SOSP: a stepwise optimal sparsity pursuit algorithm for practical compressed sensing

Compressed Sensing (CS), as a promising paradigm for acquiring signals, is playing an increasing important role in many real-world applications. One of the major components of CS is sparse signal recovery in which greedy algorithm is well-known for its speed and performance. Unfortunately, in many classic greedy algorithms, such as OMP and CoSaMP, the real sparsity is a key prior information, but it is blind. In another words, the true sparsity is not available for many practical applications. Due to this disadvantage, the performance of these algorithms are significantly reduced. In order to avoid too much dependence of classic greedy algorithms on the true sparsity, this paper proposed an efficient reconstruction greedy algorithm for practical Compressed Sensing, termed stepwise optimal sparsity pursuit (SOSP). Differs from the existing algorithms, the unique feature of SOSP algorithm is that the assumption of sparsity is needed instead of the true sparsity. Hence, the limitations of sparsity in practical application can be tackled. Based on an arbitrary initial sparsity satisfying certain conditions, the SOSP algorithm employs two variable step sizes to hunt for the optimal sparsity step by step by comparing the final reconstruction residues. Since the proposed SOSP algorithm preserves the ideas of original algorithms and innovates the prior information of sparsity, thus it is applicable to any effective algorithm requiring known sparsity. Extensive experiments are conducted in order to demonstrate that the SOSP algorithm offers a superior reconstruction performance in terms of discarding the true sparsity.