Physically-Based Inverse Rendering Framework for PET Image Reconstruction

Abstract: Differentiable rendering has been widely adopted in computer graphics as a powerful approach to inverse problems, enabling efficient gradient-based optimization by differentiating the image formation process with respect to millions of scene parameters. Inspired by this paradigm, we propose a physically-based inverse rendering (IR) framework, the first ever platform for PET image reconstruction using Dr.Jit, for PET image reconstruction. Our method integrates Monte Carlo sampling with an analytical projector in the forward rendering process to accurately model photon transport and physical process in the PET system. The emission image is iteratively optimized using voxel-wise gradients obtained via automatic differentiation, eliminating the need for manually derived update equations. The proposed framework was evaluated using both phantom studies and clinical brain PET data acquired from a Siemens Biograph mCT scanner. Implementing the Maximum Likelihood Expectation Maximization (MLEM) algorithm across both the CASToR toolkit and our IR framework, the IR reconstruction achieved a higher signal-to-noise ratio (SNR) and improved image quality compared to CASToR reconstructions. In clinical evaluation compared with the Siemens Biograph mCT platform, the IR reconstruction yielded higher hippocampal standardized uptake value ratios (SUVR) and gray-to-white matter ratios (GWR), indicating enhanced tissue contrast and the potential for more accurate tau localization and Braak staging in Alzheimer's disease assessment. The proposed IR framework offers a physically interpretable and extensible platform for high-fidelity PET image reconstruction, demonstrating strong performance in both phantom and real-world scenarios.