Edge errors in inverse and Wiener filter restorations of motion-blurred images and their windowing treatment

Abstract

The sensitivity of the inverse filter to noise is often thought to be the reason that inverse filter restorations of motion-blurred images are normally dominated by errors. In this paper, we show that even in the absence of noise, there is a large error component, called the edge error, that arises due to the fact that real images seldom have the periodicity implicitly assumed by discrete Fourier transform operation. An analysis shows that the edge error has a triangular-wave structure with an amplitude proportional to the difference between the average pixel intensity levels of the left and right edges of the image. For the central region of an image, the edge error may be reduced by using Wiener filtering instead of inverse filtering. However, the restored images show reduced resolution as well as ghosting and ringing effects. We also derive mathematically a special window for treatment of the edge error. A significant improvement in the quality of restorations is achieved with the use of this special window. The best restorations are obtained by subjecting the windowed-blurred image to a Wiener filter of large signal-to-noise ratio. © 1991.