Abstract:

A gradient projection method combining Barzilai-Borwein stepsize and nonmonotone line search is proposed and applied to signal reconstruction in compressive sensing. The computation of Barzilai-Borwein stepsize is analyzed, A corresponding nonmonotone line search method is introduced. To reduce influence of line search, an adaptive nonmonotone line search is designed. Convergence analysis of the algorithm is given. Experiment shows that the proposed algorithm can get good performances of signal reconstruction with different sparsity, seems better than Basis Pursuit, Orthogonal Matching Pursuit and other gradient projection algorithms. 

Key words: compressive sensing, signal reconstruction, gradient projection, Barzilai-Borwein stepsize, nonmonotone line search