Deblurring with Framelets in the Sparse Analysis Setting




Danniels, Travis

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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.



image processing, inverse problems, deblurring, convex optimization, sparsity, wavelets