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.
M. J. Peyrovian and A. A. Sawchuk, "Restoration of noisy blurred images by a smoothing spline filter," Appl. Opt. 16, 3147-3153 (1977)