Noise level free regularisation of general linear inverse problems under unconstrained white noise
Numerical Analysis
2023-01-12 v3 Numerical Analysis
Abstract
In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian) noise is controlled via introducing an auxiliary discretisation dimension and choosing it in an adaptive fashion. We first show convergence for completely arbitrary compact forward operator and ground solution. Then the uncertainty of reaching the optimal convergence rate is quantified in a specific Bayesian-like environment.
Keywords
Cite
@article{arxiv.2207.05997,
title = {Noise level free regularisation of general linear inverse problems under unconstrained white noise},
author = {Tim Jahn},
journal= {arXiv preprint arXiv:2207.05997},
year = {2023}
}
Comments
25 pages, 8 tables