Space-variant filtering through the Wigner distribution function

Space-invariant and space-variant filtering of discrete images with unidimensional variation is performed in this paper through the Wigner distribution function (WDF). Low-pass, bandpass, and high-pass filtering is used in the Fourier domain and in the Wigner distribution, to compare their different behavior in both cases. A space-variant filter is generated to modify the WDF of an object to obtain, after inversion, a spatially variant filtered image. Finally, spatially variant defocused images generated through the Wigner distribution are restored by Wiener based filters applied in the Wigner domain. The method applied to recover the filtered images can easily be generalized to bidimensional images.