This paper presents a method for designing finite impulse response (FIR) filters for samples of a 2-D signal, e.g., an image, and its gradient. The filters, which are called blended filters, are decomposable in three filters, each separable in 1-D filters on subsets of the data set. Optimality in the minimum mean square error sense (MMSE) of blended filtering is shown for signals with separable autocorrelation function. Relations between correlation functions for signals and their gradients are derived. Blended filters may be composed from FIR Wiener filters using these relations. Simple blended filters are developed and applied to the problem of gray value image reconstruction from bilevel (scanned) clustered-dot halftone images, which is an application useful in the graphic arts. Reconstruction results are given, showing that reconstruction with higher resolution than the halftone grid is achievable with blended filters.

A new method for coding scanned halftone images is proposed. It is information-lossy, but still preserving the image quality, compression rates of 16-35 have been achieved for a typical test image scanned on a high resolution scanner. The bi-level halftone images are filtered, in phase with the halftone grid, and converted to a gray level representation. A new digital description of (halftone) grids has been developed for this purpose. The gray level values are coded according to a scheme based on states derived from a segmentation of gray values. To enable real-time processing of high resolution scanner output, the coding has been parallelized and implemented on a transputer system. For comparison, the test image was coded using existing (lossless) methods giving compression rates of 2-7. The best of these, a combination of predictive and binary arithmetic coding was modified and optimized achieving a compression rate of 9.>