On the Kantorovich Theorem and the Regularization of Total Variation Denoising Problems

Published

August 2, 2010

Author(s)

Anthony J. Kearsley, Luis A. Melara

Abstract

Total variation methods are an optimization-based approach for solving image restoration problems. The mathematical formulation results in an equality constrained optimization problem. A solution to this optimization problem can be obtained using Newton's method. This note is motivated by the numerical results of an augmented Lagrangian homotopy method for the regularization of total variation problems. The numerical technique uses the regularization parameter as a homotopy parameter which is reduced to zero. As a result, a sequence of equality constrained optimization problems is solved using Newton's method. In this report the convergence of an augmented Lagrangian homotopy method for total variation minimization is addressed. We present a relationship between the homotopy parameter and the radius of the Kantorovich ball.

Citation

Rocky Mountain Journal of Mathematics

Volume

40

Issue

2

Pub Type

Journals

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Keywords

Total variation, Newton's Method, augmented Lagrangian

Citation

Kearsley, A. and Melara, L. (2010), On the Kantorovich Theorem and the Regularization of Total Variation Denoising Problems, Rocky Mountain Journal of Mathematics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=152148 (Accessed October 20, 2025)