earticle

영어

1l norm is a popular regularizer in various linear inverse problems including image processing, compressed sensing and machine learning. But the non-zero entries of the sparsity solution obtained by 1l are independent with each other, which always leads to biased result to real solution. Actually, there always exist some different correlations among those non-zero entries in an image signal domain or various analysis domains. In this paper, based on a simple observation that the non-zero entries of the sparsity vector in various image analysis domains should be also approximate when the relevant signal values are proximate, we proposed a nonlocal-approximate sparsity regularizer in analysis domains by minimizing the sum of the 2l norms of those vectors with the same nonzero pattern like signal vectors. This regularizer is applied to image denoising, edge detecting, inpainting and decomposition models successively. The numerical experiments demonstrate the effectiveness of our method in terms of PSNR, visual effect and edge preserving.