Optimal time-activity basis selection for exponential spectral analysis: application to the solution of large dynamic emission tomographic reconstruction problems

Abstract

The clinical application of dynamic ECT reconstruction algorithms for inconsistent projection (IP) data has been beset with difficulties. These include poor scalability, numerical instability of algorithms, problems of nonuniqueness of solutions, the need to oversimplify tracer kinetics, and impractical computational burden. The authors present a stable reconstruction algorithm with low computational cost that is able to recover the tracer kinetics of several hundred image regions at realistic noise levels. Through optimal selection of a small set of nonnegative basis functions to describe regional time-activity curves (TACs), the authors are able to solve for the first-order compartmental model kinetics of each region. A nonuniform resolution pixelization of image space is employed to obtain highest resolution in regions of interest. These spatial and temporal simplifications improve numerical conditioning, provide robustness against noise, and greatly decrease the computational burden of dynamic reconstruction. The authors apply this algorithm to IP phantom data whose source distribution, kinetics, and count statistics are modeled after a clinical myocardial SPECT dataset. TACs of phantom regions are recovered to within a mean square error of 6%, an accuracy that proves sufficient to allow for quantitative detection of a myocardial perfusion defect within healthy myocardial tissue.