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

摘要： 由于单正则化图像复原算法所利用的先验信息有限，影响了复原图像的质量。为克服此类算法的不足，融入更多的先验信息，改善图像复原的效果。在稀疏表示的理论框架下，提出了一种多正则优化图像复原算法。该算法将图像复原表示为含多正则项的全局优化问题，为有效处理这一复杂的图像复原问题，采用交替优化策略并借助变量分裂将其分解为若干优化子问题。其中，[uj+1]子问题可微，可直接得到其解析解。不可微的[wj+1]和[vj+1]子问题，则通过邻近映射求解。实验过程中对三种不同类型的退化图像进行了复原，所得结果验证了该算法的有效性。与FISTA（Fast Iterative Shrinkage-Thresholding Algorithm）和Split Bregman等单正则化图像复原算法相比，所提算法的复原效果和时间性能更优。

关键词: 图像复原, 稀疏表示, 交替优化, 变量分裂, 邻近映射