Optimization methods for regularization-based ill-posed problems： a survey and a multi-objective framework  

作　　者：Maoguo GONG Xiangming JIANG Hao LI 

机构地区：[1]Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi'an 710071, China

出　　处：《Frontiers of Computer Science》2017年第3期362-391,共30页中国计算机科学前沿（英文版）

摘　　要：Ill-posed problems are widely existed in signat processing. In this paper, we review popular regularization models such as truncated singular value decomposi- tion regularization, iterative regularization, variational regularizafion. Meanwhile, we also retrospect popular optimiza- tion approaches and regularization parameter choice meth- ods. In fact, the regularization problem is inherently a multi- objective problem. The traditional methods usually combine the fidelity term and the regularization term into a single- objective with regularization parameters, which are difficult to tune. Therefore, we propose a multi-objective framework for ill-posed problems, which can handle complex features of problem such as non-convexity, discontinuity. In this framework, the fidelity term and regularization term are optimized simultaneously to gain more insights into the ill-posed prob- lems. A case study on signal recovery shows the effectiveness of the multi-objective framework for ill-posed problems.Ill-posed problems are widely existed in signat processing. In this paper, we review popular regularization models such as truncated singular value decomposi- tion regularization, iterative regularization, variational regularizafion. Meanwhile, we also retrospect popular optimiza- tion approaches and regularization parameter choice meth- ods. In fact, the regularization problem is inherently a multi- objective problem. The traditional methods usually combine the fidelity term and the regularization term into a single- objective with regularization parameters, which are difficult to tune. Therefore, we propose a multi-objective framework for ill-posed problems, which can handle complex features of problem such as non-convexity, discontinuity. In this framework, the fidelity term and regularization term are optimized simultaneously to gain more insights into the ill-posed prob- lems. A case study on signal recovery shows the effectiveness of the multi-objective framework for ill-posed problems.

关 键 词：ill-posed problem REGULARIZATION multi- objective optimization evolutionary algorithm signal processing 

分 类 号：O177.6[理学—数学] TP391.41[理学—基础数学]