关键词: 图像复原, 稀疏表示, 交替优化, 变量分裂, 邻近映射

Abstract: For single-regularized algorithms, there is limited prior knowledge available for image deconvolution, thus posing negative effects on restored results. To overcome this drawback of single-regularized algorithms, in the framework of sparse representation, this paper proposes a new multi-regularized image deconvolution algorithm which introduces more prior knowledge to improve the quality of restored images. In the proposed algorithm, image deconvolution is cast as a global optimization problem with multiple regularized terms. To solve this complex global optimization problem, the alternating optimization and variable splitting are employed to decompose it into a sequence of subproblems. The analytical solution of[ uj+1 ]subproblem can be directly obtained due to its differentiability, whereas for non-differentiable[ wj+1 ]and[ vj+1 ]subproblems, the proximity mapping is applied. In the experiment, three kinds of degraded images are successfully restored by the proposed algorithm, which verifies the effectiveness of it. Compared with FISTA（Fast Iterative Shrinkage-Thresholding Algorithm） and Split Bregman, the proposed algorithm shows better performances on restored results and speed.

Key words: image deconvolution, sparse representation, alternating optimization, variable splitting, proximity mapping