Deblurring with Framelets in the Sparse Analysis Setting
Date
2013-12-23
Authors
Danniels, Travis
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Abstract
In this thesis, algorithms for blind and non-blind motion deblurring
of digital images are proposed. The non-blind algorithm is based on a convex program
consisting of a data fitting term and a sparsity-promoting regularization term.
The data fitting term is the squared l_2 norm of the residual between the blurred image
and the latent image convolved with a known blur kernel.
The regularization term
is the l_1 norm of the latent image under a wavelet frame (framelet) decomposition.
This convex program is solved with the first-order primal-dual algorithm proposed by Chambolle and Pock. The proposed blind deblurring algorithm
is based on the work of Cai, Ji, Liu, and Shen.
It works by embedding the proposed non-blind algorithm in an alternating minimization scheme
and imposing additional constraints in order
to deal with the challenging non-convex nature of the blind deblurring problem.
Numerical experiments are performed on artificially and naturally blurred images,
and both proposed algorithms are found to be competitive with recent deblurring methods.
Description
Keywords
image processing, inverse problems, deblurring, convex optimization, sparsity, wavelets