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Fast sparsity adaptive multipath matching pursuit for compressed sensing problems

Abstract. The high computational complexity of tree-based multipath search approaches makes putting them into practical use difficult. However, reselection of candidate atoms could make the search path more accurate and efficient. We propose a multipath greedy approach called fast sparsity adaptive multipath matching pursuit (fast SAMMP), which performs a sparsity adaptive tree search to find the sparsest solution with better performances. Each tree branch acquires K atoms, and fast SAMMP reselects the best K atoms among 2K atoms. Fast SAMMP adopts sparsity adaptive techniques that allow more practical applications for the algorithm. We demonstrated the reconstruction performances of the proposed fast scheme on both synthetically generated one-dimensional signals and two-dimensional images using Gaussian observation matrices. The experimental results indicate that fast SAMMP achieves less reconstruction time and a much higher exact recovery ratio compared with conventional algorithms.