科研之友
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摘要
Low-rank regularization approximated by a nuclear norm has been proven its ability in image denoising. However, the nuclear norm is just a suboptimization of the rank norm, resulting in a big error when reducing noise. In this paper, a novel smooth and convex surrogate function, which is closer to the rank norm, is firstly proposed as a replacement of the prior nuclear norm. Then, the proposed surrogate function is approximated by its first-order Taylor expansion. Finally, a novel model called iterative weighted nuclear norm minimization scheme, solved by the single and effective alternating directions method of multipliers with a weighted singular-value thresholding operator, is formed for image denoising. Both quantitative and qualitative results obtained by applying advanced denoising methods to synthetic images will verify the effectiveness of the proposed method. Extensive application of these state-of-the-art methods to denoising of clinical X-ray cardiovascular angiograms further validates that our proposed approach performs better on reducing noise and preserving structures (especially capillaries), demonstrating that the method can yield clear X-ray angiograms with integral cardiovascular trees which are beneficial for clinicians to diagnose and analyze cardiovascular diseases.
