Numeric Solutions of Eigenvalue Problems for Generic Nonlinear Operators

09/12/2019

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by   Ester Hait-Fraenkel, et al.

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Numerical methods for solving linear eigenvalue problem are widely studiedand used in science and engineering. In this paper, we propose a generalizednumerical method for solving eigenproblems for generic, nonlinear opera-tors. This has potentially wide implications, since most image processingalgorithms (e.g. denoising) can be viewed as nonlinear operators, whoseeigenproblem analysis provides information on the most- and least-suitablefunctions as input. We solve the problem by a nonlinear adaptation of thepower method, a well known linear eigensolver. An analysis and valida-tion framework is proposed, as well as preliminary theory. We validate themethod using total-variation (TV) and demonstrate it on the EPLL denoiser(Zoran-Weiss). Finally, we suggest an encryption-decryption application.