Publication

Investigation of Redundant Dictionaries for Distributed Source Coding

2004
Reports

Abstract

In this project, we investigate the possibility of using the Matching Pursuit algorithm to generate image representations of a pair of correlated images for distributed source coding. We propose to use constrained dictionaries by appropriately selecting neighbouring atoms to increase the correlation between parameters, and with this, enable the application of the distributed framework.

Official source

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2004
Reports

Abstract

Official source

Related concepts (18)

Matching pursuit

Matching pursuit (MP) is a sparse approximation algorithm which finds the "best matching" projections of multidimensional data onto the span of an over-complete (i.e., redundant) dictionary . The basic idea is to approximately represent a signal from Hilbert space as a weighted sum of finitely many functions (called atoms) taken from . An approximation with atoms has the form where is the th column of the matrix and is the scalar weighting factor (amplitude) for the atom . Normally, not every atom in will be used in this sum.

Sparse approximation

Sparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding these solutions and exploiting them in applications have found wide use in , signal processing, machine learning, medical imaging, and more. Consider a linear system of equations , where is an underdetermined matrix and . The matrix (typically assumed to be full-rank) is referred to as the dictionary, and is a signal of interest.

Basis pursuit

Basis pursuit is the mathematical optimization problem of the form where x is a N-dimensional solution vector (signal), y is a M-dimensional vector of observations (measurements), A is a M × N transform matrix (usually measurement matrix) and M < N. It is usually applied in cases where there is an underdetermined system of linear equations y = Ax that must be exactly satisfied, and the sparsest solution in the L1 sense is desired. When it is desirable to trade off exact equality of Ax and y in exchange for a sparser x, basis pursuit denoising is preferred.

Related publications (4)

Investigation of Redundant Dictionaries for Distributed Source Coding

Chat with Graph Search

Sparse Decompositions for Ventricular and Atrial Activity Separation

A Matching Pursuit Full Search Algorithm for Image Approximations

Evolutionary Multiresolution Matching Pursuit and its relations with the Human Visual System