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On the existence of a variational regularization parameter under Morozov's discrepancy principle for nonlinear inverse problems
Journal article   Peer reviewed

On the existence of a variational regularization parameter under Morozov's discrepancy principle for nonlinear inverse problems

Liang Ding, Long Li, Weimin Han and Wei Wang
Inverse problems and imaging (Springfield, Mo.), Vol.22, pp.178-198
2026
DOI: 10.3934/ipi.2025049

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Abstract

Morozov’s discrepancy principle is commonly adopted in Tikhonov regularization for choosing the regularization parameter. Nevertheless, for a general nonlinear inverse problem, the discrepancy ∥F (xδ α) − yδ ∥Y does not depend continuously on α and it is questionable whether there exists a regularization parameter α such that τ1δ ≤ ∥F (xδ α) − yδ ∥Y ≤ τ2δ (1 ≤ τ1 < τ2). In this paper, we prove the existence of α under Morozov’s discrepancy principle if τ2 ≥ (3 + 2γ)τ1 or τ1 ≤ τ2/(3 + 2γ), where γ > 0 is a parameter in a tangential cone condition for the nonlinear operator F . Furthermore, we present results on the convergence of the regularized solutions under Morozov’s discrepancy principle. Numerical results are reported on the efficiency of the proposed approach
 Non-linear inverse problem Morozov's discrepancy principle tangential cone condition convex penalty

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