GASA Based Signal Reconstruction for Compressive Sensing

Reconstruction, which is the core of compressive sensing (CS), can be implemented by l₀ norm minimization. In practice, l₀ norm minimization is a NP-hard problem that requires exhaustively listing all possibilities of the original signal and is difficult to achieve by traditional algorithms. This paper proposes a signal reconstruction algorithm combining genetic algorithm with simulated annealing algorithm which is famous for their superior performance in solving combinatorial optimization problems. The method in this paper can solve l₀ norm minimization directly and can reconstruct noiseless signal accurately. It has been proved through numerical simulations that the theoretical optimization performance for signal reconstruction can be achieved. The quality of reconstruction based on the proposed method is superior to that of OMP, smooth l₀ norm (SL0) algorithm, Lasso and BP algorithm.