.png){kind=icon}
返回
A FRAMEWORK FOR REGULARIZATION VIA OPERATOR APPROXIMATION
.png){kind=icon}
PRE
AI
DOI：10.1137/130945363.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
Regularization approaches based on spectral filtering can be highly effective in solving ill-posed inverse problems. These methods, however, require computing the singular value decomposition (SVD) and choosing appropriate regularization parameters. These tasks can be prohibitively expensive for large-scale problems. In this paper, we present a framework that uses operator approximations to efficiently obtain good regularization parameters without an SVD of the original operator. Instead, we approximate the original operator with a nearby structured or separable one whose SVD is easily computable. Highly effective methods can then be used to efficiently compute good regularization parameters for the nearby problem. Then, we solve the original problem iteratively using the regularization determined for the approximate problem. A variety of regularization approaches can be incorporated into this framework, but we focus here on the recently developed windowed regularization, a generalization of Tikhonov regularization in which different regularization parameters are used in different regions of the spectrum. We derive bounds on the perturbation to the computed solution and residual resulting from using the regularization determined for the approximate operator. We demonstrate the effectiveness of our method in computations using operator approximations such as sums of Kronecker products, block circulant with circulant blocks matrices, and Krylov subspace approximations.
Keyword:
singular value decomposition
Tikhonov regularization
inverse problem
ill-posed
deconvolution
Kronecker approximation
spectral filter
Golub-Kahan
parameter selection
hybrid iterative methods
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
2.6
论文数:
5.1K
被引数:
1.8W
机构
引用论文
.png){kind=icon}
分享收藏Photoelectrocatalytic activity PbO2 loaded highly oriented TiO2 nanotubes arrays光电催化活性PbO2负载高取向TiO2纳米管阵列
PREAI
分享收藏
查看更多内容