P³E-Based Image Processing Algorithms and Techniques

Abstract

The impetus for this chapter lies in determining the completeness of our model, i.e., determining whether or not the same architecture is appropriate for obtaining a digital approximation not only to the Radon transform, but also to the inverse Radon transform. Thus, we have focussed on image processing applications in which Radon data must be backprojected to recover the image. These applications are presented in the following sections, and they include: (1) digital image reconstruction using the non-iterative techniques of convolution backprojection and filtered backprojection; (2) digital image reconstruction using the iterative Kacmarz method; (3) 2-D convolution of an image with a kernel; (4) rotation and translation of images; and (5) CT reconstruction, which uses exact sampled-continuous as opposed to digital projection data. In all of the experiments, we used 256 × 256 8-bit images. We utilized 180 projections for each image, at orientations θ = 0°, 1°, 2°,…, 179°. As will be seen, our model is complete, and the architecture presented in Chap. 3 does support both the projection and backprojection operations.