Quadratic optimization for image reconstruction. I

✍ Scribed by Gabor T. Herman; Arnold Lent

• Book ID: 104290645
• Publisher: Elsevier Science
• Year: 1976
• Weight: 833 KB
• Volume: 5
• Category: Article
• ISSN: 0146-664X
• DOI: 10.1016/s0146-664x(76)80011-1

✦ Synopsis

We attack the problem of recovering an image (a function of two variables) frora experimentally available integrals of its grayness over thin strips. This problem is of great importance in a large number of scientific areas. An important version of the problem in medicine is tha~ of obtaining the exact density distribution within ~he htunan body fl'om X-ray projections.

A large number of methods have been proposed to solve this problem. In this paper we show that some of these methods are special cases of the same iterative quach'atic optimization algorithm. We prove the convergence of ~his algorithm and characterize the image to which it converges. Thus, our restflts provide proofs of convergence of previously used reconstruction methods where no such proofs existed before. We discnss the efficacy of the quadratic optimisation approach for practical image reconstruction.