Multilevel Methods for Image Deblurring

When
Start: 11/04/2010 - 4:15pm
End  : 11/04/2010 - 5:15pm

Category
Statistics/OR/Math Finance Seminar

Speaker
Malena Espanol, CalTech

Abstract

In this talk, I will introduce multilevel methods for discrete ill-posed problems arising from the discretization of Fredholm integral equations of the first kind. In particular, I will present wavelet-based multilevel methods for signal and image restoration problems as well as for blind deconvolution problems. In these methods, orthogonal wavelet transforms are used 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. I will show results that indicate the promise of these approaches on restoration of signals and images with edges as well as restoration of blurring operator in the case of the blind deconvolution problem.

This is joint work Misha Kilmer.

Where
Harvey Mudd College 3rd floor Sprague. Refreshments at 4pm.