Image Gathering and Restoration

Abstract

This chapter focuses the mathematical development begun in Chapter 2 on digital image restoration. First, Section 3.1 develops the unconstrained Wiener filter that restores the image with an interpolation lattice that is sufficiently dense to completely suppress the blurring and raster effects of the image-display process. Therefore, the resultant image has the absolute minimum mean-square restoration error (MSRE) for any given image gathering and display devices. Next, Section 3.2 extends the development to the constrained Wiener filter that allows the density of the interpolation to be constrained and, therefore, must account for the blurring and raster effects of the image-display process. Section 3.3 further extends the development to the Wiener-characteristic filter that includes a linear filter to minimize the MSRE for a particular spatial feature of the scene, such as edges and boundaries. Section 3.4, in turn, develops the small-kernel Wiener filter that allows the amount of digital processing to be constrained as well as the density of the interpolation. Finally, Section 3.5 presents the Wiener-Gaussian enhancement (WIGE) filter that combines the Wiener filter with an enhancement function that allows the user to interactively control the visual quality of the restored image.