On Some Smoothing Techniques Used in Image Restoration

SUMMARY The problem is considered of restoring a blurred and/or noisy image using various regularization prescriptions. Preliminary work concerns the invertibility of point spread functions and the construction of a stochastic model for images. A simple linear regularization procedure is introduced, as well as the special cases of constrained deconvolution, maximum entropy restoration and least-squares filtering. Optimal choices for the degree of smoothing are obtained for the case of low noise-to-signal ratios. Certain techniques, prevalent in the image-restoration literature for choosing the degree of smoothing, are shown to oversmooth, in a well-defined sense.