Publication

The M-Term Pursuit for Image Representation and Progressive Compression

Pascal Frossard, Pierre Vandergheynst
2005
Conference Papers

Abstract

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 (MP); it expands the image into a linear combination of atoms, selected from a large collection of spatial atoms. The MTP relies on the concept of dictionary partitioning, i.e., as splitting the dictionary into $L$ disjoint sub-dictionaries, each carrying some specific information. Then, it iteratively finds a $K$ -term approximation, by selecting $M$ atoms at a time, where $M

Official source

https://infoscience.epfl.ch/entities/publication/8ce55047-42f4-4237-a535-a55444ed6b3f

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Pascal Frossard, Pierre Vandergheynst
2005
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/8ce55047-42f4-4237-a535-a55444ed6b3f

About this result

Related concepts (32)

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 dictionary learning

Sparse dictionary learning (also known as sparse coding or SDL) is a representation learning method which aims at finding a sparse representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves. These elements are called atoms and they compose a dictionary. Atoms in the dictionary are not required to be orthogonal, and they may be an over-complete spanning set. This problem setup also allows the dimensionality of the signals being represented to be higher than the one of the signals being observed.

Image compression

Image compression is a type of data compression applied to s, to reduce their cost for storage or transmission. Algorithms may take advantage of visual perception and the statistical properties of image data to provide superior results compared with generic data compression methods which are used for other digital data. Image compression may be lossy or lossless. Lossless compression is preferred for archival purposes and often for medical imaging, technical drawings, clip art, or comics.

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