Wavelet-Based Priors Accelerate Maximum-a-Posteriori Optimization in Bayesian Inverse Problems

Wacker PK, Knabner P (2019)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2019

Journal

Methodology and Computing in Applied Probability Springer Verlag (Germany)

Book Volume: 22

Pages Range: 853-879

DOI: 10.1007/s11009-019-09736-2

Abstract

Wavelet (Besov) priors are a promising way of reconstructing indirectly measured fields in a regularized manner. We demonstrate how wavelets can be used as a localized basis for reconstructing permeability fields with sharp interfaces from noisy pointwise pressure field measurements in the context of the elliptic inverse problem. For this we derive the adjoint method of minimizing the Besov-norm-regularized misfit functional (this corresponds to determining the maximum a posteriori point in the Bayesian point of view) in the Haar wavelet setting. As it turns out, choosing a wavelet–based prior allows for accelerated optimization compared to established trigonometrically–based priors.

Authors with CRIS profile

Philipp Konstantin Wacker Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

How to cite

APA:

Wacker, P.K., & Knabner, P. (2019). Wavelet-Based Priors Accelerate Maximum-a-Posteriori Optimization in Bayesian Inverse Problems. Methodology and Computing in Applied Probability, 22, 853-879. https://dx.doi.org/10.1007/s11009-019-09736-2

MLA:

Wacker, Philipp Konstantin, and Peter Knabner. "Wavelet-Based Priors Accelerate Maximum-a-Posteriori Optimization in Bayesian Inverse Problems." Methodology and Computing in Applied Probability 22 (2019): 853-879.

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