Image Processing

Iterative regularized least-mean mixed-norm image restoration

[+] Author Affiliations
Min-Cheol Hong

Soongsil University, School of Electronic Engineering, Seoul, Korea E-mail: mhong@e.ssu.ac.kr

Tania Stathaki

Imperial College, Signal Processing and Digital System Section, London, United Kingdom E-mail: t.stathaki@ic.ac.uk

Aggelos K. Katsaggelos

Northwestern University, McCormick School of Engineering and Applied Science, Department of Electrical and Computer Engineering, Evanston, Illinois?60208 E-mail: aggk@ece.nwu.edu

Opt. Eng. 41(10), 2515-2524 (Oct 01, 2002). doi:10.1117/1.1503072
History: Received Mar. 30, 2001; Revised Feb. 27, 2002; Accepted Mar. 13, 2002; Online September 20, 2002
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We develop a regularized mixed-norm image restoration algorithm to deal with various types of noise. A mixed-norm functional is introduced, which combines the least mean square (LMS) and the least mean fourth (LMF) functionals, as well as a smoothing functional. Two regularization parameters are introduced: one to determine the relative importance of the LMS and LMF functionals, which is a function of the kurtosis, and another to determine the relative importance of the smoothing functional. The two parameters are chosen in such a way that the proposed functional is convex, so that a unique minimizer exists. An iterative algorithm is utilized for obtaining the solution, and its convergence is analyzed. The novelty of the proposed algorithm is that no knowledge of the noise distribution is required, and the relative contributions of the LMS, the LMF, and the smoothing functionals are adjusted based on the partially restored image. Experimental results demonstrate the effectiveness of the proposed algorithm. © 2002 Society of Photo-Optical Instrumentation Engineers.

© 2002 Society of Photo-Optical Instrumentation Engineers

Citation

Min-Cheol Hong ; Tania Stathaki and Aggelos K. Katsaggelos
"Iterative regularized least-mean mixed-norm image restoration", Opt. Eng. 41(10), 2515-2524 (Oct 01, 2002). ; http://dx.doi.org/10.1117/1.1503072


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