SPLIT BREGMAN METHODS AND FRAME BASED IMAGE RESTORATION
SPLIT BREGMAN METHODS AND FRAME BASED IMAGE RESTORATION
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DOI：
10.1137/090753504
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发表时间：
2009-01-01
影响因子：
1.6
通讯作者：
Shen, Zuowei
中科院分区：
文献类型：
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作者：
Cai, Jian-Feng;Osher, Stanley;Shen, Zuowei
在[T. Goldstein和S. Osher，SIAM J.影像科学，第2卷（2009年），第页。323-343]已经被证明是用于解决总变差范数最小化问题的有效工具，该总变差范数最小化问题产生于基于偏微分方程的图像恢复，诸如图像去噪和来自稀疏样本的磁共振成像重建。本文证明了分裂Bregman迭代的收敛性，其中内迭代次数固定为1。此外，我们表明，这些分裂Bregman迭代可以用来解决最小化问题所产生的分析为基础的方法在文献中的图像恢复。我们将这些分裂Bregman迭代应用于基于分析的图像恢复方法，其分析算子来自于[A.罗恩和Z. Shen，J. Funct.分析：148（1997），pp. 408-447]。这给出了一套新的基于帧的图像恢复算法，涵盖了图像重建中的几个主题，如图像去噪，去模糊，修复和卡通纹理图像分解。给出了几个数值模拟结果。
Split Bregman methods introduced in [T. Goldstein and S. Osher, SIAM J. Imaging Sci., 2 (2009), pp. 323-343] have been demonstrated to be efficient tools for solving total variation norm minimization problems, which arise from partial differential equation based image restoration such as image denoising and magnetic resonance imaging reconstruction from sparse samples. In this paper, we prove the convergence of the split Bregman iterations, where the number of inner iterations is fixed to be one. Furthermore, we show that these split Bregman iterations can be used to solve minimization problems arising from the analysis based approach for image restoration in the literature. We apply these split Bregman iterations to the analysis based image restoration approach whose analysis operator is derived from tight framelets constructed in [A. Ron and Z. Shen, J. Funct. Anal., 148 (1997), pp. 408-447]. This gives a set of new frame based image restoration algorithms that cover several topics in image restorations, such as image denoising, deblurring, inpainting, and cartoon-texture image decomposition. Several numerical simulation results are provided.