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The Bayesian Approach to Inverse Problems: Computational Aspects

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If you have a question about this talk, please contact Carola-Bibiane Schoenlieb.

In the second talk, I want to discuss some practical aspects of Bayesian inference applied to inverse problems. As an exemplary application, I will consider solving high-dimensional inverse problems using sparsity constraints as a-priori information, e.g., the well-known total variation (TV) minimization constraint. After explaining the basic principles and algorithms of Markov chain Monte Carlo (MCMC) based posterior inference, I will show that contrary to what is commonly believed about the applicability of MCMC schemes, they are not in general slow and scale bad with increasing dimension. In addition, I will outline why I think that designing efficient optimization and sampling techniques is conceptually similar, and highlight some recent work on enhancing sampling by incorporating ideas from optimization.

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This talk is part of the Bayesian approach in inverse problems series.

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