Asymptotically Optimized Subspace Pursuit for sparse signal recovery

A novel greedy algorithm, termed the Asymptotically Optimized Subspace Pursuit (AOSP), is proposed in this paper for recovery of sparse signals. In the Subspace Pursuit (SP) algorithm, the measurement vector is projected onto the optimal subspace and the original sparse signals are recovered on the basis of the projection coefficients. However, the SP algorithm uses the sparsity K as a priori to determine the dimension of the optimal subspace, which makes it difficult to be applied in real applications. To avoid this deficiency, we use a statistical method to progressively estimate the dimension of the optimal subspace. Therefore, the priori signal sparsity isn´t needed any more and the proposed AOSP can be adaptive to any natural signals. Numerical experiments are implemented for sparse signal models when the measurement is perturbed by the Gaussian white noise. The simulation results show that the proposed AOSP can achieve the higher recovery accuracy compared to other several typical greedy algorithms. Finally, the experiment of compressed sensing for image recovery is implemented, and the simulation results show that among several candidate greedy algorithms the proposed AOSP can achieve the best image quality.