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首页> 外文期刊>Journal of visual communication & image representation >From two-dimensional nonlinear diffusion to coupled Haar wavelet shrinkage
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From two-dimensional nonlinear diffusion to coupled Haar wavelet shrinkage

机译：从二维非线性扩散到耦合Haar小波收缩

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This paper studies the connections between discrete two-dimensional schemes for shift-invariant Haar wavelet shrinkage on one hand, and nonlinear diffusion on the other. We show that using a single iteration on a single scale, the two methods can be made equivalent by the choice of the nonlinearity which controls each method: the shrinkage function, or the diffusivity function, respectively. In the two-dimensional setting, this diffusion-wavelet connection shows an important novelty compared to the one-dimensional framework or compared to classical 2-D wavelet shrinkage: The structure of two-dimensional diffusion filters suggests to use a coupled, synchronised shrinkage of the individual wavelet coefficient channels. This coupling enables to design Haar wavelet filters with good rotation invariance at a low computational cost. Furthermore, by transferring the channel coupling of vector- and matrix-valued nonlinear diffusion filters to the Haar wavelet setting, we obtain well-synchronised shrinkage methods for colour and tensor images. Our experiments show that these filters perform significantly better than conventional shrinkage methods that process all wavelets independently.
机译：本文一方面研究了离散二维方案的不变位移Haar小波收缩，另一方面研究了非线性扩散之间的联系。我们表明，在单个尺度上使用一次迭代，可以通过选择控制每种方法的非线性来使这两种方法等效：分别控制收缩函数或扩散函数。在二维环境中，与一维框架或经典的二维小波收缩相比，此扩散-小波连接显示出重要的新颖性：二维扩散滤波器的结构建议使用耦合的，同步的收缩各个小波系数通道。这种耦合使得能够以较低的计算成本设计具有良好的旋转不变性的Haar小波滤波器。此外，通过将向量值和矩阵值非线性扩散滤波器的通道耦合转移到Haar小波设置，我们获得了色彩和张量图像的同步良好的收缩方法。我们的实验表明，这些滤镜的性能明显优于独立处理所有小波的常规收缩方法。

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