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 non-uniqueness of solutions, the need to oversimplify tracer kinetics, and impractical computational burden. The authors present a stable, low computational cost reconstruction algorithm which is able to recover the tracer kinetics of several hundred image regions at realistic noise levels. Through optimal selection of a small set of non-negative 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 non-uniform 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 10%, an accuracy which proves sufficient to allow detection of a myocardial perfusion defect within healthy myocardial tissue.