The Mathematical Institute, University of Oxford, Eprints Archive

CGIHT: Conjugate Gradient Iterative Hard Thresholding
for Compressed Sensing and Matrix Completion

Blanchard, Jeffrey D. and Tanner, Jared and Wei, Ke (2014) CGIHT: Conjugate Gradient Iterative Hard Thresholding
for Compressed Sensing and Matrix Completion.
Technical Report. Oxford University Press, Information and Inference: A Journal of the IMA. (Submitted)

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Abstract

We introduce the Conjugate Gradient Iterative Hard Thresholding (CGIHT) family of algorithms for the efficient solution of constrained underdetermined linear systems of equations arising in compressed sensing, row sparse approximation, and matrix completion. CGIHT is designed to balance the low per iteration complexity of simple hard thresholding algorithms with the fast asymptotic convergence rate of employing the conjugate gradient method. We establish provable recovery guarantees and stability to noise for variants of CGIHT with sufficient conditions in terms of the restricted isometry constants of the sensing operators. Extensive empirical performance comparisons establish significant computational advantages for CGIHT both in terms of the size of problems which can be accurately approximated and in terms of overall computation time.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1833
Deposited By: Helen Taylor
Deposited On:24 Apr 2014 07:39
Last Modified:29 May 2015 19:31

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