Quaternionic Sparse Approximation

ISBN 978-0-8176-4267-9International audienceIn this paper, we introduce a new processing procedure for quaternionic signals through consideration of the well-known orthogonal matching pursuit (OMP), which provides sparse approximation. We present a quaternionic extension, the quaternionic OMP, that can be used to process a right-multiplication linear combination of quaternionic signals. As validation, this quaternionic OMP is applied to simulated data. Deconvolution is carried out and presented here with a new spikegram that is designed for visualization of quaternionic coefficients, and finally this is compared to multivariate OMP

Decomposition and dictionary learning for 3D trajectories

International audienceA new model for describing a three-dimensional (3D) trajectory is proposed in this paper. The studied trajectory is viewed as a linear combination of rotatable 3D patterns. The resulting model is thus 3D rotation invariant (3DRI). Moreover, the temporal patterns are considered as shift-invariant. This paper is divided into two parts based on this model. On the one hand, the 3DRI decomposition estimates the active patterns, their coefficients, their rotations and their shift parameters. Based on sparse approximation, this is carried out by two non-convex optimizations: 3DRI matching pursuit (3DRI-MP) and 3DRI orthogonal matching pursuit (3DRI-OMP). On the other hand, a 3DRI learning method learns the characteristic patterns of a database through a 3DRI dictionary learning algorithm (3DRI-DLA). The proposed algorithms are first applied to simulation data to evaluate their performances and to compare them to other algorithms. Then, they are applied to real motion data of cued speech, to learn the 3D trajectory patterns characteristic of this gestural language

Color Sparse Representations for Image Processing: Review, Models, and Prospects

International audienceSparse representations have been extended to deal with color images composed of three channels. A review of dictionary-learning-based sparse representations for color images is made here, detailing the differences between the models, and comparing their results on real data and simulated data. These models are considered in a unifying framework that is based on the degrees of freedom of the linear filtering/transformation of the color channels. Moreover, this allows it to be shown that the scalar quaternionic linear model is equivalent to constrained matrix-based color filtering, which highlights the filtering implicitly applied through this model. Based on this reformulation, the new color filtering model is introduced, using unconstrained filters. In this model, spatial morphologies of color images are encoded by atoms, and colors are encoded by color filters. Color variability is no longer captured in increasing the dictionary size, but with color filters, this gives an efficient color representation

About QLMS Derivations

International audienceIn this letter, a review of the quaternionic least mean squares (QLMS) algorithm is proposed. Three versions coming from three derivation ways exist: the original QLMS based on component wise gradients, the HR-QLMS based on a quaternion gradient operator and iQLMS based on an involutions-gradient. Noting and investigating the differences between the three QLMS formulations, we show that the original QLMS suffers from a mistake in the derivation calculus. Thus, we propose to derive rigorously the criterion following the first way, giving the correct version of QLMS. A comparison with the other QLMS versions validates these results on simulated data

A framework for the comparison of different EEG acquisition solutions

The purpose of this work is to propose a framework for the benchmarking of EEG amplifiers, headsets, and electrodes providing objective recommendation for a given application. The framework covers: data collection paradigm, data analysis, and statistical framework. To illustrate, data was collected from 12 different devices totaling up to 6 subjects per device. Two data acquisition protocols were implemented: a resting-state protocol eyes-open (EO) and eyes-closed (EC), and an Auditory Evoked Potential (AEP) protocol. Signal-to-noise ratio (SNR) on alpha band (EO/EC) and Event Related Potential (ERP) were extracted as objective quantification of physiologically meaningful information. Then, visual representation, univariate statistical analysis, and multivariate model were performed to increase results interpretability. Objective criteria show that the spectral SNR in alpha does not provide much discrimination between systems, suggesting that the acquisition quality might not be of primary importance for spectral and specifically alpha-based applications. On the contrary, AEP SNR proved much more variable stressing the importance of the acquisition setting for ERP experiments. The multivariate analysis identified some individuals and some systems as independent statistically significant contributors to the SNR. It highlights the importance of inter-individual differences in neurophysiological experiments (sample size) and suggests some device might objectively be superior to others when it comes to ERP recordings. However, the illustration of the proposed benchmarking framework suffers from severe limitations including small sample size and sound card jitter in the auditory stimulations. While these limitations hinders a definite ranking of the evaluated hardware, we believe the proposed benchmarking framework to be a modest yet valuable contribution to the field

Comparaison de descripteurs pour la classification de décompositions parcimonieuses invariantes par translation

