Social-sparsity brain decoders: faster spatial sparsity

Spatially-sparse predictors are good models for brain decoding: they give accurate predictions and their weight maps are interpretable as they focus on a small number of regions. However, the state of the art, based on total variation or graph-net, is computationally costly. Here we introduce sparsity in the local neighborhood of each voxel with social-sparsity, a structured shrinkage operator. We find that, on brain imaging classification problems, social-sparsity performs almost as well as total-variation models and better than graph-net, for a fraction of the computational cost. It also very clearly outlines predictive regions. We give details of the model and the algorithm.Comment: in Pattern Recognition in NeuroImaging, Jun 2016, Trento, Italy. 201

A priori par normes mixtes pour les problèmes inverses Application à la localisation de sources en M/EEG

National audienceOn s'intéresse aux problèmes inverses sous déterminés, et plus particulièrement à la localisation de sources en magnéto et électro- encéphalographie (M/EEG). Dans ces problèmes, bien que l'on ait à disposition un modèle physique de la diffusion (ou du “mélange”) des sources, le caractère très sous-déterminé des problèmes rend l'inversion très difficile. La nécessité de trouver des a priori forts et pertinent physiquement sur les sources est une des parties difficiles de ce problème.Dans ces problèmes, la parcimonie classique mesurée par une norme l1 n'est pas suffisante, et donne des résultats non réalistes. On propose ici de prendre en compte une parcimonie structurée grâce à l'utilisation de normes mixtes, notamment d'une norme mixte sur trois niveaux. La méthode est utilisée sur des signaux MEG issus d'expériences de stimulation somesthésique. Lorsqu'ils sont stimulés, les différents doigts de la main activent des régions distinctes du cortex sensoriel primaire. L'utilisation d'une norme mixte à trois niveaux permet d'injecter cet a priori dans le problème inverse et ainsi de retrouver la bonne organisation corticale des zones actives. Nous montrons également que les méthodes classiquement utilisées dans le domaine échouent dans cette tâche

Sparsity and persistence in time-frequency sound representations

13 pagesInternational audienceIt is a well known fact that the time-frequency domain is very well adapted for representing audio signals. The main two features of time-frequency representations of many classes of audio signals are sparsity (signals are generally well approximated using a small number of coefficients) and persistence (significant coefficients are not isolated, and tend to form clusters). This contribution presents signal approximation algorithms that exploit these properties, in the framework of hierarchical probabilistic models. Given a time-frequency frame (i.e. a Gabor frame, or a union of several Gabor frames or time-frequency bases), coefficients are first gathered into groups. A group of coefficients is then modeled as a random vector, whose distribution is governed by a hidden state associated with the group. Algorithms for parameter inference and hidden state estimation from analysis coefficients are described. The role of the chosen dictionary, and more particularly its structure, is also investigated. The proposed approach bears some resemblance with variational approaches previously proposed by the authors (in particular the variational approach exploiting mixed norms based regularization terms). In the framework of audio signal applications, the time-frequency frame under consideration is a union of two MDCT bases or two Gabor frames, in order to generate estimates for tonal and transient layers. Groups corresponding to tonal (resp. transient) coefficients are constant frequency (resp. constant time) time-frequency coefficients of a frequency-selective (resp. time-selective) MDCT basis or Gabor frame

Sparse signal decomposition on hybrid dictionaries using musical priors

International audienceThis paper investigates the use of musical priors for sparse expansion of audio signals of music on overcomplete dictionaries taken from the union of two orthonormal bases. More specifically, chord information is used to build structured model that take into account dependencies between coefficients of the decomposition. Evaluation on various music signals shows that our approach provides results whose quality measured by the signal-to-noise ratio corresponds to state-of-the-art approaches, and shows that our model is relevant to represent audio signals of Western tonal music and opens new perspectives

