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Sparsity & [and] dictionaries - algorithms & [and] design

Publications associées (126)

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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 modelling of multi-modal data using redundant dictionaries

Gianluca Monaci

Real-world phenomena involve complex interactions between multiple signal modalities. As a consequence, humans are used to integrate at each instant perceptions from all their senses in order to enrich their understanding of the surrounding world. This par ...

EPFL2007

Dimensionality Reduction with Adaptive Approximation

Pascal Frossard, Effrosyni Kokiopoulou

In this paper, we propose the use of (adaptive) nonlinear approximation for dimensionality reduction. In particular, we propose a dimensionality reduction method for learning a parts based representation of signals using redundant dictionaries. A redundant ...

2007

Average Performance Analysis for Thresholding

Pierre Vandergheynst, Karin Schnass

In this article is shown that with high probability the thresholding algorithm can recover signals that are sparse in a redundant dictionary as long as the {\it 2-Babel function} is growing slowly. This implies that it can succeed for sparsity levels up to ...

2007

On finding nearest neighbors in a set of compressible signals

Pierre Vandergheynst, Philippe Jost

Numerous applications demand that we manipulate large sets of very high-dimensional signals. A simple yet common example is the problem of finding those signals in a database that are closest to a query. In this paper, we tackle this problem by restricting ...

2007

Multichannel thresholding with sensing dictionaries

Pierre Vandergheynst, Rémi Gribonval, Karin Schnass

This paper shows introduces the use sensing dictionaries for p-thresholding, an algorithm to compute simultaneous sparse approximations of multichannel signals over redundant dictionaries. We do both a worst case and average case recovery analyses of this ...

2007

Annihilating filter-based decoding in the compressed sensing framework - art. no. 670121

Martin Vetterli, Ali Hormati

Recent results in compressed sensing or compressive sampling suggest that a relatively small set of measurements taken as the inner product with universal random measurement vectors can well represent a source that is sparse in some fixed basis. By adaptin ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2007

Matching Pursuit with Block Incoherent Dictionaries

Pierre Vandergheynst, Lorenzo Peotta

There has been an intense activity recently in the field of sparse approximations with redundant dictionaries, largely motivated by the practical performances of algorithms such as Matching Pursuit and Basis Pursuit. However, most of the theoretical result ...

2007

Slowness and Sparseness Lead to Place, Head-Direction, and Spatial-View Cells

We present a model for the self-organized formation of place cells, head-direction cells, and spatial-view cells in the hippocampal formation based on unsupervised learning on quasi-natural visual stimuli. The model comprises a hierarchy of Slow Feature An ...

Public Library of Science2007

A simple test to check the optimality of a sparse signal approximation

Pierre Vandergheynst, Rémi Gribonval

Approximating a signal or an image with a sparse linear expansion from an overcomplete 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 ...

2006