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Gong, Maoguo; Jiang, Xiangming; Li, Hao

Optimization methods for regularization-based ill-posed problems: a survey and a multi-objective framework. (English) Zbl 1405.94024

Front. Comput. Sci. 11, No. 3, 362-391 (2017).
Summary: 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.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
90C29 Multi-objective and goal programming
90C59 Approximation methods and heuristics in mathematical programming

Keywords:

ill-posed problem; regularization; multi-objective optimization; evolutionary algorithm; signal processing

Software:

UTV; LSMR; PDCO; TwIST; NESTA; NSGA-II; MOEA/D; SPEA2
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Full Text: DOI

References:

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