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

Philipp Wacker () and Peter Knabner
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Philipp Wacker: Friedrich-Alexander-Universität Erlangen-Nürnberg
Peter Knabner: Friedrich-Alexander-Universität Erlangen-Nürnberg

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 3, 853-879

Abstract: 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.

Keywords: Bayesian inverse problems; Besov priors; Optimization; Elliptical inverse problem; 65M32; 62F15; 65K10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-019-09736-2

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