Open AccessCharacterization of the Solution of Linear Inverse Problems with Generalized TV Regularization
Author(s) -
Michaël Unser
Publication year - 2016
Publication title -
imaging and applied optics
Language(s) - English
Resource type - Conference proceedings
DOI - 10.1364/math.2016.mw5h.1
Subject(s) - regularization (linguistics) , inverse problem , mathematics , spline (mechanical) , differential operator , inverse , total variation denoising , backus–gilbert method , operator (biology) , inverse scattering problem , mathematical analysis , mathematical optimization , computer science , tikhonov regularization , regularization perspectives on support vector machines , physics , geometry , artificial intelligence , biochemistry , chemistry , repressor , transcription factor , gene , image (mathematics) , thermodynamics
Ill-posed inverse problems are often constrained by imposing a bound on the total variation of the solution. Here, we consider a generalized version of total-variation regularization that is tied to some differential operator L. We then show that the general form of the solution is a nonuniform L-spline with fewer knots than the number of measurements.
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