Synthesis-based sparse reconstrucion with analysis-based solvers

Synthesis sparsity model received great attention in the past decade. Signal reconstruction based analysis model appears recently and has a high accurate reconstruction rate., which constitutes a solid basis for practical applications. In this paper, we transform the sparse signal reconstruction issue of synthesis model to an analysis one with some additional restraints. Therefore the existing algorithms based on analysis model are able to solve the exact reconstruction problem of synthesis model. This approach is called the Synthesis-By-Analysis(SBA) approach. The proposed approach is evaluated by comparing it with the Orthogonal Matching Pursuit algorithm, which is a classic algorithm base on the synthesis model. Experiment results show that this approach is another option for reconstruction problem based on synthesis model, meanwhile allowing many algorithms for analysis cosparse model to be used for synthesis signal reconstruction as well.