Department of Mathematics
Approximation BFGS methods for nonlinear image restoration
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 (n log n) 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. © 2008 Elsevier B.V. All rights reserved.
Nonlinear image restoration, Optimization, Regularization
Source Publication Title
Journal of Computational and Applied Mathematics
Link to Publisher's Edition
Lu, L., Ng, M., & Lin, F. (2009). Approximation BFGS methods for nonlinear image restoration. Journal of Computational and Applied Mathematics, 226 (1), 84-91. https://doi.org/10.1016/j.cam.2008.05.056