梯度投影法求解压缩感知信号重构问题

将结合Barzilai-Borwein步长和非单调线搜索的梯度投影法用于压缩感知信号重构.分析了Barzilai-Borwein步长计算方法,结合其特点给出了非单调线搜索方法,为降低线搜索对算法性能的影响,引入了自适应的策略,最后给出了算法收敛性分析.实验结果表明,该算法能很好地重构不同稀疏度的信号,且在相同条件下,计算效率优于经典的基追踪法、正交匹配追踪和其他梯度投影法.

Problem of Signal Reconstruction of Compressive Sensing Solved by Gradient Projection

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.