当前位置: X-MOL 学术SIAM J. Sci. Comput. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A Three-Operator Splitting Algorithm for Nonconvex Sparsity Regularization
SIAM Journal on Scientific Computing ( IF 3.1 ) Pub Date : 2021-08-05 , DOI: 10.1137/20m1326775
Fengmiao Bian , Xiaoqun Zhang

SIAM Journal on Scientific Computing, Volume 43, Issue 4, Page A2809-A2839, January 2021.
Sparsity regularization has been widely adopted in many fields, such as signal and image processing and machine learning. In this paper, we mainly consider nonconvex minimization problems involving three terms, for applications such as sparse signal recovery and low rank matrix recovery. We employ a three-operator splitting proposed by Davis and Yin [Set-Valued Var. Anal., 25 (2017), pp. 829--858] (namely, DYS) to solve the resulting possibly nonconvex problems and develop the convergence theory for this three-operator splitting algorithm in the nonconvex case. We show that when the step size is chosen less than a computable threshold, the whole sequence converges to a stationary point. By defining a new decreasing energy function associated with the DYS method, we establish the global convergence of the whole sequence and a local convergence rate under an additional assumption that $F$, $G$, and $H$ are semialgebraic. We also provide sufficient conditions for the boundedness of the generated sequence. Finally, some numerical experiments are conducted to compare the DYS algorithm with some classical efficient algorithms for sparse signal recovery and low rank matrix completion. The numerical results indicate that DYS outperforms the existing methods for these applications.


中文翻译:

非凸稀疏正则化的三算子分裂算法

SIAM 科学计算杂志,第 43 卷,第 4 期,第 A2809-A2839 页,2021 年 1 月。
稀疏正则化已被广泛应用于许多领域,例如信号和图像处理以及机器学习。在本文中,我们主要考虑涉及三个项的非凸最小化问题,用于稀疏信号恢复和低秩矩阵恢复等应用。我们采用 Davis 和 Yin [Set-Valued Var. Anal., 25 (2017), pp. 829--858](即 DYS)来解决由此产生的可能的非凸问题,并在非凸情况下为这种三算子分裂算法开发收敛理论。我们表明,当逐步缩小的时间小于可计算阈值时,整个序列会聚到静止点。通过定义与 DYS 方法相关的新能量递减函数,我们在 $F$、$G$ 和 $H$ 是半代数的额外假设下建立了整个序列的全局收敛和局部收敛率。我们还为生成序列的有界性提供了充分条件。最后,进行了一些数值实验,将DYS算法与一些经典有效的稀疏信号恢复和低秩矩阵完成算法进行了比较。数值结果表明 DYS 优于这些应用的现有方法。
更新日期:2021-08-07
down
wechat
bug