An adaptive augmented regularization method and its applications

Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP estimates of posterior probability distributions. Considering th...

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Bibliographic Details
Published inarXiv.org
Main Authors Jia, Junxiong, Sun, Qihang, Wu, Bangyu, Peng, Jigen
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.06.2019
Subjects
Bayesian analysis
Conditional probability
Inverse method
Inverse problems
Iterative algorithms
Iterative methods
Mathematical models
Medical imaging
Regularization
Regularization methods
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Summary:Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP estimates of posterior probability distributions. Considering this connection, we construct a prior probability distribution with several hyper-parameters and provide the relevant Bayes' formula, then we propose a corresponding adaptive augmented regularization model (AARM). According to the measured data, the proposed AARM can adjust its form to various regularization models at each discrete point of the estimated function, which makes the characterization of local smooth properties of the estimated function possible. By proposing a modified Bregman iterative algorithm, we construct an alternate iterative algorithm to solve the AARM efficiently. In the end, we provide some numerical examples which clearly indicate that the proposed AARM can generates a favorable result for some examples compared with several Tikhonov and Total-Variation regularization models.
ISSN:2331-8422