Publication

Guaranteed recovery of a low-rank and joint-sparse matrix from incomplete and noisy measurements

Pierre Vandergheynst
2011
Talks

Résumé

Assume a multichannel data matrix, which due to the column-wise dependencies, has low-rank and joint-sparse representation. This matrix wont have many degrees of freedom. Enormous developments over the last decade in areas of compressed sensing and low-rank matrix recovery, let us thinking of acquiring the whole matrix elements from very few non-adaptive linear measurements. This paper attempts to answer the following questions: what should be those measurements? How to design a computationally tractable algorithm to recover data from noisy measurements? Finally, how the recovery method performs, and is it stable for approximately low-rank or not exactly joint-sparse matrices?

Source officielle

https://infoscience.epfl.ch/entities/publication/0866d18d-1e57-44fb-b87e-ee00fcbd7798

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Pierre Vandergheynst
2011
Talks

Résumé

Source officielle

https://infoscience.epfl.ch/entities/publication/0866d18d-1e57-44fb-b87e-ee00fcbd7798

À propos de ce résultat

Concepts associés (32)

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.

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.

Acquisition comprimée

L'acquisition comprimée (en anglais compressed sensing) est une technique permettant de trouver la solution la plus parcimonieuse d'un système linéaire sous-déterminé. Elle englobe non seulement les moyens pour trouver cette solution mais aussi les systèmes linéaires qui sont admissibles. En anglais, elle porte le nom de Compressive sensing, Compressed Sampling ou Sparse Sampling.

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Publications associées (3)

Guaranteed recovery of a low-rank and joint-sparse matrix from incomplete and noisy measurements

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