Blind motion deblurring from a single Blind motion deblurring from a single image using sparse approximationimage using sparse approximation

Jian-Feng Caiy, Hui Jiz, Chaoqiang Liuy and Zuowei ShenzNational University of Singapore, Singapore 117542

Center for Wavelets, Approx. and Info. Proc.y and Department of Mathematicsz

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報告者：黃智勇

CVPR 2009

OutlineOutlineIntroductionTight framelet system and curvelet systemSparse representation under framelet and

curvelet systemFormulation of our minimizationNumerical algorithm and analysisExperiments

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IntroductionIntroduction

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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.

Tight famelet systemTight famelet system

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Sparse representation under Sparse representation under framelet andframelet and curvelet systemcurvelet system

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Formulation of our minimizationFormulation of our minimization

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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.

Numerical algorithm and analysisNumerical algorithm and analysis

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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.

Numerical algorithm and analysisNumerical algorithm and analysis

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ExperimentsExperiments

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ExperimentsExperiments

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ExperimentsExperiments

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