Many problems arising in image processing and signal recovery with
multi-regularization can be formulated as minimization of a sum of three convex
separable functions. Typically, the objective function involves a smooth
function with Lipschitz continuous gradient, a linear composite nonsmooth
function and a nonsmooth function. In this paper, we propose a primal-dual
fixed-point (PDFP) scheme to solve the above class of problems. The proposed
algorithm for three block problems is a fully splitting symmetric scheme, only
involving explicit gradient and linear operators without inner iteration, when
the nonsmooth functions can be easily solved via their proximity operators,
such as $\ell_1$ type regularization. We study the convergence of the proposed
algorithm and illustrate its efficiency through examples on fused LASSO and
image restoration with non-negative constraint and sparse regularization.

本文提出了一个用于解决图像处理和信号恢复问题的基于原始 - 对偶不动点的算法，用于处理涉及三个凸可分函数总和的最小化问题，证明了其收敛性，并通过在融合 LASSO 和带非负约束和稀疏正则化的图像恢复等例子中的应用展示了其效率。