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The residual method for regularizing ill-posed problems

Applied Mathematics and Computation, 2011
Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov regularization, where a series of new results for regularization in Banach spaces has been published in the recent years.
Markus Grasmair, Markus Haltmeier, Otmar Scherzer +2 more
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On the Optimality of Methods for Ill-Posed Problems

Zeitschrift für Analysis und ihre Anwendungen, 1987
The optimality of a class of regularization methods for linear ill-posed problems is investigated. The general results are applied to Lavrentjew’s and Tikhonov’s methods and to a class of iteration methods and their continuous versions.
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Projection Methods for Ill-Posed Problems Revisited [PDF]

Computational Methods in Applied Mathematics, 2015
Abstract We consider the discretization of least-squares problems for linear ill-posed operator equations in Hilbert spaces. The main subject of this article concerns conditions for convergence of the associated discretized minimum-norm least-squares solution to the exact solution using exact attainable data.
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Ill-posed analysis of time-domain deconvolution identification of ice load on the shell structures of ice-going vessels. [PDF]

Sci Rep
Kong S, Lei J.
europepmc +1 more source

Input Layer Regularization and Automated Regularization Hyperparameter Tuning for Myelin Water Estimation Using Deep Learning. [PDF]