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

Spatiotemporal reconstruction of cardiac-gated SPECT images permits us 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, we show that the compression and signal decorrelation properties of the Karhunen-Loève (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. Our 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, we can achieve savings in computation time because fewer reconstructions are needed in comparison to conventional frame-by-frame reconstructions.