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Blind motion deblurring from a single image using sparse approximation Jian-Feng Caiy, Hui Jiz, Chaoqiang Liuy and Zuowei Shenz National University of Singapore, Singapore Center for Wavelets, Approx. and Info. Proc.y and Department of Mathematicsz 2014/10/101 報告者：黃智勇 CVPR 2009

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Outline Introduction Tight framelet system and curvelet system Sparse representation under framelet and curvelet system Formulation of our minimization Numerical algorithm and analysis Experiments 2014/10/102

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Introduction 3 We propose to use framelet system (Ron and Shen et al. [24]) to find the sparse approximation to the image under framelet domain. We use the curvelet system (Candes and Donoho [8]) to find the sparse approximation to the blur kernel under curvelet domain.

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Tight famelet system 2014/10/104

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Sparse representation under framelet and curvelet system 2014/10/105

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Formulation of our minimization 2014/10/10 6 We denote the image g (or the kernel p) as a vector g (or p). Let “ 。 ” denote the usual 2D convolution after column concatenation, then we have Let u = Ag denote the framelet coefficients of the clear image g, and let v = Cp denote the curvelet coefficients of the blur kernel p.

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Numerical algorithm and analysis 2014/10/107 there exist only two difficult problems (14) and (15) of the same type. For such a large-scale minimization problem with up to millions of variables, there exists a very efficient algorithm based on so-called linearized Bregman iteration technique.

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Numerical algorithm and analysis 2014/10/108

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Experiments 9

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Experiments 10

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Experiments 2014/10/1011

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