COORDINATED DESIGN OF RESTORATION ALGORITHM AND CODED APERTURE (RECONSTRUCTION, TOMOGRAPHY).

Abstract

Coded-aperture systems are indirect imaging systems that have been used to image x-ray and (gamma)-ray sources. Coded aperture systems are also capable of recording tomographic information and because they involve no detector motion they are natural candidates for use in dynamic studies in nuclear medicine. Computer simulations suggest that an orthogonal-view coded-aperture system, which circumvents the problem of limited angular view, is capable of restoring clinically useful tomographic information. The restoration is performed with the aid of the iterative back-projection algorithm which is shown to yield the Moore-Penrose generalized inverse in the limit of many iterations. The convergence behavior of this algorithm is also examined. In order to improve reconstructions, the problems of optimizing coded aperture design is addressed. The concept of "alignment" is introduced in which the aperture parameters are adjusted until the system is tuned to measure well the object class of interest. A mean-square error figure of merit is derived that indicates the degree of alignment of a system. Aperture design may then be seen as a multidimensional optimization problem in which system parameters are adjusted in order to find a global minimum value for the figure of merit. The figure of merit presumes the use of an optimum restoration filter in the reconstruction process. Various restoration algorithms are suggested which fulfill this requirement. Finally, simple proof-of-principle simulations are given that demonstrate a degree of plausibility to the alignment approach.