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...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.展开更多
文摘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.
