Wiener restoration of sampled image data: end-to-end analysis

Traditional formulations of the Wiener filter for image restoration have accounted for the blurring and noise that occur in (digital) image gathering, but they have failed to account for (1) the insufficient sampling that causes further degradations by aliasing and (2) the image-reconstruction degradations that ordinarily occur when the processed digital data are reproduced as a continuous representation. In this paper we formulate the Wiener filter as a function of the basic image-gathering and image-reconstruction constraints, thereby providing a method for minimizing the mean-squared error between the (continuous-input) radiance field and its restored (continuous-output) representation. Simulations demonstrate that this filter restores clearer and sharper images than the traditional filter. We also formulate the Wiener-characteristic filter to provide a method for explicitly specifying the characteristic, or feature, of the scene that one wishes to enhance or extract.