3 dimensions sont estimés avec les spécificités propres à l’échantillon puis retirées numériquement. Des images brutes et restaurées sur 5 µm de l’ultrastructure fine du muscle illustrent la robustesse du pipeline FAMOUS.

X-ray tomographic imaging, known as CT scanning, is available in clinical diagnostic routines thanks to the scanner. CT scanners allow precise differentiation of human tissues. However, these performances are obtained by technical choices incompatible with interventional use where the imaging system must not prevent access to the patient. Interventional X-ray C-arms have thus been equipped with an alternative tomographic technology: Cone-Beam Computed Tomography (CBCT). CBCT offers high spatial resolution for vessel imaging but remains limited for low contrast visualization, especially in the presence of injected contrast media and metallic therapeutic objects always under-sampled during the acquisition. Simplified acquisitions that are more dose-saving and faster, obtained by reducing the angular amplitude covered by the measurements or the number of measurements, are desirable but exacerbate under-sampling issues.The problem of reconstructing an anatomical region from projections can be efficiently solved by minimizing a cost function that compensates for under-sampling through a priori information about the region to be reconstructed. The minimization can be performed by an iterative algorithm built on a fixed point scheme. Four essential components in iterative methods are (i) the choice of the data fidelity, (ii) the regularization, and (iii) the discretization of the linear operators involved in these two terms (e.g., the projector and its adjoint, the backprojector), and (iv), the choice of the iterative algorithm. In practice, these methods are not used in a framework ensuring their convergence. In this thesis, we propose methodological contributions leading to iterative reconstruction methods that are theoretically convergent and applicable to acquisitions for interventional radiology.To achieve this objective, we extend the convergence conditions of a set of proximal algorithms when the projector adjoint is replaced by another operator, such as the voxel-driven backprojector often used in analytical reconstruction.One of the motivations for this change is the lack of management of sampling variations by the classical projector based on linear interpolation. The convergence of the algorithms is proved under conditions based on the cocoercivity of some linear operators.We then show that the modeling of sampling variations in an interpolation scheme allows for the derivation of an accurate discretization of the projector and the backprojector. Starting from an existing resampling algorithm for image enlargement, we design new projectors and backprojectors adapted to the cone-beam geometry with a flat detector, with different accuracy and speed trade-offs.Next, we propose an iterative method for reconstructing percutaneous needles from acquisitions with limited angular amplitude. We adopt a volume decomposition strategy associated with different directional regularization terms for each component and thus reconstruct an anatomical background on which the needles are superimposed.Finally, we propose a new regularized formulation for reconstructing an anatomical region from low angular density acquisitions. The combination of a robust data fidelity term with a total variation regularization limits artifacts from intense objects present in the projections but out of the reconstruction grid. To reach an accurate and fast reconstruction, we exploit recent advances in deep learning to propose an iterative unfolded algorithm allowing supervised learning of the problem parameters in a limited number of iterations. We show that a better reconstruction is obtained by learning the adjoint of the linear operators in the regularization term.; L'imagerie tomographique par rayons X, appelée tomodensitométrie, est accessible en routine clinique diagnostique grâce au scanner. Le scanner permet de différencier très précisément les tissus humains mais ses performances sont obtenues par des choix techniques incompatibles avec une utilisation interventionnelle où le système d'imagerie ne doit pas empêcher l'accès au patient. Les arceaux rayons X interventionnels ont donc été dotés d'une technologie tomographique alternative, le Cone-Beam Computed Tomography (CBCT). Le CBCT est très performant en résolution spatiale mais limité pour la visualisation des faibles contrastes, surtout en présence de produit de contraste et d'objets thérapeutiques métalliques toujours sous-échantillonnés lors de l'acquisition. Des acquisitions plus économes en dose et plus rapides, obtenues en réduisant l'amplitude angulaire des mesures ou le nombre de mesures, sont souhaitables mais aggravent les problèmes liés au sous-échantillonnage.La résolution du problème de reconstruction d'une région anatomique (ROI) à partir de projections s'effectue efficacement via la minimisation d'une fonction de coût compensant le sous-échantillonnage grâce à l'injection d'informations a priori sur la ROI. La minimisation peut être effectuée par un algorithme itératif lié à un schéma de point fixe. Quatre points essentiels sont (i) le choix du terme d'attache aux données, (ii) de la régularisation, (iii) la discrétisation des opérateurs linéaires présents dans ces deux termes et enfin, (iv) le choix de l'algorithme itératif. Souvent, ces méthodes ne sont pas utilisées dans un cadre assurant leur convergence. Dans cette thèse, nous proposons des méthodes de reconstruction itérative qui sont théoriquement convergentes et applicables à des acquisitions pour la radiologie interventionnelle.Pour répondre à cet objectif, nous étendons les conditions de convergence d'un ensemble d'algorithmes proximaux lorsque l'adjoint du projecteur est remplacé par un autre opérateur. Une des motivations pour ce changement est l'absence de gestion des variations d'échantillonnage par le projecteur classique basé sur l'interpolation linéaire.La convergence des algorithmes est prouvée sous des conditions s'appuyant sur le caractère cocoercif de certains opérateurs linéaires.Nous montrons ensuite qu'une modélisation des variations d'échantillonnage dans un schéma d'interpolation permet d'obtenir une discrétisation à la fois précise du projecteur et du rétroprojecteur. En partant d'un algorithme de rééchantillonnage proposé pour agrandir des images, nous concevons de nouveaux projecteurs et rétroprojecteurs adaptés à la géométrie conique avec un détecteur plan, avec différents compromis de précision et rapidité.Par ailleurs, nous proposons une méthode itérative pour la reconstruction d'aiguilles percutanées à partir d'acquisitions ayant une amplitude angulaire limitée. Nous adoptons une stratégie de décomposition du volume associés à différents termes de régularisation directionnelle pour chaque composante et ainsi reconstruire un fond anatomique sur lequel sont superposées les aiguilles.Enfin, nous proposons une nouvelle formulation régularisée pour la reconstruction d'une région anatomique à partir d'acquisitions ayant une faible densité angulaire. La combinaison d'un terme d'attache aux données robuste et d'une régularisation de variation totale permet de limiter les artéfacts issus d'objets intenses présents dans les projections mais en dehors de la grille de reconstruction. Pour permettre une reconstruction précise et rapide, nous exploitons les apports des techniques d'apprentissage pour proposer un algorithme itératif déroulé permettant un apprentissage supervisé des paramètres du problème en un nombre d'itération restreint. Nous montrons qu'une meilleure reconstruction est obtenue en apprenant l'adjoint des opérateurs linéaires présent dans le terme de régularisation.