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Publications associées (112)

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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

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

Some Recovery Conditions for Basis Learning by L1-Minimization

Rémi Gribonval, Karin Schnass

Many recent works have shown that if a given signal admits a sufficiently sparse representation in a given dictionary, then this representation is recovered by several standard optimization algorithms, in particular the convex

\ell^1

minimization approac ...

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

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 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

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

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

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

Some Recovery Conditions for Basis Learning by L1-Minimization

Rémi Gribonval, Karin Schnass

\ell^1

minimization approac ...

2008