Variable step-size matching pursuit based on oblique projection for compressed sensing

The development of compressive sensing has focused on sparse signal reconstruction in recent years. Most existing greedy algorithms achieve satisfactory reconstruction performance only when the sparsity of the target signal has been known as prior information. Moreover, some greedy algorithms always involve either high-computational expenses or low-reconstruction accuracy caused by the process of adaptive adjustment of signal sparsity. To address these concerns, a novel variable step-size matching pursuit based on oblique projection (VSMPOP) for compressed sensing is proposed. The proposed VSMPOP algorithm estimates the initial sparsity based on the restricted isometry property criterion. The algorithm creates a support set of the target signal after a preliminary test and oblique projection test between the sensing matrix and the residual. VSMPOP realises a similar approach to the sparsity level with a variable step size. The experimental results demonstrated that the proposed VSMPOP algorithm provides superior performance in terms of computational complexity and reconstruction efficiency compared with most of the available matching pursuit algorithms.