## Selection of regularization parameter in total variation image restoration

JOSA A, Vol. 26, Issue 11, pp. 2311-2320 (2009)

http://dx.doi.org/10.1364/JOSAA.26.002311

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### Abstract

We consider and study total variation (TV) image restoration. In the literature there are several regularization parameter selection methods for Tikhonov regularization problems (e.g., the discrepancy principle and the generalized cross-validation method). However, to our knowledge, these selection methods have not been applied to TV regularization problems. The main aim of this paper is to develop a fast TV image restoration method with an automatic selection of the regularization parameter scheme to restore blurred and noisy images. The method exploits the generalized cross-validation (GCV) technique to determine inexpensively how much regularization to use in each restoration step. By updating the regularization parameter in each iteration, the restored image can be obtained. Our experimental results for testing different kinds of noise show that the visual quality and SNRs of images restored by the proposed method is promising. We also demonstrate that the method is efficient, as it can restore images of size

© 2009 Optical Society of America

**OCIS Codes**

(100.1830) Image processing : Deconvolution

(100.2000) Image processing : Digital image processing

(100.3020) Image processing : Image reconstruction-restoration

**ToC Category:**

Image Processing

**History**

Original Manuscript: April 8, 2009

Revised Manuscript: August 13, 2009

Manuscript Accepted: September 8, 2009

Published: October 9, 2009

**Citation**

Haiyong Liao, Fang Li, and Michael K. Ng, "Selection of regularization parameter in total variation image restoration," J. Opt. Soc. Am. A **26**, 2311-2320 (2009)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-11-2311

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