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.

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