Analysis on greedy reconstruction algorithms based on compressed sensing

Due to the fast reconstruction and low complexity of mathematical framework, a family of iterative greedy algorithms has been widely used in compressed sensing recently. In this paper, we focus on two types of greedy algorithms―matching pursuit and gradient pursuit, including MP, OMP, StOMP, CoSaMP, GP, CGP, etc. The mathematical framework of all types of greedy algorithms is introduced, and all of the greedy algorithms are classified according to the strategy of element selection and the update of the residual error. The performance of greedy algorithms is analyzed under the same conditions of running time, reconstruction error, SNR, etc. The relationship among the reconstruction performance, signal sparsity and the number of measurements is provided through the simulation experiments. The results show that the reconstruction error of StOMP, and CoSaMP is significantly better than the MP, OMP, GP and CGP algorithm in the case of small sparsity or more measurements, but the Gradient Pursuit approaches are much faster than Matching Pursuit.