Fast analytical reconstruction of gated cardiac spect with non-uniform attenuation compensation

Conventionally, the inverse problem of gated cardiac SPECT is solved by reconstructing the images frame-by-frame, ignoring the inter-frame correlation along the time dimension. To compensate for the non-uniform attenuation for quantitative cardiac imaging, iterative image reconstruction has been a choice which could utilize a priori constraint on the inter-frame correlation for a penalized maximum likelihood (ML) solution. However, iterative image reconstruction in the 4D space involves intensive computations. In this paper, an efficient method for 4D gated SPECT reconstruction is developed based on Karhune-Loève (KL) transform and Novikov's inverse formula. The temporal KL transform is first applied on the data sequence to de-correlate the inter-frame correlation and then the 3D principal components in the KL domain are reconstructed frame-by-frame using Novikov's inverse formula with non-uniform attenuation compensation. Finally an inverse KL transform is performed to obtain quantitatively-reconstructed 4D images in the original space. With the proposed method, 4D reconstruction can be achieved at a reasonable computational cost. The results from computer simulations are very encouraging as compared to conventional frame-by-frame filtered back-projection and iterative ordered-subsets ML reconstructions. By discarding high-order KL components for further noise reduction, the computation time could be further reduced.