Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Regularizing Inverse Preconditioners for Symmetric Band Toeplitz Matrices | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2007 Article ID 85606 9 pages doi 2007 85606 Research Article Regularizing Inverse Preconditioners for Symmetric Band Toeplitz Matrices P. Favati 1 G. Lotti 2 and O. Menchi3 1 Istituto di Informatica e Telematica IIT CNR Via G. Moruzzi 1 56124 Pisa Italy 2 Dipartimento di Matematica Universita di Parma Parco Area delle Scienze 53 A 43100 Parma Italy 3 Dipartimento di Informatica Universita di Pisa Largo Pontecorvo 3 56127 Pisa Italy Received 22 September 2006 Revised 31 January 2007 Accepted 16 March 2007 Recommended by Paul Van Dooren Image restoration is a widely studied discrete ill-posed problem. Among the many regularization methods used for treating the problem iterative methods have been shown to be effective. In this paper we consider the case of a blurring function defined by space invariant and band-limited PSF modeled by a linear system that has a band block Toeplitz structure with band Toeplitz blocks. In order to reduce the number of iterations required to obtain acceptable reconstructions in 1 an inverse Toeplitz preconditioner for problems with a Toeplitz structure was proposed. The cost per iteration is of O n2 log n operations where n2 is the pixel number of the 2D image. In this paper we propose inverse preconditioners with a band Toeplitz structure which lower the cost to O n2 and in experiments showed the same speed of convergence and reconstruction efficiency as the inverse Toeplitz preconditioner. Copyright 2007 P. Favati et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. INTRODUCTION Many image restoration problems can be modeled by the linear system Ax b - w 1 where x b and w represent the original image the observed image and the noise respectively. Matrix A is defined by the .
