SOSP: a stepwise optimal sparsity pursuit algorithm for practical compressed sensing
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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.
KeywordsCompressed sensing Sparsity pursuit Estimated sparsity Reconstruction Greedy algorithm
The authors would like to thank their colleagues for many useful comments. In particular, they are grateful to Xuefei Bai of Shanxi University for many discussions on the OMP and CoSaMP code. This work was supported by the National Science Foundation of China (No. 61273294) and Youth Foundation of Shanxi Province, China (201601D202040). F. Hao’s work was supported by the Fundamental Research Funds for the Central Universities, China (Grant No. GK201703059) and the Natural Science Foundation for Young Scientists of Shanxi Province, China (Grant No. 2015021102). D.S. Park’s work was supported by Basic Science Research program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2017R1A2B1008421).
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