Solving linear inverse problem via mixture regularization

The iterative shrinkage/thresholding algorithm (ISTA) with the regularizer gives good efficiency to solve the linear inverse problem. In fact, the maximum a posteriori (MAP) estimator with the probability density function (PDF) and ISTA with the regularizer are similar, and we imply that PDF is similar to the regularizer. In general cases, the mixture PDF created from many ordinary PDFs gives better efficiency than the ordinary PDF. Consequently, we present the simple method based on the linear combination of various ordinary regularizers to create the mixture regularizer, and also present the simple-mixture regularizer for ISTA to solve the linear inverse problem. Experimental results of the generated and real signals show that our method outperforms the state-of-the-art methods.