Deconvolution of two-dimensional images with zeros in the transfer function

Although it is generally believed that the information at the zeros of the transfer function is lost and cannot be recovered, this is not true: the information can be recovered, even in the presence of noise, because the lost information is coded into intermediate points where the transfer function is not zero. We extend our previous one-dimensional treatment [Can. J. Phys. 49: 1865 (1971)] to two dimensions and apply the results to the restoration of images degraded by noise and by linear filtering, such as movement blurring. The filter used is an honest filter in the sense that in the absence of noise, it yields a perfect restoration, including frequencies at the zeros of the transfer function. It is shown that the method considerably improves the restoration of linearly degraded real images.