Publication

Redundancy in Non-Orthogonal Transforms

Publications associées (52)

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Fast orthogonal sparse approximation algorithms over local dictionaries

Pierre Vandergheynst, Rémi Gribonval

In this work we present a new greedy algorithm for sparse approximation called LocOMP. LocOMP is meant to be run on local dictionaries made of atoms with much shorter supports than the signal length. This notably encompasses shift-invariant dictionaries an ...

2011

Use of Learned Dictionaries in Tomographic Reconstruction

Martin Vetterli, Ivana Jovanovic, Vincent Etter

We study the use and impact of a dictionary in a tomographic reconstruction setup. First, we build two different dictionaries: one using a set of bases functions (Discrete Cosine Transform), and the other that is learned using patches extracted from traini ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2011

Sensing and Recovery under Sparsity Constraints

Ali Hormati

Popular transforms, like the discrete cosine transform or the wavelet transform, owe their success to the fact that they promote sparsity. These transforms are capable of extracting the structure of a large class of signals and representing them by a few t ...

EPFL2010

Ultrasound Tomography with Learned Dictionaries

Martin Vetterli, Pascal Frossard, Ivana Tosic, Ivana Jovanovic

We propose a new method for imaging sound speed in breast tissue from measurements obtained by ultrasound tomography (UST) scan- ners. Given the measurements, our algorithm finds a sparse image representation in an overcomplete dictionary that is adapted t ...

2010

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

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

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

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