Spatially-adaptive analytical reconstruction of quantitative gated cardiac SPECT in KL domain

Gated cardiac SPECT imaging has been widely used in the evaluation of cardiac functions. The acquired four-dimensional (4D) sinogram data have both inter-frame correlation among the time sequence and intra-frame correlation within each 3D frame. The unique features of Karhune-Loeve (KL) transform for de-correlating the data sequence for noise reduction, feature extraction, etc, have been well recognized in the past. Based on the previous work utilizing the KL features, we propose an improved method for 4D quantitative SPECT reconstruction for both noise reduction and computation saving. It considers the similarity among the gated frames in a cardiac cycle. This similarity exists when the heart goes from diastole to systole and then back to diastolic state. All the dynamic sequences are first grouped by unsupervised clustering means based on their similarity, where the similarity between any two frames is measured inversely by the summation of the intensity errors between all sinogram pixels of the two frames. Those frames sharing similar motion state are grouped together until all the error summation exceeds a preset threshold. Then different KL transforms are applied independently in different groups to de-correlate the inter-frame correlation. In the KL domain, an analytical algorithm based on Novikov's inverse formula for non-uniform attenuation compensation is developed to reconstruct each principal component for its corresponding image component in the KL domain. Noise reduction is adaptive to each principal component in the proposed algorithm. The higher order principal components could be discarded for further noise reduction and computation saving. The 4D image sequence is reconstructed by the corresponding inverse KL transform of each group, respectively. Both simulation study using the NCAT phantom and clinical experiment using the DigiRad SPECT system were performed, showing that the proposed method can achieve better performance than the one using a global KL transform for all frames.