A box constrained gradient projection algorithm for compressed sensing

Authors:
R. L. Broughton;I. D. Coope;P. F. Renaud;R. E. H. Tappenden
Affiliations:
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand;Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand;Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand;Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
Venue:
Signal Processing
Year:
2011

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Abstract

A new algorithm is presented which aims to solve problems from compressed sensing - under-determined problems where the solution vector is known a priori to be sparse. Upper bounds on the solution vector are found so that the problem can be reformulated as a box-constrained quadratic programme. A sparse solution is sought using a Barzilai-Borwein type projection algorithm. New insight into the choice of step length is provided through a study of the special structure of the underlying problem together with upper bounds on the step length. Numerical experiments are conducted and results given, comparing this algorithm with a number of other current algorithms.