Deblurring and denoising of images by nonlocal functionals
Deblurring and denoising of images by nonlocal functionals
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DOI：
10.1137/050622249
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发表时间：
2005-01-01
影响因子：
1.6
通讯作者：
Jones, PW
中科院分区：
文献类型：
--
作者：
Kindermann, S;Osher, S;Jones, PW
本文研究了具有非局部相关项的正则化泛函在图像去噪和图像去模糊中的应用。这些泛函被表示为像素空间的笛卡尔乘积上的积分。我们证明了邻域过滤器的类可以在这个框架中描述。使用这些泛函，我们可以考虑其中一些邻域滤子的泛函解析性质，并展示它们如何使用普罗霍罗夫度量的平滑版本被视为正则项。更重要的是，我们。这是众所周知的有界变差正则化的非局部变量，它不受阶梯效应的影响。对于去噪和去模糊问题，我们证明了相应的正则化泛函的极小元的存在性，并给出了一些数值例子，将非局部形式与有界变差正则化和非局部均值滤波进行了比较。
This paper investigates the use of regularization functionals with nonlocal correlation terms for the problem of image denoising and image deblurring. These functionals are expressed as integrals over the Cartesian product of the pixel space. We show that the class of neighborhood filters can be described in this framework. Using these functionals we can consider the functional analytic properties of some of these neighborhood filters and show how they can be seen as regularization terms using a smoothed version of the Prokhorov metric. Moreover, we de. ne a nonlocal variant of the well-known bounded variation regularization, which does not suffer from the staircase effect. We show existence of a minimizer of the corresponding regularization functional for the denoising and deblurring problem, and we present some numerical examples comparing the nonlocal version to the bounded variation regularization and the nonlocal mean filter.