Iterative hard thresholding for compressed sensing

Blumensath, T. and Davies, M.E. (2009) Iterative hard thresholding for compressed sensing. Applied and Computational Harmonic Analysis, 27, (3), 265-274. (doi:10.1016/j.acha.2009.04.002).


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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

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/j.acha.2009.04.002
ISSNs: 1063-5203 (print)
1096-603X (electronic)
Keywords: algorithms, compressed sensing, sparse inverse problem, signal
Subjects: Q Science > Q Science (General)
Divisions : University Structure - Pre August 2011 > Other
Faculty of Engineering and the Environment > Institute of Sound and Vibration Research > Signal Processing & Control Research Group
ePrint ID: 142507
Accepted Date and Publication Date:
November 2009Published
Date Deposited: 31 Mar 2010 15:52
Last Modified: 31 Mar 2016 13:18

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