A fast higher degree total variation minimization method for image restoration |
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Authors: | Pengfei Liu Jun Zhang |
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Affiliation: | 1. School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, China;2. School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu, China |
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Abstract: | Based on the spectral decomposition theory, this paper presents a unified analysis of higher degree total variation (HDTV) model for image restoration. Under this framework, HDTV is reinterpreted as a family of weighted L1–L2 mixed norms of image derivatives. Due to the equivalent formulation of HDTV, we construct a modified functional for HDTV-based image restoration. Then, the minimization of the modified functional can be decoupled into two separate sub-problems, which correspond to the deblurring and denoising. Thus, we design a fast and efficient image restoration algorithm using an iterative Wiener deconvolution with fast projected gradient denoising (IWD-FPGD) scheme. Moreover, we show the convergence of the proposed IWD-FPGD algorithm for the special case of second-degree total variation. Finally, the systematic performance comparisons of the proposed IWD-FPGD algorithm demonstrate the effectiveness in terms of peak signal-to-noise ratio, structural similarity and convergence rate. |
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Keywords: | higher degree total variation (HDTV) image restoration iterative Wiener deconvolution fast projected gradient denoising convergence |
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