Approximation BFGS methods for nonlinear image restoration

Authors:
Lin-Zhang Lu;Michael K. Ng;Fu-Rong Lin
Affiliations:
School of Mathematics and Computer Science, Guizhou Normal University, PR China and School of Mathematical Science, Xiamen University, PR China;Centre for Mathematical Imaging and Vision, Hong Kong Baptist University, Kowloon Tong, Hong Kong and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong;Department of Mathematics, Shantou University, Shantou, Guangdong 515063, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

We consider the iterative solution of unconstrained minimization problems arising from nonlinear image restoration. Our approach is based on a novel generalized BFGS method for such large-scale image restoration minimization problems. The complexity per step of the method is of O(nlogn) operations and only O(n) memory allocations are required, where n is the number of image pixels. Based on the results given in [Carmine Di Fiore, Stefano Fanelli, Filomena Lepore, Paolo Zellini, Matrix algebras in quasi-Newton methods for unconstrained minimization, Numer. Math. 94 (2003) 479-500], we show that the method is globally convergent for our nonlinear image restoration problems. Experimental results are presented to illustrate the effectiveness of the proposed method.