Abstract

The problem of reconstructing a two-dimensional (2D) function from its ID projections arises, typically in the context of cross-sectional imaging, in a diversity of disciplines [1-3]. In this problem, a 2D function f(x) is estimated from samples of its Radon, transform (line integral measurements) where $\underset{\_}{\text{θ}}\text{=}{\left(\text{cosθ}\text{sinθ}\right)}^{\text{¢}}$. The major emphasis of research and applications in this area has been on producing accurate, high-resolution cross-sectional images (requiring a large number of high signal-to-noise ratio (SNR) measurements taken over a wide viewing angle [4,5]) which in practice are post-processed, perhaps by humans, to remove artifacts and extract the information of interest about the cross-section. For example, in nondestructive testing applications [3], reconstructed images are post-processed to determine whether flaws or defects are present within a homogeneous medium; in oceanographic applications, reconstructed images are post-processed to determine where within the cross section an oceanographic cold-core ring is located [2]. Such post-processing is effectively the utilization of a priori information about the medium being measured to enhance and extract specific pieces of information.

© 1983 Optical Society of America