FAST DUAL MINIMIZATION OF THE VECTORIAL TOTAL VARIATION NORM AND APPLICATIONS TO COLOR IMAGE PROCESSING
FAST DUAL MINIMIZATION OF THE VECTORIAL TOTAL VARIATION NORM AND APPLICATIONS TO COLOR IMAGE PROCESSING
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DOI：
10.3934/ipi.2008.2.455
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发表时间：
2008-11-01
影响因子：
1.3
通讯作者：
Chan, Tony F.
中科院分区：
文献类型：
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作者：
Bresson, Xavier;Chan, Tony F.
我们提出了一个彩色/矢量图像的正则化算法，这是快速，易于编码和数学上的适定性。更确切地说，正则化模型是基于向量全变差（VTV）范数的对偶公式，并且它可以被视为Chambolle在[13]中针对灰度/标量图像定义的对偶方法的向量扩展。所提出的模型提供了几个优点。首先，它最小化确切的VTV范数，而标准方法使用正则化范数。然后，最小化的数值方案是直接实现的，最后，达到解决方案的迭代次数很低，这给出了一个快速的正则化算法。最后，我们可能更重要的是，所提出的VTV最小化方案可以很容易地扩展到许多标准应用。我们将L-1矢量正则化算法应用于以下问题：颜色逆尺度空间、色度-亮度颜色表示的颜色去噪、彩色图像修复、彩色小波收缩、彩色图像分解、彩色图像去模糊以及流形上的颜色去噪。一般来说，这种VTV最小化方案可用于需要矢量场（颜色、其他特征矢量）正则化同时保留不连续性的问题。
We propose a regularization algorithm for color/vectorial images which is fast, easy to code and mathematically well-posed. More precisely, the regularization model is based on the dual formulation of the vectorial Total Variation (VTV) norm and it may be regarded as the vectorial extension of the dual approach defined by Chambolle in [13] for gray-scale/scalar images. The proposed model offers several advantages. First, it minimizes the exact VTV norm whereas standard approaches use a regularized norm. Then, the numerical scheme of minimization is straightforward to implement and finally, the number of iterations to reach the solution is low, which gives a fast regularization algorithm. Finally, we maybe more importantly, the proposed VTV minimization scheme can be easily extended to many standard applications. We apply the L-1 vectorial regularization algorithm to the following problems: color inverse scale space, color denoising with the chromaticity-brightness color representation, color image inpainting, color wavelet shrinkage, color image decomposition, color image deblurring, and color denoising on manifolds. Generally speaking, this VTV minimization scheme can be used in problems that required vector field (color, other feature vector) regularization while preserving discontinuities.