From two-dimensional nonlinear diffusion to coupled Haar wavelet shrinkage
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- 作者：Pavel Mrá ; zek ; Joachim Weickert
- 关键词：Nonlinear diffusion ; Wavelet shrinkage ; Rotation invariance ; Colour ; Vector- and tensor-valued data
- 刊名：Journal of Visual Communication and Image Representation
- 出版年：2007
- 出版时间：April 2007
- 年：2007
- 卷：18
- 期：2
- 页码：162-175
- 全文大小：1085 K
文摘
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.