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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 CVPR 2009 報告者：黃智勇 2017/4/6

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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 2017/4/6

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Introduction 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. 2017/4/6

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Tight famelet system 2017/4/6

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**Sparse representation under framelet and curvelet system**

2017/4/6

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**Formulation of our minimization**

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. 2017/4/6

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**Numerical algorithm and analysis**

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. 2017/4/6

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**Numerical algorithm and analysis**

2017/4/6

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Experiments 2017/4/6

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Experiments 2017/4/6

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Experiments 2017/4/6

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