Reconstruction Methods for Nuclear Emission Tomography.

Abstract

An investigation is performed to find an optimal image reconstruction method for use with a new nuclear medical imaging device named SPRINT. This novel instrument, under development at The University of Michigan, is intended for single-photon transverse axial emission tomography. The unique characteristics of SPRINT provide advantages over other existing and proposed emission imaging instruments, but also render several existing reconstruction methods inappropriate. The reconstruction problem is first formulated in a general form applicable to several imaging devices including nuclear emission and x-ray transmission tomography systems. Evaluation criteria are presented with which to grade potential reconstruction methods. Reconstruction methods are defined here to include both the numerical reconstruction algorithm and the digital processor hardware used to implement the algorithm. The present work begins by selecting from potential algorithms a small subset appearing best suited for use with SPRINT. The selected set of reconstruction algorithms includes modified forms of existing algorithms. A new iterative reconstruction algorithm (CSIM) is presented which is found superior in several cases. With certain parameter values CSIM is shown to be equivalent to the Jacobi iterative method (method of simultaneous displacements) applied to the normal equations but without calculation and storage of the large, nonsparse normal equation matrix. It is concluded that iterative methods, applied to an optimization formulation of the reconstruction problem, are superior to direct methods in this application. Optimization methods are used because the forward transform, from image to data, is singular and the measured data contains r and om error. Nonsingular approximations to the forward transform can be used: however, these ignore, or only approximately account for, several of the various complex physical processes involved, including photon scatter, inverse square attenuation, beam divergence, nonuniform efficiency within the beam, aperture thickness effects, and nonuniform beam width. Iterative methods are used because the matrices involved are sparse, large, and r and omly structured. Iterative methods are also less sensitive to sampling nonuniformities and extend easily to multiple image planes with noncoplanar raysum sets. The primary superior characteristic of direct methods is the computation time requirement. Reconstructions from both real (phantom) and computer simulated SPRINT data are presented. Simulations include a wide range of source distributions and statistics regimes. Relaxation parameter studies are performed for selected algorithms. It is shown that optimal relaxation factors for these nonlinear methods vary with signal-to-noise ratio and source distribution. Special purpose digital processor designs for high-speed implementation of the reconstruction algorithms are proposed and characterized for use in this application. It is concluded that computation time, which has limited the usefulness of nondirect solution strategies, is, if not already, rapidly becoming an obsolete consideration. Therefore the only apparent deficiency of iterative algorithms is, or soon will be, negligible. SPRINT utilizes a time modulated pseudor and om aperture sequence for raysum measurements. The present work includes an empirical study of effects on the image of the chosen aperture sequence. It is concluded that a broad class of source distributions will be best imaged with apertures of mean transmittance in the range 20-70%. Several procedures have been developed for improvement of images produced by SPRINT. These include iterative deconvolution of raw count data, adaptive prefiltering of projection data, and corrections for scatter, leakage, and aperture thickness effects.