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Inverse Problems and Imaging (IPI)
 

Iterative choice of the optimal regularization parameter in TV image restoration

Pages: 1171 - 1191, Volume 9, Issue 4, November 2015      doi:10.3934/ipi.2015.9.1171

 
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Alina Toma - CREATIS, CNRS UMR 5220; INSERM U1044; INSA de Lyon; Université de Lyon 1, Université de Lyon, 69621, Villeurbanne Cedex, France (email)
Bruno Sixou - CREATIS, CNRS UMR 5220; INSERM U1044; INSA de Lyon; Université de Lyon 1, Université de Lyon, 69621, Villeurbanne Cedex, France (email)
Françoise Peyrin - CREATIS, CNRS UMR 5220; INSERM U1044; INSA de Lyon; Université de Lyon 1, Université de Lyon, 69621, Villeurbanne Cedex, France (email)

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.

Keywords:  Linear inverse problems, total variation regularization, regularization parameter, Morozov principle, UPRE.
Mathematics Subject Classification:  Primary: 65J22, 65J20, 65K10; Secondary: 52A41.

Received: June 2014;      Revised: April 2015;      Available Online: October 2015.

 References