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Publications associées (55)

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Dictionary Identification - Sparse Matrix-Factorisation via $\ell_1$-Minimisation

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 can also be seen as factorising a

\ddim \times \nsig

matrix $Y=(y_1 \ldots y_\nsig), , y_n\in \R^\ ...

Institute of Electrical and Electronics Engineers2010

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 Learning Based Dimensionality Reduction for Classification

Pierre Vandergheynst, Karin Schnass

In this article we present a signal model for classification based on a low dimensional dictionary embedded into the high dimensional signal space. We develop an alternate projection algorithm to find the embedding and the dictionary and finally test the c ...

2008

Compressed sensing and redundant dictionaries

Pierre Vandergheynst, Karin Schnass

This article extends the concept of it compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a deterministic ...

2008

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

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

Nonlinear approximation with redundant multi-component dictionaries

Lorenzo Granai

The problem of efficiently representing and approximating digital data is an open challenge and it is of paramount importance for many applications. This dissertation focuses on the approximation of natural signals as an organized combination of mutually c ...

EPFL2006

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

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