Improved KL domain inversion of the attenuated radon transform for quantitative gated cardiac SPECT

Abstract

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Objectives: Fully 4D quantitative gated cardiac SPECT was explored by iterative penalized maximum likelihood reconstruction with local smoothing penalty in the 3D space and the 1D time domain. Both advantage and drawback were recognized. An alternative non-iterative or analytical 4D reconstruction by inverting the attenuated Radon transform, which is the fundamental equation for quantitative SPECT, in the KL domain was recently proposed with promising results. The noise is handled very well by the KL strategy and the non-uniform attenuation is efficiently compensated by Novikov’s inversion of the attenuated Radon transform. This work explores two modifications aiming to improve the alternative analytical approach. Methods: One modification 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 diastole state. Those frames which satisfy a similarity measure are grouped for a corresponding KL transform. Another modification is similar to the work of Brankov et al. It considers the similarity of the time-activity curves (TACs) of spatial regions in all the gated sequence. A corresponding KL transform is applied to each region grouped with similar TACs separately. After adaptive noise treatment of all KL components, the FBP-type inversion is performed, followed by the corresponding inverse KL transforms of the gated image sequence. Results: The presented modifications above were tested by computer simulations and experimental data. The NCAT digital phantom of 128 cubic array was used to simulate 128 parallel-beam projections of 128 square size evenly spaced over 360 degree for 16 frames with Poisson noise. The experimental data were acquired by a DigiRad SPECT system, consisting of 32 parallel-beam projections of 64 square size evenly spaced over 180 degree for 8 frames. The modification by the spatial region similarity showed improvement over our previous approach of using a single KL transform for all voxels in the gated sequence. Further improvement was seen by the modification of considering the similarity among the gated frames. Conclusions: Modeling the heart motion by adaptive KL transform is promising for gated cardiac SPECT.