Nonmonotone Projected Barzilai-Borwein Method for Compressed Sensing

In this paper, we present a new nonmonotone projected BB (Barzilai-Borwein) method for minimizing regularization problem in compressed sensing. The proposed method exploits the idea of determining the search stepsize in monotone projected BB algorithm (MPBB) of nonnegative matrix factorization, and provides a direct calculation method of search stepsize which doesnt need line search and satisfies nonmonotonicity. Finally, the proposed algorithm is theoretically proved to be globally convergent. Numerical experiment results demonstrate that the proposed algorithm is effective and outruns the GPSR and SpaRSA as the sparseness degrees range.