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On the exponential convergence of Matching Pursuits in quasi-incoherent dictionaries

Publications associées (35)

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Tree-Based Pursuit: Algorithm and Properties

Pascal Frossard, Pierre Vandergheynst, Philippe Jost

This paper proposes a tree-based pursuit algorithm that efficiently trades off complexity and approximation performance for overcomplete signal expansions. Finding the sparsest representation of a signal using a redundant dictionary is, in general, a NP-Ha ...

2006

The subconvexity problem for Rankin-Selberg $L$-functions and equidistribution of Heegner points. II

Philippe Michel

We prove a general subconvex bound in the level aspect for Rankin–Selberg L-functions associated with two primitive holomorphic or Maass cusp forms over Q. We use this bound to establish the equidistribution of incomplete Galois orbits of Heegner points on ...

2006

Tree-Based Pursuit: Algorithm and Properties

Pascal Frossard, Pierre Vandergheynst, Philippe Jost

2005

On the exponential convergence of matching pursuits in quasi-incoherent dictionaries

Pierre Vandergheynst, Rémi Gribonval

The purpose of this paper is to extend results by Villemoes about exponential convergence of Matching Pursuit with some structured dictionaries for simple functions in finite or infinite dimension. Our results are based on an extension of Tropps results ...

2004

Image compression with learnt tree-structured dictionaries

Pierre Vandergheynst, Gianluca Monaci, Philippe Jost

In the present paper we propose a new framework for the construction of meaningful dictionaries for sparse representation of signals. The dictionary approach to coding and compression proves very attractive since decomposing a signal over a redundant set o ...

2004

A Matching Pursuit Full Search Algorithm for Image Approximations

Pierre Vandergheynst, Oscar Divorra Escoda

There is a growing interest on adapted signal expansions for efficient sparse approximations. For this purpose, signal expansions on over-complete bases are of high interest. Several strategies exist in order to get sparse approximations of a signal as a s ...

2004

Investigation of Redundant Dictionaries for Distributed Source Coding

In this project, we investigate the possibility of using the Matching Pursuit algorithm to generate image representations of a pair of correlated images for distributed source coding. We propose to use constrained dictionaries by appropriately selecting ne ...

2004

The PROSITE database, its status in 2002

Philipp Bucher, Amos Bairoch

PROSITE [Bairoch and Bucher (1994) Nucleic Acids Res., 22, 3583-3589; Hofmann et al. (1999) Nucleic Acids Res., 27, 215-219] is a method of identifying the functions of uncharacterized proteins translated from genomic or cDNA sequences. The PROSITE databas ...

2002

Redundancy in Non-Orthogonal Transforms

Pascal Frossard, Pierre Vandergheynst

Compression efficiency is mainly driven by redundancy of the overcomplete set of functions chosen for the signal decomposition. In Matching Pursuit algorithms for example, the redundancy of the dictionary influences the convergence of the residual energy. ...

EUSIPCO2001

Approximations for the Hantush M function

David Andrew Barry

A recent paper (Trefry, M.G., 1998. Analytical series expressions for Hanhrsh's M and S functions. Water Resour. Res. 34, 909-913) provided several interesting results concerning the Hantush M function, an integral that arises often in analytical solutions ...

1999