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

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Wacker PK, Knabner P
Zeitschrift: Methodology and Computing in Applied Probability
Jahr der Veröffentlichung: 2019
Seitenbereich: 1-27
ISSN: 1387-5841


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.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Knabner, Peter Prof. Dr.
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)
Wacker, Philipp Konstantin Dr.
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)


Zitierweisen

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, 1-27. 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 (2019): 1-27.

BibTeX: 

Zuletzt aktualisiert 2019-02-08 um 12:38