Simultaneous sparse learning algorithm of structured approximation with transformation analysis embedded in Bayesian framework

Abstract. Sparse approximation is critical to the applications of signal or image processing, and it is conducive to estimate the sparse signals with the joint efforts of transformation analysis. A simultaneous Bayesian framework is extended for sparse approximation by structured shared support, and a simultaneous sparse learning algorithm of structured approximation is proposed with transformation analysis, which leads to the feasible solutions more sensibly. Then the improvements of sparse Bayesian learning and iterative reweighting are embedded into the framework to achieve rapid convergence and high efficiency with robustness. Furthermore, the iterative optimization and transformation analysis are embedded in the overall learning process to obtain the relative optima for sparse approximation. Finally, compared with conventional reweighting algorithms for simultaneous sparse models with l1 and l2, simulation results present the preponderance of the proposed approach to solve the sparse structure and iterative redundancy in processing sparse signals. The fact indicates that the proposed method will be effective to sparsely approximate the various signals and images, which does accurately analyze the target in optimal transformation. It is envisaged that the proposed model could be suitable for a wide range of data in sparse separation and signal denoising.

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