Iterative hard thresholding for compressed sensing
Iterative hard thresholding for compressed sensing
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
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)
• It gives near-optimal error guarantees.
• It is robust to observation noise.
• It succeeds with a minimum number of observations.
• It can be used with any sampling operator for which the operator and its adjoint can be computed.
• The memory requirement is linear in the problem size.
• Its computational complexity per iteration is of the same order as the application of the measurement operator or its adjoint.
• It requires a fixed number of iterations depending only on the logarithm of a form of signal to noise ratio of the signal.
• Its performance guarantees are uniform in that they only depend on properties of the sampling operator and signal sparsity
algorithms, compressed sensing, sparse inverse problem, signal
265-274
Blumensath, T.
470d9055-0373-457e-bf80-4389f8ec4ead
Davies, M.E.
2f97d5ab-efda-4d6f-936d-00ae95d19e65
November 2009
Blumensath, T.
470d9055-0373-457e-bf80-4389f8ec4ead
Davies, M.E.
2f97d5ab-efda-4d6f-936d-00ae95d19e65
Blumensath, T. and Davies, M.E.
(2009)
Iterative hard thresholding for compressed sensing.
Applied and Computational Harmonic Analysis, 27 (3), .
(doi:10.1016/j.acha.2009.04.002).
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
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)
• It gives near-optimal error guarantees.
• It is robust to observation noise.
• It succeeds with a minimum number of observations.
• It can be used with any sampling operator for which the operator and its adjoint can be computed.
• The memory requirement is linear in the problem size.
• Its computational complexity per iteration is of the same order as the application of the measurement operator or its adjoint.
• It requires a fixed number of iterations depending only on the logarithm of a form of signal to noise ratio of the signal.
• Its performance guarantees are uniform in that they only depend on properties of the sampling operator and signal sparsity
More information
Published date: November 2009
Keywords:
algorithms, compressed sensing, sparse inverse problem, signal
Organisations:
Other, Signal Processing & Control Grp
Identifiers
Local EPrints ID: 142507
URI: http://eprints.soton.ac.uk/id/eprint/142507
ISSN: 1063-5203
PURE UUID: 57de7036-0fdf-4d46-b37d-9356fe5a5b36
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Date deposited: 31 Mar 2010 15:52
Last modified: 14 Mar 2024 02:55
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Contributors
Author:
M.E. Davies
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