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Iterative hard thresholding for compressed sensing

By T. Blumensath and M.E. Davies

Abstract

Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding algorithm when<br/>applied to the compressed sensing recovery problem. We show that the algorithm has the following properties (made more precise in the main text of the paper) <br/>• It gives near-optimal error guarantees.<br/>• It is robust to observation noise.<br/>• It succeeds with a minimum number of observations.<br/>• It can be used with any sampling operator for which the operator and its adjoint can be computed.<br/>• The memory requirement is linear in the problem size.<br/>• Its computational complexity per iteration is of the same order as the application of the measurement operator or its adjoint.<br/>• It requires a fixed number of iterations depending only on the logarithm of a form of signal to noise ratio of the signal.<br/>• Its performance guarantees are uniform in that they only depend on properties of the sampling operator and signal sparsit

Topics: Q1
Year: 2009
OAI identifier: oai:eprints.soton.ac.uk:142507
Provided by: e-Prints Soton
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