Reconstruction of an axisymmetric image from its noisy projection

Abstract

The Abel inversion is used to reconstruct an axisymmetric image from a one-dimensional projection. It finds application in a wide variety of fields, such as astronomy, optical-fiber refractive-index measurements and spray-droplet studies where the geometry is often cylindrically or spherically symmetric. However, all Abel inversion methods have drawbacks. One such arises from the singularity in the lower limit of the integral. The smoothing techniques also usually consume a large amount of computer time and the error propagation calculations are tedious. Two methods with a different approach are presented in this thesis. They are the Integral transforms and the onion-peeling method. They are both easier and simpler to compute. Also, no curve fitting is needed and the problem of handling the singularity will not arise. The noise and artifact properties of these two methods are investigated.