Image deblurring is a fundamental problem in image processing. Conventional methods often deal with the degraded image as a whole while ignoring that an image contains two different components: cartoon and texture. Recently, total variation (TV) based image decomposition methods are introduced into image deblurring problem. However, these methods often suffer from the well-known stair-casing effects of TV. In this paper, a new cartoon -texture based sparsity regularization method is proposed for non-blind image deblurring. Based on image decomposition, it respectively regularizes the cartoon with a combined term including framelet-domain-based sparse prior and a quadratic regularization and the texture with the sparsity of discrete cosine transform domain. Then an adaptive alternative split Bregman iteration is proposed to solve the new multi-term sparsity regularization model. Experimental results demonstrate that our method can recover both cartoon and texture of images simultaneously, and therefore can improve the visual effect, the PSNR and the SSIM of the deblurred image efficiently than TV and the undecomposed methods.
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