Kernel-based Maximum likelihood reconstruction of attenuation and activity (MLAA) in SPECT imaging for improved attenuation correction and activity quantification: Simulation, phantom and patient validation studies

OBJECTIVE: Quantitative SPECT/CT for radiopharmaceutical therapy relies on accurate attenuation map (µ-map). Because attenuation is energy dependent, CT-derived maps must be converted to radionuclide-specific values, typically via bilinear scaling (BLS), which can introduce bias to activity quantification. To address this, we investigate the application of a kernel-based maximum-likelihood attenuation and activity (MLAA) algorithm that incorporates CT-derived anatomical features and SPECT emission data to improve µ-map accuracy. Approach: The MLAA algorithm jointly estimates µ-map and activity distribution by maximizing the Poisson log likelihood. Activity is updated using standard OSEM, while the µ-map is refined via gradient ascent from a CT-derived initialization. However, standard MLAA suffers from attenuation-activity crosstalk. To mitigate this effect, we introduce kernel MLAA, incorporating CT-based features to enhance attenuation-activity separation and constrain µ-map updates. Performance was evaluated using Monte Carlo simulations and experimental data from both a NEMA phantom and a patient scan. The entire method is implemented in the PyTomography platform, which is publicly available and GPU-accelerated for efficient 3D reconstruction. Main results: In simulations, standard MLAA exhibited strong crosstalk artifacts, whereas kernel MLAA substantially suppressed these artifacts and reduced µ-map bias, achieving an approximately 84% decrease in liver voxel-wise MAE compared with BLS. It also improved activity quantification accuracy, with the recovery-coefficient bias converging to 0.90%±0.34% across 20 noise realizations. The simulated iodinated contrast-induced activity bias decreased from 18.11% to 1.51%. Phantom and patient data validated that kernel MLAA restored perturbed µ-values, reducing mean bias from 13.6% to 0.6% (phantom) and from 13.7% to 0.3% (patient). Noise remained controlled across iterations, whereas standard MLAA tended to amplify noise. Significance: Kernel MLAA provides a robust approach for improving attenuation correction in quantitative SPECT by automatically detecting and correcting µ-map bias, offering a potential solution when CT-derived attenuation maps are biased or unreliable.