|M.Sc Student||Vaisbourd Yakov|
|Subject||The Chebyshev Center Approach for Image Deblurring|
|Department||Department of Industrial Engineering and Management||Supervisor||Professor Amir Beck|
|Full Thesis text|
We consider the problem of reconstructing an image from a blurred and noisy representation. We apply the Chebyshev center approach for finding regularized solutions to image deblurring problems. This approach aims to minimize the norm of the estimation error rather than the norm of the data error. Clearly, it is not possible to minimize the estimation error directly as the true image is unknown. Instead, the Chebyshev center approach suggests to minimize the maximal estimation error for all the solutions that reside in the so-called feasible parameter set.
Usually, an image will be of a very large size, a fact that prevents the possibility of applying a conventional solver to solve the arising optimization problem. We use spectral decomposition methods combined with a bisection or an ellipsoid method in order to solve the minimization problems proposed for finding the Chebyshev center. We propose to apply a redundant constraint removal technique to reduce the complexity of the optimization problems solved by the ellipsoid algorithm. Finally, we provide numerical comparisons with the Tikhonov regularization solution based on several well-established parameter choice methods such as the discrepancy principal, regularized least squares (RLS), generalized cross validation (GCV) and the l-curve criterion. We show that the proposed approach can significantly improve the reconstruction quality in terms of the relative error.