A box constrained gradient projection algorithm for compressed sensing

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.