Publications related to Dictionary Identification - Sparse Matrix-Factorisation via $\ell_1$-Minimisation

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

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 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

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 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

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

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

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

Sparse Approximation Using M-Term Pursuits with Applications to Image and Video Compression

Pascal Frossard, Pierre Vandergheynst, Adel Rahmoune

This paper introduces an algorithm for sparse approximation in redundant dictionaries, called the M-Term Pursuit (MTP), based on the matching pursuit approach (MP). This algorithm decomposes the signal into a linear combination of selected atoms, chosen to ...

2005

The M-Term Pursuit for Image Representation and Progressive Compression

Pascal Frossard, Pierre Vandergheynst, Adel Rahmoune

This paper introduces a sparse signal representation algorithm in redundant dictionaries, called the M-Term Pursuit (MTP), with an application to image representation and scalable coding. The MTP algorithm belongs to the framework of the matching pursuit ( ...

EUSIPCO2005

A simple test to check the optimality of sparse signal approximations

Pierre Vandergheynst, Rémi Gribonval

Approximating a signal or an image with a sparse linear expansion from an over-complete 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 ...

2005

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

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

Dictionary Identifiability from Few Training Samples

Dictionary Learning Based Dimensionality Reduction for Classification

On the modelling of multi-modal data using redundant dictionaries

On the Use of A Priori Information for Sparse Signal Approximations

Nonlinear approximation with redundant multi-component dictionaries

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

Sparse Approximation Using M-Term Pursuits with Applications to Image and Video Compression

The M-Term Pursuit for Image Representation and Progressive Compression

A simple test to check the optimality of sparse signal approximations

Nonlinear approximation with redundant multi-component dictionaries

On the Use of A Priori Information for Sparse Signal Approximations

On the modelling of multi-modal data using redundant dictionaries

A simple test to check the optimality of sparse signal approximations

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

Dictionary Learning Based Dimensionality Reduction for Classification

Dictionary Identifiability from Few Training Samples

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

Sparse Approximation Using M-Term Pursuits with Applications to Image and Video Compression

The M-Term Pursuit for Image Representation and Progressive Compression