Digital image gathering and minimum mean-square error restoration

Most digital image restoration algorithms are inherently incomplete because they are conditioned on a discrete-input, discrete-output model which only accounts for blurring during image gathering and additive noise. For those restoration applications where sampling and reconstruction (display) are important the restoration algorithm should be based on a more comprehensive end-to-end model which also accounts for the potentially important noise-like effects of aliasing and the low-pass filtering effects of interpolative reconstruction. In this paper we demonstrate that, although the mathematics of this more comprehensive model is more complex, the increase in complexity is not so great as to prevent a complete development and analysis of the associated minimum mean-square error (Wiener) restoration filter. We also survey recent results related to the important issue of implementing this restoration filter, in the spatial domain, as a computationally efficient small convolution kernel.