M06-379 1 Abstract — Recent researches have shown promise in applying KL transform to 4D gated sinogram for pre-reconstruction temporal smoothing and quasi-4D inversion of attenuated Radon transform. To achieve quantitative 4D reconstruction, this work aims to compensate for the major degradation factors, including distance-dependent collimator resolution variation and object- specific photon scatter, simultaneously within the KL framework. To alleviate the influence of cardiac motion on reconstruction, heart motion was classified into several groups based on inter-frame similarities and each group underwent a corresponding KL transform. In the KL domain, non-stationary Poisson noise was stabilized by Anscombe transform and treated by adaptive Wiener filtration. Scatter contribution to the primary energy window was then estimated and removed based on photon detection energy spectrum and the triple-energy- window acquisition formula after noise treatment. The scatter- corrected data was further subject to a depth-dependent deconvolution, based on the distance frequency relationship, with measured detector response kernel in the KL domain. The deconvoluted sinograms were reconstructed by inverting the attenuated Radon transform for each KL component and the 4D SPECT images were obtained by a corresponding inverse KL transform for each group. The simultaneous compensation strategy in the KL domain was tested by computer simulations from digital phantoms of 128 cubic array and clinical data from a patient. The adaptive KL transform for different groups consisting of frames with similar activity dynamics showed noticeable improvement over our previous work of using a single KL transform for all frames. Improvement was also seen by the adaptive noise treatment of all the KL components over previous work of discarding the higher-order components. Further improvement by considering the scatter and resolution variation was demonstrated. This work was partly supported by the National Natural Science Foundation of China under Grant No.60772020 ,30470490 and NIH Grant #CA082402 and #CA120917 of the National Cancer Institute. Yi Fan is with the Department of Computer Application, Forth Military Medical University, Xi’an, Shaanxi, China, 710032 and Department of Radiology, State University of New York, Stony Brook, NY 11794 USA (e- mail: yifan@mil.sunysb.edu). Chun Jiao is with the Department of Computer Application, Fourth Military Medical University Xi’an, Shaanxi 710032, China. Hongbing Lu is with the Department of Computer application, Fourth Military Medical University, Xi’an, Shaanxi 710032, China. Su Wang is with the Department of Radiology, State University of New York, Stony Brook, NY 11794 USA. Zhengrong Liang is with the Department of Radiology and Computer Science, State University of New York, Stony Brook, NY 11794 USA. Index Terms — Image reconstruction, non-uniform attenuation, noise reduction, photon scatter, detector response I. INTRODUCTION n single photon emission computed tomography (SPECT), Poisson noise distribution, non-uniform attenuation, photon scatter as well as detector response are the dominating degradation factors which suffer the image quality. To achieve quantitative reconstruction for clinical application, those factors should be compensated carefully. While, for fully 4D reconstruction, it is difficult to seek for an analytical solution which could consider multi-degradation factors simultaneously. A lot of efforts have been devoted to include a penalty for a penalized maximum likelihood (pML) solution, where the intra- and inter-frame correlations are considered in the penalty [1]. This classic approach is attractive because it searches for a statistical optimal solution but has several drawbacks, e.g., the reconstruction is time consuming because the solution is numerically tractable only by iterative algorithms and furthermore the solution strongly depends on several freely-adjustable parameters in the penalty. An alternative approach has been explored by the use of the Karhune-Loève (KL) transform to address the temporal correlation [2]. Our previously works showed that the proposed approach could compensate for non-uniform attenuation together with the treatment of Poisson noise distribution in KL domain accurately [3-4]. In this paper, we extend our previously work to a thoroughly frame work by incorporating well studied algorithms aim to compensate the degradation factors discussed above. Based on the linear property of KL transform, we proved that the system matrix of SPECT remain same both in temporal space and in KL domain. So, the well studied FBP-Type algorithm could be applied directly in KL domain to compensate for the non-uniform attenuation exactly and reconstruct the de-correlated principle components [5-7]. Also, we proved that the Poisson distribution property remained in KL domain, thus our well designed Wiener filter could smooth the noise very well in KL domain [8]. The contribution of photon scatter is treated simply by the triple- energy-window acquisition method [9] and the depth- dependent deconvolution is adopted to correct the detector response separately in KL space [10]. Considering the properties of degradation factors and validated by our simulation study, the following flowchart of compensation scheme in KL domain were adopted in this study. Yi Fan, Chun Jiao, Hongbing Lu, Su Wang and Zhengrong Liang Fully 4D Cardiac Gated SPECT Reconstruction with Simultaneous Compensation in KL Domain I 4232 978-1-4244-2715-4/08/$25.00 ©2008 IEEE 2008 IEEE Nuclear Science Symposium Conference Record M06-379