Wacker PK, Knabner P (2019)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2019
Book Volume: 22
Pages Range: 853-879
DOI: 10.1007/s11009-019-09736-2
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.
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://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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