Iterative choice of the optimal regularization parameter in TV image restoration

Alina  Toma; Bruno  Sixou; Françoise  Peyrin

doi:10.3934/ipi.2015.9.1171

Article Contents

2015, Volume 9, Issue 4: 1171-1191. Doi: 10.3934/ipi.2015.9.1171

This issue Previous Article Bilevel optimization for calibrating point spread functions in blind deconvolution Next Article

Iterative choice of the optimal regularization parameter in TV image restoration

1.
CREATIS, CNRS UMR 5220; INSERM U1044; INSA de Lyon; Université de Lyon 1, Université de Lyon, 69621, Villeurbanne Cedex

Received: May 31, 2014

Revised: March 31, 2015

Published: October 2015

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Abstract

We present iterative methods for choosing the optimal regularization parameter for linear inverse problems with Total Variation regularization. This approach is based on the Morozov discrepancy principle or on a damped version of this principle and on an approximating model function for the data term. The theoretical convergence of the method of choice of the regularization parameter is demonstrated. The choice of the optimal parameter is refined with a Newton method. The efficiency of the method is illustrated on deconvolution and super-resolution experiments on different types of images. Results are provided for different levels of blur, noise and loss of spatial resolution. The damped Morozov discrepancy principle often outerperforms the approaches based on the classical Morozov principle and on the Unbiased Predictive Risk Estimator. Moreover, the proposed methods are fast schemes to select the best parameter for TV regularization.

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Mathematics Subject Classification: Primary: 65J22, 65J20, 65K10; Secondary: 52A41.

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