| Presented is an application of operations research methods to the estimation and graphical depiction of unknown functional distributions from huge amounts of measurement data--an important activity in industrial testing, diagnostic medicine, a variety of the natural sciences, and economic modeling. The current work addresses the well-known problem of image reconstruction from projections. Commonly used solution techniques produce poor graphical images in certain circumstances. This results in the exclusion of the technology from many industrial testing environments, as well as the unavailability of important diagnostic procedures to many medical patients. Mathematical optimization can improve image quality in such cases, but implementations have been hindered by the problem's enormous size. Proposed is a new data-collection protocol designed to induce useful algebraic structure in the image-reconstruction model. This structure is used to dramatically improve the speed of existing iterative reconstruction methods. Decomposition of the problem is also permitted, with subproblems transformed into variants of the classical transportation problem and solved in parallel. A computerized testing system with scanning simulator, image reconstructor, and image display, is used to demonstrate the effectiveness of the transportation subproblem solutions in helping to obtain useful images. The importance of the testing methodologies in addressing real-world problems in medicine and industry is also discussed. |
