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Near-Optimal Bayesian Localization via Incoherence and Sparsity

Publications associées (45)

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Dictionary preconditioning for greedy algorithms

Pierre Vandergheynst, Karin Schnass

This article presents an alteration of greedy algorithms like thresholding or (Orthogonal) Matching Pursuit which improves their performance in finding sparse signal representations in redundant dictionaries. These algorithms can be split into a sensing an ...

2008

Compressed Sensing For Multi-View Tracking And 3-D Voxel Reconstruction

Volkan Cevher

Compressed sensing (CS) suggests that a signal, sparse in some basis, can be recovered from a small number of random projections. In this paper, we apply the CS theory on sparse background-subtracted silhouettes and show the usefulness of such an approach ...

2008

Algorithms and methods for sparse approximation in structured dictionaries

Lorenzo Peotta

In the last decade we observed an increasing interaction between data compression and sparse signals approximations. Sparse approximations are desirable because they compact the energy of the signals in few elements and correspond to a structural simplific ...

EPFL2007

Algorithmic aspects of sparse approximations

Philippe Jost

Typical tasks in signal processing may be done in simpler ways or more efficiently if the signals to analyze are represented in a proper way. This thesis deals with some algorithmic problems related to signal approximation, more precisely, in the novel fie ...

EPFL2007

On the Use of A Priori Information for Sparse Signal Approximations

Pierre Vandergheynst, Lorenzo Granai, Oscar Divorra Escoda

Recent results have underlined the importance of incoherence in redundant dictionaries for a good behavior of decomposition algorithms like Matching and Basis Pursuits. However, appropriate dictionaries for a given application may not necessarily be able t ...

2006

The M-Term Pursuit for Image Representation and Progressive Compression

Pascal Frossard, Pierre Vandergheynst, Adel Rahmoune

This paper introduces a sparse signal representation algorithm in redundant dictionaries, called the M-Term Pursuit (MTP), with an application to image representation and scalable coding. The MTP algorithm belongs to the framework of the matching pursuit ( ...

EUSIPCO2005

A simple test to check the optimality of sparse signal approximations

Pierre Vandergheynst, Rémi Gribonval

Approximating a signal or an image with a sparse linear expansion from an over-complete dictionary of atoms is an extremely useful tool to solve many signal processing problems. Finding the sparsest approximation of a signal from an arbitrary dictionary is ...

2005

Toward sparse and geometry adapted video approximations

Oscar Divorra Escoda

Video signals are sequences of natural images, where images are often modeled as piecewise-smooth signals. Hence, video can be seen as a 3D piecewise-smooth signal made of piecewise-smooth regions that move through time. Based on the piecewise-smooth model ...

EPFL2005

Sparse image approximation with application to flexible image coding

Natural images are often modeled through piecewise-smooth regions. Region edges, which correspond to the contours of the objects, become, in this model, the main information of the signal. Contours have the property of being smooth functions along the dire ...

EPFL2005

Sparse Approximation by Linear Programming using an L1 Data-Fidelity Term

Pierre Vandergheynst, Lorenzo Granai

This paper studies the problem of sparse signal approximation over redundant dictionaries. Our attention is focused on the minimization of a cost function where the error is measured by using the L1 norm, giving thus less importance to outliers. We show a ...

IEEE2005