Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Regularization, Bayesian Inference and Machine Learning methods for Inverse Problems†

Version 1 : Received: 1 November 2021 / Approved: 3 November 2021 / Online: 3 November 2021 (20:18:51 CET)

How to cite: Mohammad-Djafari, A. Regularization, Bayesian Inference and Machine Learning methods for Inverse Problems†. Preprints 2021, 2021110092 (doi: 10.20944/preprints202111.0092.v1). Mohammad-Djafari, A. Regularization, Bayesian Inference and Machine Learning methods for Inverse Problems†. Preprints 2021, 2021110092 (doi: 10.20944/preprints202111.0092.v1).

Abstract

Classical methods for inverse problems are mainly based on regularization theory. In particular those which are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond, respectively, to the likelihood and prior probability models.

Keywords

Inverse problems; Regularization; Bayesian inference; Machine Learning; Artificial Intelligence; Gauss-Markov-Potts; Variational Bayesian Approach (VBA); Physics Informed ML

Subject

MATHEMATICS & COMPUTER SCIENCE, Computational Mathematics

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