We consider a statistical inversion computational model with Gaussian distributions for the numerical solution of the Cauchy problem for the Laplace equation. The a priori model is built up from Gaussian Markov random fields. Different precision matrices for the Cauchy problem are introduced. We take advantage of the relationship between the a priori distribution and traditional Tikhonov regularization to propose different models where smooth and non-smooth regularization is possible. A low range analysis allow us to estimate the optimal dimension of data and its relation to the the unknown.

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Published on 01/07/21 Accepted on 01/07/21 Submitted on 01/07/21

Volume CT10 - Optimization and Inverse Problems, 2021 DOI: 10.23967/admos.2021.064 Licence: CC BY-NC-SA license