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

  • Philipp WackerEmail author
  • Peter Knabner


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.


Bayesian inverse problems Besov priors Optimization Elliptical inverse problem 

Mathematics Subject Classification (2010)

65M32 62F15 65K10 


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P.W. is thankful for a fruitful discussion with Youssef Marzouk, a very helpful email from Donald Estep and in particular for the guidance of Claudia Schillings which ultimately led to the idea of this paper.


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Authors and Affiliations

  1. 1.Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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