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Compressed sensing and redundant dictionaries

Related publications (36)

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

Karin Schnass

With the flood of information available today the question how to deal with high dimensional data/signals, which are cumbersome to handle, to calculate with and to store, is highly important. One approach to reducing this flood is to find sparse signal rep ...

EPFL2009

Spread spectrum for imaging techniques in radio interferometry

Pierre Vandergheynst, Yves Wiaux, Gilles Puy

We consider the probe of astrophysical signals through radio interferometers with small field of view and baselines with non-negligible and constant component in the pointing direction. In this context, the visibilities measured essentially identify with a ...

Wiley-Blackwell2009

Spread spectrum for imaging techniques in radio interferometry and strings detection

Yves Wiaux, Gilles Puy

This poster is a summary of recent work published in: Spread spectrum for imaging techniques in radio interferometry, Y. Wiaux, G. Puy, Y. Boursier, and P. Vandergheynst, Mon. Not. R. Astron. Soc., 2009, Preprint arXiv:0907.0944v1. We consider the probe of ...

2009

Greedy dictionary selection for sparse representation

Volkan Cevher

We develop an efficient learning framework to construct signal dictionaries for sparse representation by selecting the dictionary columns from multiple candidate bases. By sparse, we mean that only a few dictionary elements, compared to the ambient signal ...

2009

Basis Identification from Random Sparse Samples

Rémi Gribonval, Karin Schnass

This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via

\ell_1

minimisation. The problem is to identify a dictionary

\dico

from a set of training samples

\Y

knowing that

\Y = \dico \X

...

2009

Dictionary Identifiability from Few Training Samples

Rémi Gribonval, Karin Schnass

This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via

ell^1

minimisation, or more precisely the problem of identifying a dictionary

dico

from a set of training samples

Y

knowing that $ ...

2008

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

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

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

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