This paper presents anisotropic regularization techniques to exploit the pi
ecewise smoothness of the image and the point spread function (PSF) in orde
r to mitigate the severe lack of information encountered in blind restorati
on of shift-invariantly and shift-variantly blurred images. The new techniq
ues, which are derived from anisotropic diffusion, adapt both the degree an
d direction of regularization to the spatial activities and orientations of
the image and the PSF. This matches the piecewise-smoothness of the image
and the PSF which may be characterized by sharp transitions in magnitude an
d by the anisotropic nature of these transitions, For shift-variantly blurr
ed images whose underlying PSF's may differ from one pixel to another, we p
arameterize the PSP and then apply the anisotropic regularization technique
s. This is demonstrated for linear motion blur and out-of-focus blur. Alter
nating minimization is used to reduce the computational load and algorithmi
c complexity.