Application of the Karhunen-Loeve transform to 4D reconstruction of cardiac gated SPECT images

Reconstruction of gated SPECT images is intrinsically a four-dimensional problem. Gated SPECT studies are normally reconstructed frame by frame; thus, the time frames are treated independently. This approach fails to exploit the strong signal correlations among the time frames which are critical for noise reduction and resolution recovery. We investigated two reconstruction approaches, developed for dynamic PET by Wernick et al., which utilize the compression and decorrelation properties of the Karhunen-Loeve (KL) transform. In Method I, we temporally filter the data by using only the first few KL components, then perform frame-by-frame reconstruction. In Method II, we KL transform the projection data, reconstruct only the significant KL component images, then perform an inverse KL transformation to obtain the full 4D image sequence. Results indicate that Methods I and II provide better noise performance than ordinary frame-by-frame reconstruction. Additionally, Method II requires substantially fewer computations than conventional reconstruction methods.