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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.