Peyrovian M J, Sawchuk A A
Appl Opt. 1977 Dec 1;16(12):3147-53. doi: 10.1364/AO.16.003147.
For the restoration of noisy blurred images, a controllable smoothing criterion based on the locally variable statistics and minimization of the second derivative is defined, and the corresponding filter, applicable to both space-variant and space-invariant degradations, is obtained. The output of this filter is a cubic spline function. The parameters of the filter determine the local smoothing window and over-all extent of smoothing, and thus the tradeoff between resolution and smoothing is controllable in a spatially nonstationary manner. The interesting properties of this filter have made it capable of restoring signal-dependent noisy images, and it has been successfully applied for filtering images degraded by film-grain noise. Since the matrices of this filter are banded circulant or Toeplitz, efficient algorithms are used for matrix manipulations.
对于噪声模糊图像的恢复，定义了一种基于局部可变统计量和二阶导数最小化的可控平滑准则，并获得了适用于空间可变和空间不变退化的相应滤波器。该滤波器的输出是一个三次样条函数。滤波器的参数决定了局部平滑窗口和整体平滑程度，因此分辨率和平滑之间的权衡可以以空间非平稳的方式进行控制。该滤波器的有趣特性使其能够恢复与信号相关的噪声图像，并且已成功应用于对受胶片颗粒噪声退化的图像进行滤波。由于该滤波器的矩阵是带状循环矩阵或托普利兹矩阵，因此使用高效算法进行矩阵运算。
