Regularized Wavelets for Solving Inverse Ill-Posed Problems

机译：解决逆病态问题的正则小波

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This paper describes regularized wavelets and numerical algorithms for a regularized wavelet-analysis based on the bayes strategy. This program includes the investigation of a possibility for finding a basis in terms of a multiresolution analysis under condition that a scaling function would satisfy the properties of a regularization operator and an orthonormal basis simultaneously. Examples of application of the regularized wavelets in the differentiation of composite simulated spectra with a fractal noise are considered.

机译：本文介绍了基于Bayes策略的正则小波分析的正则小波和数值算法。该程序包括调查在缩放函数同时满足正则化运算符和正交基准的条件下，根据多分辨率分析寻找基础的可能性。考虑了正则小波在具有分形噪声的合成模拟光谱的微分中的应用示例。

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《Bayesian Inference and Maximum Entropy Methods in Science and Engineering》|2001年|p.259-269|共11页
会议地点 Baltimore MD(US)
作者
Kharintsev S.S.; Salakhov M.Kh.;
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作者单位

Physics Department, Kazan State University Kremlevskaya str. 16, Kazan, Russia, 420008;

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原文格式 PDF
正文语种 eng
中图分类科学、科学研究;
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专利

1. 求解病态问题的一种改进的Tikhonov正则化--(1)正则化方法的建立 [J] . 王家军, 李功胜数学季刊（英文版） . 2000,第002期
2. Regularization of the ill-posed problem of extrapolation with the Malvar-Wilson wavelets [J] . K Drouiche, D Kateb, C Noiret Inverse Problems: An International Journal of Inverse Problems, Inverse Methods and Computerised Inversion of Data . 2001,第5期

机译：Malvar-Wilson小波对不适定外推问题的正则化
3. Convergence of regularization methods with filter functions for a regularization parameter chosen with GSURE and mildly ill-posed inverse problems [J] . Journal of Computational and Applied Mathematics . 2020,第期

机译：具有滤波器函数的正规化方法的融合，用于使用GSURE和轻微不良逆问题选择的正则化参数
4. Some remarks about utilization of wavelets for solving ill-posed problems [J] . HANDROCK-MEYER S. Zeitschrift fur Angewandte Mathematik und Mechanik . 1996,第S4期

机译：关于利用小波解决不适定问题的一些评论
5. Regularized wavelets for solving inverse Ill-posed problems [C] . Kharintsev S. S., Salakhov M. Kh. International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering . 2002

机译：解决逆出不良问题的正则小波
6. Total variation regularization for linear ill-posed inverse problems: Extensions and applications. [D] . Stefan, Wolfgang. 2008

机译：线性不适定反问题的总变化正则化：扩展和应用。
7. Physics-driven Spatiotemporal Regularization for High-dimensional Predictive Modeling: A Novel Approach to Solve the Inverse ECG Problem [O] . Bing Yao, Hui Yang -1

机译：物理驱动的时空正则化以进行高维预测建模：一种解决心电逆问题的新方法
8. Complex wavelet regularization for solving inverse problems in remote sensing [O] . Carlavan Mikael, Weiss Pierre, Blanc-Féraud Laure, 2009

机译：复杂小波正则化解决遥感反问题
9. Smoothing, Regularization and Ill-Posed Inverse Problems; Robust and Convex Estimation of Functions of Several Variables [R] . Wahba, G. 1983

机译：平滑，正则化和不适当的反问题;几个变量函数的鲁棒与凸估计

Regularized Wavelets for Solving Inverse Ill-Posed Problems

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