Hybrid OSEM-PDHG reconstruction for SPECT with non-smooth total variation regularization

We propose a novel hybrid reconstruction method for SPECT imaging that integrates the OSEM algorithm with Condat's extension of the PDHG method, enabling the usage of non-smooth TV functional as a prior. Unlike traditional OSL scheme that requires smoothed version of TV, our approach directly incorporates non-smooth TV. To ensure spatially uniform regularization strength, even when attenuation is modeled, we introduce a sensitivity-based compensation strategy in the PDHG update step. This adjustment improves regularization consistency and simplifies the selection of regularization parameters. We evaluate the method using Monte Carlo simulations of a Jaszczak phantom under varying noise conditions. The proposed OSEM-PDHG framework outperforms OSL-TV in terms of PSNR, SSIM, and noise suppression, particularly in low-SNR scenarios. While increased regularization reduces contrast in small structures such as cold rods, the method achieves significantly improved image quality without compromising stability. Our results suggest that this framework is a robust and flexible alternative for noise-aware SPECT reconstruction.