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

被引:0
作者
Maoguo Gong
Xiangming Jiang
Hao Li
机构
[1] Xidian University,Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education
来源
Frontiers of Computer Science | 2017年 / 11卷
关键词
ill-posed problem; regularization; multi-objective optimization; evolutionary algorithm; signal processing;
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中图分类号
学科分类号
摘要
Ill-posed problems are widely existed in signal processing. In this paper, we review popular regularization models such as truncated singular value decomposition regularization, iterative regularization, variational regularization. Meanwhile, we also retrospect popular optimization approaches and regularization parameter choice methods. 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 problems. A case study on signal recovery shows the effectiveness of the multi-objective framework for ill-posed problems.
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页码:362 / 391
页数:29
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