Fast restoration of finite objects degraded by finite PSF

The problem of restoring a class of continuous, finite random objects degraded by finite space invariant PSF and additive noise is considered. For infinite images this problem is solved easily via Fourier domain Wiener filtering. For finite intervals, this solution is no longer valid. Here we show that a modification of the image data by the boundary observations gives a solution of the Wiener filtering problem in such a way that the restored object is obtained exactly in terms of a Fourier series expansion which can be implemented in practice via a fast Fourier transform algorithm. Examples of two-dimensional images are given.