FILTERS INVOLVING DERIVATIVES WITH APPLICATION TO RECONSTRUCTION FROMSCANNED HALF-TONE IMAGES

This paper presents a method for designing finite impulse response (FI R) filters for samples of a 2-D signal, e.g., an image, and its gradie nt, The filters, which are called blended filters, are decomposable in three filters, each separable in 1-D filters on subsets of the data s et. Optimality in the minimun mean square error sense (MMSE) of blende d filtering is shown for signals with separable autocorrelation functi on, Relations between correlation functions for signals and their grad ients are derived, Blended filters may be composed from FIR Wiener fil ters using these relations, Simple blended filters are developed and a pplied to the problem of gray value image reconstruction from bilevel (scanned) clustered-dot halftone images, which is an application usefu l in the graphic arts, Reconstruction results are given, showing that reconstruction with higher resolution than the halftone grid is achiev able with blended filters.