Error bounds on the reconstruction of binary images from low resolution scans

Abstract

In this paper, we consider the problem of reconstructing a high- resolution binary image from several low-resolution scans. Each of the pixels in a low-resolution scan yields the value of the sum of the pixels in a rectangular region of the high-resolution image. For any given set of such pixel sums, we derive an upper bound on the difference between a certain binary image which can be computed efficiently, and any binary image that corresponds with the given measurements. We also derive a bound on the difference between any two binary images having these pixel sums. Both bounds are evaluated experimentally for different geometrical settings, based on simulated scan data for a range of images. © 2011 Springer-Verlag.