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

Recovery of clustered sparse signals from compressive measurements

We introduce a new signal model, called (K,C)-sparse, to capture K-sparse signals in N dimensions whose nonzero coefficients are contained within at most C clusters, with C < K < N. In contrast to the existing work in the sparse approximation and compress ...

2009

Compressed sensing for radio interferometry: spread spectrum imaging techniques

Pierre Vandergheynst, Yves Wiaux, Gilles Puy

We consider the problem of reconstruction of astrophysical signals probed by radio interferometers with baselines bearing a non-negligible component in the pointing direction. The visibilities measured essentially identify with a noisy and incomplete Fouri ...

2009

A low complexity orthogonal matching pursuit for sparse signal approximation with shift-invariant dictionaries

Pierre Vandergheynst, Rémi Gribonval

We propose a variant of Orthogonal Matching Pursuit (OMP), called LoCOMP, for scalable sparse signal approximation. The algorithm is designed for shift- invariant signal dictionaries with localized atoms, such as time-frequency dictionaries, and achieves a ...

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

Learning bimodal structure in audio-visual data

Pierre Vandergheynst, Gianluca Monaci

A novel model is presented to learn bimodally informative structures from audio-visual signals. The signal is represented as a sparse sum of audio- visual kernels. Each kernel is a bimodal function consisting of synchronous snippets of an audio waveform an ...

2009

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

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

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

On finding approximate nearest neighbours 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 ...

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

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

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Recovery of clustered sparse signals from compressive measurements

Compressed sensing for radio interferometry: spread spectrum imaging techniques

A low complexity orthogonal matching pursuit for sparse signal approximation with shift-invariant dictionaries

Basis Identification from Random Sparse Samples

Learning bimodal structure in audio-visual data

Compressed sensing and redundant dictionaries

Dictionary preconditioning for greedy algorithms

Dictionary Learning Based Dimensionality Reduction for Classification

On finding approximate nearest neighbours in a set of compressible signals

Algorithms and methods for sparse approximation in structured dictionaries

A low complexity orthogonal matching pursuit for sparse signal approximation with shift-invariant dictionaries

Learning bimodal structure in audio-visual data

Dictionary preconditioning for greedy algorithms

Dictionary Learning Based Dimensionality Reduction for Classification

Basis Identification from Random Sparse Samples

Recovery of clustered sparse signals from compressive measurements

Compressed sensing for radio interferometry: spread spectrum imaging techniques

Algorithms and methods for sparse approximation in structured dictionaries

Compressed sensing and redundant dictionaries

On finding approximate nearest neighbours in a set of compressible signals