A Simultaneous Sparse Learning Algorithm of Structured Approximation with Transformation Analysis Embedded in Bayesian Framework

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. In this study, a simultaneous Bayesian framework was extended for sparse approximation by structured shared support, and a simultaneous sparse learning algorithm of structured approximation (SSL-SA) is proposed with transformation analysis which leads to the feasible solutions more sensibly. Then the improvements of sparse Bayesian learning and iterative reweighting were embedded in the framework to achieve speedy convergence as well as high efficiency with robustness. Furthermore, the iterative optimization and transformation analysis were embedded in the overall learning process to obtain the relative optima for sparse approximation. Finally, compared to 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 proposed method will be effective to sparsely approximate the various signals and images, which does accurately analyse 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 denosing.