Quadratic optimization for image reconstruction, II

Abstract We attack the problem of recovering an image (a function of two variables) from experimentally available integrals of its grayness over thin strips. This problem is of great importance in a large number or scientific areas. An important version of the problem in medicine is that of obtaining the exact density distribution within the human body from X-ray projections. A large number or methods have been proposed to solve this problem. In Part I of this paper we have shown that some methods are special cases of the same iterative quadratic optimization algorithm. In the present paper we discuss alternative iterative algorithms (conjugate gradient, nonstationary Richardson, semi-iterative) for quadratic optimization and compare their performance in image reconstruction with the previously used methods. The choice of the quadratic function to be minimized and the use of heuristic tricks to improve convergence are also discussed. The methods are illustrated by the reconstruction of a mathematically described phantom representing a cross section of the human head from simulated low-dose X-ray data. This paper is self-contained.