National audienceNous étudions les descripteurs adaptés à la classification de décompositions parcimonieuses invariantes par translation. Nous comparons les différents descripteurs de l'état de l'art sur les mêmes données et avec le même classifieur, ce qui permet d'évaluer leurs efficacités et nous testons aussi leur robustesse à la translation. Grâce à un nouveau fenêtrage, une famille de nouveaux descripteurs est proposée, dépassant l'état de l'art tout en étant robuste à la translation

Preprocessing for classification of sparse data: application to trajectory recognition

International audienceOn one hand, sparse coding, which is widely used in signal processing, consists of representing signals as linear combinations of few elementary patterns selected from a dedicated dictionary. The output is a sparse vector containing few coding coefficients and is called sparse code. On the other hand, Multilayer Perceptron (MLP) is a neural network classification method that learns non linear borders between classes using labeled data examples. The MLP input data are vectors, usually normalized and preprocessed to minimize the inter-class correlation. This article acts as a link between sparse coding and MLP by converting sparse code into convenient vectors for MLP input. This original association assures in this way the classification of any sparse signals. Experimental results obtained by the whole process on trajectories data and comparisons to other methods show that this approach is efficient for signals classification

Apprentissage de Dictionnaires Multivariés et Décomposition Parcimonieuse Invariante par Translation et par Rotation 2D

National audienceThis article presents a new tool, Multivariate Dictionary Learning Algorithm, able to learn online the elementary structures associated to a multivariate signals set. Once learned, Multivariate Orthogonal Matching Pursuit codes sparsely all signals of this set. These methods are specified to the 2D rotation-invariant case which induces a small-sized kernels dictionary. Our methods are applied to 2D handwritten data to extract the characteristic patterns of this signals set.Cet article présente le Multivariate Dictionary Learning Algorithm qui apprend en ligne les structures élémentaires associées à un ensemble de signaux multivariés. Une fois apprises, le Multivariate Orthogonal Matching Pursuit décompose tous les signaux de cet ensemble avec parcimonie. Ces méthodes sont spécifiées dans le cas d'invariance par rotation qui produit un dictionnaire restreint de noyaux. Nos méthodes sont appliquées à des données d'écriture manuscrite, afin d'extraire les motifs caractéristiques de cette base de signaux

Shift & 2D Rotation Invariant Sparse Coding for Multivariate Signals

International audienceClassical dictionary learning algorithms (DLA) allow unicomponent signals to be processed. Due to our interest in two-dimensional (2D) motion signals, we wanted to mix the two components to provide rotation invariance. So, multicomponent frameworks are examined here. In contrast to the well-known multichannel framework, a multivariate framework is first introduced as a tool to easily solve our problem and to preserve the data structure. Within this multivariate framework, we then present sparse coding methods: multivariate orthogonal matching pursuit (M-OMP), which provides sparse approximation for multivariate signals, and multivariate DLA (M-DLA), which empirically learns the characteristic patterns (or features) that are associated to a multivariate signals set, and combines shift-invariance and online learning. Once the multivariate dictionary is learned, any signal of this considered set can be approximated sparsely. This multivariate framework is introduced to simply present the 2D rotation invariant (2DRI) case. By studying 2D motions that are acquired in bivariate real signals, we want the decompositions to be independent of the orientation of the movement execution in the 2D space. The methods are thus specified for the 2DRI case to be robust to any rotation: 2DRI-OMP and 2DRI-DLA. Shift and rotation invariant cases induce a compact learned dictionary and provide robust decomposition. As validation, our methods are applied to 2D handwritten data to extract the elementary features of this signals set, and to provide rotation invariant decomposition

Généralisation des micro-états EEG par apprentissage régularisé temporellement de dictionnaires topographiques

National audienceThe microstate model describes EEG signals as series of topographies remaining stable during several tens of milliseconds and associated to brain states. The proposed generalization in this paper is based on an overcomplete model allowing several states to be active simultaneously. A dictionary learning algorithm with a temporal regularization is proposed to extract these states. The representation effectiveness of both models is compared on artificial and real signals for the extraction of the evoked potential P300.Le modèle des micro-états décrit les signaux EEG par des suites de topographies associées à des états cérébraux demeurant stables durant quelques dizaines de millisecondes. La généralisation proposée dans cet article considère un modèle redondant autorisant plusieurs états à être actifs simultanément. Un apprentissage de dictionnaire régularisé temporellement est proposé afin d'extraire ces états. L'efficacité de représentation des deux modèles est comparée sur des signaux de synthèse ainsi que sur des signaux réels pour l'étude du potentiel évoqué P300