Abstract：The regularization parameter of sparse representation model is determined by the unknown noise and sparsity. Meanwhile, it can directly affect the performances of sparsity reconstruction. However, the optimization algorithm of sparsity representation issue, which is solved with parameter setting by expert reasoning, priori knowledge or experiments, can not set the parameter adaptively. In order to solve the issue, the sparsity Bayesian learning algorithm which can set the parameter adaptively without priori knowledge is proposed. Firstly, the parameters in the model is constructed with the probability. Secondly, on the basis of the framework of Bayesian learning, the issue of parameter setting and sparsity resolving is transformed to the convex optimization issue which is the addition of a series of mixture L1 normal and the weighted L2 normal. Finally, the parameter setting and sparsity resolving are achieved by the iterative optimization. Theoretical analysis and simulations show that the proposed algorithm is competitive and even better compared with other parameter non-adjusted automatically iterative reweighted algorithms when ideal parameter is known, and the reconstruction performance of the proposed algorithm is significantly better than the other algorithms when choosing the non-ideal parameters.
2014, Vol. 36 
