Parameter Choice by Fast Balancing
Frank Bauer
TL;DR
This paper introduces a fast Lepskij balancing principle for selecting regularization parameters in inverse problems, effective under deterministic and stochastic noise conditions, improving computational efficiency.
Contribution
It presents a novel, faster version of the Lepskij balancing method for Tikhonov regularization, applicable in various noise regimes.
Findings
Validates the method for deterministic noise
Effective in stochastic noise scenarios
Reduces computational complexity
Abstract
Choosing the regularization parameter for inverse problems is of major importance for the performance of the regularization method. We will introduce a fast version of the Lepskij balancing principle and show that it is a valid parameter choice method for Tikhonov regularization both in a deterministic and a stochastic noise regime as long as minor conditions on the solution are fulfilled.
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Taxonomy
TopicsNumerical methods in inverse problems · Structural Health Monitoring Techniques · Electrical and Bioimpedance Tomography