This paper considers the class of Iterative Shrinkage Threshold Algorithm (ISTA) to solve the linear inverse problem that occurs in magnetic resonance (MR) image recovery. The ISTA algorithm adheres to the principle of minimizing the L1 norm. This method can be considered as an extension of the classical gradient algorithm. However, it is known that the ISTA algorithm converges slowly, and the accuracy of the algorithm is not sufficient. In many MR image recovery problems, using non-convex log-sum norm minimization can often obtain better results than the l1-norm minimization. In this paper, we firstly transform the MR image recovery into a non-convex optimization problem with log-sum norm regularization and combine it with a faster global convergence method. Then a Log-sum generalized iterated shrinkage threshold algorithm (LISTA) for solving the MR image recovery problem is proposed. Finally, numerical experiments are conducted to show the superiority of our algorithm.
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