Improving M/EEG source localization with an inter-condition sparse prior

International audienceThe inverse problem with distributed dipoles models in M/EEG is strongly ill-posed requiring to set priors on the solution. Most common priors are based on a convenient $\ell_2$ norm. However such methods are known to smear the estimated distribution of cortical currents. In order to provide sparser solutions, other norms than $\ell_2$ have been proposed in the literature, but they often do not pass the test of real data. Here we propose to perform the inverse problem on multiple experimental conditions simultaneously and to constrain the corresponding active regions to be different, while preserving the robust $\ell_2$ prior over space and time. This approach is based on a mixed norm that sets a $\ell_1$ prior between conditions. The optimization is performed with an efficient iterative algorithm able to handle highly sampled distributed models. The method is evaluated on two synthetic datasets reproducing the organization of the primary somatosensory cortex (S1) and the primary visual cortex (V1), and validated with MEG somatosensory data

Décompositions parcimonieuses et persistantes de signaux multicanaux. Applications aux signaux MEEG.

International audienceOn considère le problème de la régression parcimonieuse de signaux multicanaux sur des repères temps-fréquences. Les signaux multicanaux sont décomposés sur un unique repère en utilisant des coefficients vectoriels (i.e. multi-canal). La parcimonie apparaît habituellement grâce à des approches type “basis pursuit denoising” : la régression s'effectue en minimisant une fonctionnel qui fait intervenir un terme d'attache aux données 2 , et une pénalité 1 sur les coefficients. Dans cette contribution, cette dernière est remplacée par une norme mixte, qui favorise la parcimonie à l'intérieur d'un canal et la persistance au travers les différents canaux (i.e. un coefficient donné est considéré “actif” dans un groupe de canaux assez large). On montre que l'optimisation des fonctionnels correspondantes se résout à l'aide d'algorithmes de seuillage généralisé itératif. On présente en plus des adaptations pour l'analyse et le débruitage de signaux EEG et MEG, où l'information topographique des canaux est prise en compte

Sparse and structured decomposition of audio signals on hybrid dictionaries using musical priors

International audienceThis paper investigates the use of musical priors for sparse expansion of audio signals of music, on an overcomplete dual-resolution dictionary taken from the union of two orthonormal bases that can describe both transient and tonal components of a music audio signal. More specifically, chord and metrical structure information are used to build a structured model that takes into account dependencies between coefficients of the decomposition, both for the tonal and for the transient layer. The denoising task application is used to provide a proof of concept of the proposed musical priors. Several configurations of the model are analyzed. Evaluation on monophonic and complex polyphonic excerpts of real music signals shows that the proposed approach provides results whose quality measured by the signal-to-noise ratio is competitive with state-of-the-art approaches, and more coherent with the semantic content of the signal. A detailed analysis of the model in terms of sparsity and in terms of interpretability of the representation is also provided, and shows that the model is capable of giving a relevant and legible representation of Western tonal music audio signals

Sparsity and persistence: mixed norms provide simple signal models with dependent coefficients

nombre de pages : 14International audienceSparse regression often uses $\ell_p$ norm priors (with p<2). This paper demonstrates that the introduction of mixed-norms in such contexts allows one to go one step beyond in signal models, and promote some different, structured, forms of sparsity. It is shown that the particular case of $\ell_{1,2}$ and $\ell_{2,1}$ norms lead to new group shrinkage operators. Mixed norm priors are shown to be particularly efficient in a generalized basis pursuit denoising approach, and are also used in a context of morphological component analysis. A suitable version of the Block Coordinate Relaxation algorithm is derived for the latter. The group-shrinkage operators are then modified to overcome some limitations of the mixed-norms. The proposed group shrinkage operators are tested on simulated signals in specific situations, to illustrate their different behaviors. Results on real data are also used to illustrate the relevance of the approach

Hybrid model and structured sparsity for under-determined convolutive audio source separation

International audienceWe consider the problem of extracting the source signals from an under-determined convolutive mixture, assuming known filters. We start from its formulation as a minimization of a convex functional, combining a classical $\ell_2$ discrepancy term between the observed mixture and the one reconstructed from the estimated sources, and a sparse regularization term of source coefficients in a time-frequency domain. We then introduce a first kind of structure, using a hybrid model. Finally, we embed the previously introduced Windowed-Group-Lasso operator into the iterative thresholding/shrinkage algorithm, in order to take into account some structures inside each layers of time-frequency representations. Intensive numerical studies confirm the benefits of such an approach