Two New Nonlinear Nonlocal Diffusions for Noise Reduction
Two New Nonlinear Nonlocal Diffusions for Noise Reduction
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DOI：
10.1007/s10851-008-0108-z
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发表时间：
2008
影响因子：
2
通讯作者：
P. Guidotti;J. Lambers
中科院分区：
文献类型：
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作者：
P. Guidotti;J. Lambers
提出了两种新的非局部非线性扩散降噪模型，并对其进行了分析和实现。它们都是著名的Perona-Malik方程的近亲。在某种程度上，它们可以被视为Perona-Malik的一种新的正则化范式。它们确实保留和增强了Perona-Malik最珍贵的特征，同时提供了承认稳定的自然离散化的良好定姿方程。然而，与其他正则化不同的是，某些分段平滑函数是（元）稳定平衡，因此，它们的动态行为及其离散实现可以被完全理解，并且不会导致任何“悖论”。非平凡均衡的存在也解释了为什么模糊会受到控制。其中一个模型已被证明是适定的。数值实验说明了新模型的主要特点，提供了对其有趣的动力学行为的见解，并证明了它们作为去噪工具的有效性。
Two new nonlocal nonlinear diffusion models for noise reduction are proposed, analyzed and implemented. They are both a close relative of the celebrated Perona-Malik equation. In a way, they can be viewed as a new regularization paradigm for Perona-Malik. They do preserve and enhance the most cherished features of Perona-Malik while delivering well-posed equations which admit a stable natural discretization. Unlike other regularizations, however, certain piecewise smooth functions are (meta)stable equilibria and, as a consequence, their dynamical behavior and that of their discrete implementations can be fully understood and do not lead to any “paradox”. The presence of nontrivial equilibria also explains why blurring is kept in check. One of the models has been proved to be well-posed. Numerical experiments are presented that illustrate the main features of the new models and that provide insight into their interesting dynamical behavior as well as demonstrate their effectiveness as a denoising tool.