Improved image quality and computation reduction in 4-D reconstruction of cardiac-gated SPECT images

Spatiotemporal reconstruction of cardiac-gated SPECT images permits one to obtain valuable information related to cardiac function. However, the task of reconstructing this four-dimensional (4-D) data set is computation intensive. Typically, these studies are reconstructed frame-by-frame: a nonoptimal approach because temporal correlations in the signal are not accounted for. In this work, the authors show that the compression and signal decorrelation properties of the Karhunen-Loeve (KL) transform may be used to greatly simplify the spatiotemporal reconstruction problem. The gated projections are first KL transformed in the temporal direction. This results in a sequence of KL-transformed projection images for which the signal components are uncorrelated along the time axis. As a result, the 4-D reconstruction task is simplified to a series of three-dimensional (3-D) reconstructions in the KL domain. The reconstructed KL components are subsequently inverse KL transformed to obtain the entire spatiotemporal reconstruction set. The authors´ simulation and clinical results indicate that KL processing provides image sequences that are less noisy than are conventional frame-by-frame reconstructions. Additionally, by discarding high-order KL components that are dominated by noise, one can achieve savings in computation time because fewer reconstructions are needed in comparison to conventional frame-by-frame reconstructions.