Technion, IEM faculty - Operations Research seminar
 
Speaker: Yakov Vaisbourd
 
Title: The Chebyshev Center Approach for Image Deblurring Applications
 
Date: 30/01/2012
 
Time: 12:30
 
Place: Bloomfield-527
 
Abstract:  <http://ie.technion.ac.il/seminar_files/1326967697_Yakov_Vaisbourd_seminar.doc>
 
Or read it here:
 
We consider the problem of reconstructing an image from a blurred and noisy representation.
We apply the Chebyshev center approach for finding regularized solution 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 bisection or 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 according to the relative error measure.
 
This talk is based on a research thesis under the supervision of Prof. Amir Beck.
 
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