Sampling and Reconstructing Signals From a Union of Linear Subspaces

Author

Blumensath, Thomas

Author_Institution

Centre for Functional MRI of the Brain, Univ. of Oxford, Oxford, UK

Volume

57

Issue

7

fYear

2011

fDate

7/1/2011 12:00:00 AM

Firstpage

4660

Lastpage

4671

Abstract

In this paper, we study the problem of sampling and reconstructing signals which are assumed to lie on or close to one of several subspaces of a Hilbert space. Importantly, we here consider a very general setting in which we allow infinitely many subspaces in infinite dimensional Hilbert spaces. This general approach allows us to unify many results derived recently in areas such as compressed sensing, affine rank minimization, analog compressed sensing and structured matrix decompositions.

Keywords

Hilbert spaces; affine transforms; matrix decomposition; signal reconstruction; signal sampling; affine rank minimization; analog compressed sensing; bi-Lipschitz embedding condition; infinite dimensional Hilbert spaces; linear subspace; projected landweber algorithm; sampling operator; signal reconstruction; signal recovery; signal sampling procedure; structured matrix decomposition; Analytical models; Approximation algorithms; Approximation methods; Compressed sensing; Computational modeling; Hilbert space; Image reconstruction; Inverse problems; nonconvexly constrained optimization; sampling; union of subspaces;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2011.2146550

Filename

5895053