Growth of discrete projection ghosts created by iteration

Abstract

Ghost images contain specially aligned pixels with intensities that are designed to sum to zero when projected at any of a pre-selected set of discrete angles. Ghost images find use in synthesizing the content of missing rows of image or projection space from data that contains some deliberate level of information redundancy. Here we examine the properties of ghost images that are constructed through a process of iterated convolution. An initial ghost is propagated by cumulative displacements into other discrete directions to expand the range of angles that have zero-sum projections. The discrete projection scheme used here is the finite Radon transform (FRT). We examine these accumulating ghosts to quantify the growth of their dynamic range of their pixel values and the spread of their spatial extent. After N propagations, a pair of points with intensity ±1 can replicate to produce a maximum total intensity of 2N . For the discrete projections of the FRT, we show that column-oriented iterations better suppress the range and rate of growth of ghost image values. After N row-based iterations, the peak pixel values of FRT ghost images grow approximately as 20.8N . After N column-based iterations, the peak pixel values of FRT ghost images grow approximately as 20.7N . The slower rate of expansion of pixel values for column iteration comes at the expense of fragmenting the compactness of the set of FRT projection angles that are chosen to sum to zero. © 2011 Springer-Verlag.