Adaptive Step-Size Matching Pursuit Algorithm for Practical Sparse Reconstruction

Abstract

A novel adaptive step-size matching pursuit algorithm (AStMP) is proposed. AStMP reduces the computational cost and increases the accuracy of reconstructing practical signals (i) whose sparsity K is unknown and/or (ii) may be corrupted by noise. AStMP accurately estimates K by combining the sparsity estimate of sparsity adaptive subspace pursuit (SASP) with the adaptively changing stepsize at each stage of sparsity adaptive matching pursuit (SAMP). Thus, AStMP can quickly achieve accurate estimation of the sparsity level and the true support set of the target signals. Meanwhile, a preselection is employed to reduce the computational complexity of each stage. When K is greater than half the number of measurements M, the probability of exact recovery is improved by analyzing the support set. Since the stepsize changes adaptively, AStMP can be applied in both the noiseless and noisy cases when the signal is not strictly sparse, allowing for exact or approximate signal recovery. Experimental results demonstrate that the AStMP is effective in fast and exact reconstruction and has good performance.