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Personne# Adel Rahmoune

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Domaines de recherche associés (10)

Dictionnaire

thumb|upright=1.2|Dictionnaire en latin constitué de plusieurs volumes, œuvre d'Egidio Forcellini (1771). Un dictionnaire est un ouvrage de référence contenant un ensemble de mots d’une langue ou d’un domaine d’activité généralement présentés par ordre alphabétique et fournissant pour chacun une définition, une explication ou une correspondance (synonyme, antonyme, cooccurrence, traduction, étymologie). Le présent article concerne les dictionnaires unilingues qui décrivent ou normalisent une langue.

Matching pursuit

Matching pursuit (MP) is a sparse approximation algorithm which finds the "best matching" projections of multidimensional data onto the span of an over-complete (i.e., redundant) dictionary . The basic idea is to approximately represent a signal from Hilbert space as a weighted sum of finitely many functions (called atoms) taken from . An approximation with atoms has the form where is the th column of the matrix and is the scalar weighting factor (amplitude) for the atom . Normally, not every atom in will be used in this sum.

MP3

Le MPEG-1 Audio Layer ou MPEG-2 Audio Layer , plus connu sous son abréviation de MP3, est la spécification audio des standards MPEG-1 et MPEG-2. Il s'agit d'un format de compression audio avec perte permettant une réduction importante de la taille du flux de données audio, tout en conservant une qualité de restitution couramment jugée acceptable, donnant le choix du débit selon le compromis taille-qualité souhaité. C'est aussi l'un des formats de musique numérique les plus répandus. L'extension de nom de fichier est .

Publications associées (11)

Pascal Frossard, Pierre Vandergheynst, Adel Rahmoune

This paper presents a highly flexible video coding scheme (MP3D), based on the use of a redundant 3-D spatio-temporal dictionary of functions. Directionality and anisotropic scaling are key ingredients to the spatial components, that form a rich collection of 2-D visual primitives. The temporal component is tuned to capture most of the energy in the temporal signal evolution, along motion trajectories in the video sequences. The MP3D video coding scheme first computes motion trajectories, that are lossless entropy coded and sent as side information to the decoder. It then applies a spatio-temporal decomposition using an adaptive approximation algorithm based on Matching Pursuit (MP). Quantized coefficients and basis function parameters are entropy-coded in a embedded stream that is constructed to respect multiple rate constraints. The geometric properties of the 2-D primitive dictionary allows for flexible spatial resolution adaptation, so that the MP3D stream allows for decoding at multiple rate and spatio-temporal resolutions. The MP3D scheme is shown to provide comparable rate-distortion performances at low and medium bit rates against state-of-the-art schemes, like H.264 and MPEG-4, or the scalable MC EZBC. It also provides an increased flexibility in stream manipulation to adapt to non-octave based spatial resolutions, or to any rate constraints. However, the use of a redundant dictionary is penalizing at high coding rates, which makes the MP3D algorithm interesting for low rate applications, or as a flexible base layer for higher rate video systems.

2006Pascal Frossard, Pierre Vandergheynst, Adel Rahmoune

This paper introduces a novel algorithm for sparse approximation in redundant dictionaries called the M-term pursuit (MTP). This algorithm decomposes a signal into a linear combination of atoms that are selected in order to represent the main signal components. The MTP algorithm provides an adaptive representation for signals in any complete dictionary. The basic idea behind the MTP is to partition the dictionary into L quasi-disjoint subdictionaries. A k-term signal approximation is then iteratively computed, where each iteration leads to the selection of M

Compact or efficient representation for either images or image sequences is key operation to performing image and video processing tasks, such as compression, analysis, etc. The efficiency of an approximation is evaluated by the sparsity measure of the approximation, i.e., the sparsest the representation is, the more efficient it is. For image processing tasks, it is often desired to decompose the image into a linear combination of few visual primitives or features selected from a large collection of waveforms, called the dictionary. These primitives are usually designed in such a way to achieve some good approximation performances by assuming a given class of functions to model images. A common class of functions for image modeling is the set of functions having discontinuities along smooth contours or boundaries, delineating smooth geometrical regions. It was shown that the well-known separable isotropically scaled two-dimensional wavelets fail to capture the geometrical regularity inherent to images. Motivated by this issue, we designed two rich dictionaries Ds and Dst, composed of multi-scaled ridge-like functions satisfying the anisotropy and the directionality features, for image and video expansions, respectively. Regarding the spatio-temporal dictionary Dst, we defined a warping operator W, which aligns these functions along the coherent motion trajectories in order to exploit the nature of the temporal evolution in the video signal. To obtain a compact representation for the visual signal over the dictionaries Ds and Dst, only the primitives that best match the signal components must be selected. This problem is well studied in approximation theory and it is known as the problem of sparse approximation in unrestricted dictionaries, whose optimal solution is NP-hard. Greedy approaches, such as MP and OMP, have been proposed to provide sub-optimal solutions by iteratively choosing one atom at a time. However, the computational complexity of these algorithms is cumbersome and limits their applicability. To alleviate this issue, we introduced a greedy algorithm, called the M-Term Pursuit MTP, whose performances are very close to those related to MP. Then we employed both algorithms, MP and MTP, for image and image sequence decompositions and we investigated their performances. A target application has been studied, which is the scalable compression, where the aim is to generate a bit-stream that can provide both SNR and geometrical scalability. Geometrical scalability refers to the spatial scalability in case the of images and to the spatio-temporal scalability in the case of video sequences. The SNR or quality scalability is related mainly to the nature of the greedy approaches and the embedded quantization and coding. To do so, we designed a rate allocation algorithm that offers a progressively refinable bit-stream, based on the subsets approach. On the other hand, the geometrical scalability is fullfiled thanks to the structure of the dictionaries, Ds and Dst, which are designed using parametric fashion. Comparisons with state-of-the-art scalable and non-scalable codecs illustrate the good performance of the proposed compression techniques at low rates.