An Adaptive Sieving Strategy for the Complex Lasso Problem

The reconstruction of complex sparse signals is widely used in magnetic resonance imaging, radar and other fields. Most of the current algorithms convert problems with complex variables into real variables, which may cause the special structure of complex numbers to be ignored. In this paper, we propose an adaptive sieving (AS) strategy to effectively reduce the size of complex domain problems. The sieving strategy makes full use of the sparsity of the solution, which can effectively and safely select the nonzero features in the problem and reduce the CPU time. We apply the fast iterative shrinkage-thresholding algorithm (FISTA) to solve the small-scale subproblems after sieving. Numerical results show that the adaptive sieving strategy on FISTA (AS-FISTA) can effectively identify the nonzero features with low computational cost and fast speed.