Español, Malena I. and Kilmer, Misha E. (2010) Multilevel Approach For Signal Restoration Problems With Toeplitz Matrices. SIAM Journal on Scientific Computing, 32 (1). pp. 299-319. ISSN 1064-8275 http://resolver.caltech.edu/CaltechAUTHORS:20100630-140856206
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We present a multilevel method for discrete ill-posed problems arising from the discretization of Fredholm integral equations of the first kind. In this method, we use the Haar wavelet transform to define restriction and prolongation operators within a multigrid-type iteration. The choice of the Haar wavelet operator has the advantage of preserving matrix structure, such as Toeplitz, between grids, which can be exploited to obtain faster solvers on each level where an edge-preserving Tikhonov regularization is applied. Finally, we present results that indicate the promise of this approach for restoration of signals and images with edges.
|Additional Information:||© 2010 Society for Industrial and Applied Mathematics. Received by the editors February 15, 2008; accepted for publication (in revised form) May 20, 2009; published electronically February 5, 2010. We thank Scott MacLachlan and the two anonymous reviewers for their careful reading of the manuscript and for valuable comments and suggestions that helped to improve the paper.|
|Subject Keywords:||ill-posed problems, multilevel, regularization, Haar wavelets, signal restoration|
|Classification Code:||AMS subject classifications: 65F10, 65F22, 65F50|
|Official Citation:||Multilevel Approach For Signal Restoration Problems With Toeplitz Matrices Malena I. Espanol and Misha E. Kilmer, SIAM J. Sci. Comput. 32, 299 (2010), DOI:10.1137/080715780|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Jason Perez|
|Deposited On:||06 Jul 2010 15:40|
|Last Modified:||26 Dec 2012 12:11|
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