A Nonlocal Denoising Algorithm for Manifold-Valued Images Using Second Order Statistics
A Nonlocal Denoising Algorithm for Manifold-Valued Images Using Second Order Statistics
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DOI：
10.1137/16m1087114
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发表时间：
2016-07
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影响因子：
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通讯作者：
Friederike Laus;M. Nikolova;Johannes Persch;G. Steidl
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文献类型：
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作者：
Friederike Laus;M. Nikolova;Johannes Persch;G. Steidl
基于非局部块的方法，特别是Lebrun、Buades和Morel（2013）的贝叶斯方法，被认为是对被中等方差的白色高斯噪声破坏的（彩色）图像进行去噪的最先进方法。本文是第一次尝试将这种技术推广到流形值图像。这样的图像，例如具有相位或方向条目或具有对称正定矩阵的流形中的值的图像，在现实世界的应用中经常遇到。将正规律推广到流形并不是规范的，人们已经考虑了不同的尝试。在这里，我们专注于一个简单的内在模型，并讨论与其他方法的特定流形。我们根据最小均方误差估计重新解释了Lebrun等人（2013）的贝叶斯方法，这激发了我们对流形上相应估计量的定义。有了这个估计在手，我们提出了一个非局部补丁为基础的方法恢复的流形值图像。各种概念证明的例子证明了所提出的算法的潜力。
Nonlocal patch-based methods, in particular the Bayes' approach of Lebrun, Buades and Morel (2013), are considered as state-of-the-art methods for denoising (color) images corrupted by white Gaussian noise of moderate variance. This paper is the first attempt to generalize this technique to manifold-valued images. Such images, for example images with phase or directional entries or with values in the manifold of symmetric positive definite matrices, are frequently encountered in real-world applications. Generalizing the normal law to manifolds is not canonical and different attempts have been considered. Here we focus on a straightforward intrinsic model and discuss the relation to other approaches for specific manifolds. We reinterpret the Bayesian approach of Lebrun et al. (2013) in terms of minimum mean squared error estimation, which motivates our definition of a corresponding estimator on the manifold. With this estimator at hand we present a nonlocal patch-based method for the restoration of manifold-valued images. Various proof of concept examples demonstrate the potential of the proposed algorithm.