GA-BFO based signal reconstruction for compressive sensing

The theory of compressive sensing (CS) mainly includes three aspects, i.e., sparse representation, uncorrelated sampling, and signal reconstruction, in which signal reconstruction serve as the core of CS. The constraint of signal sparsity can be implemented by l0 norm minimization, which is an NP-hard problem that requires exhaustively listing all possibilities of the original signal and is difficult to achieve by the traditional algorithm. This paper proposes a signal reconstruction algorithm based on intelligent optimization algorithm which combines genetic algorithm (GA) and Bacteria Foraging Optimization (BFO) algorithm. This method can find the global optimal solution by genetic and evolutionary operation to the group, which can solve l0 norm minimization directly. It has been proved through numerical simulations that the theoretical optimization performance can be achieved and the result is superior to that of OMP algorithm.