Learning Generalized Mapping Functions Via Deep-Unrolling for PET Image Reconstruction - Khunti, Hitesh D.; Rao, Bhaskar D. (IEEE transactions on computational imaging, 2025)
This paper presents a novel unified framework that synergically combines model-based iterative algorithms with deep learning-based approaches for tomographic image reconstruction. In particular, the proposed method integrates the interpretability and adaptability of model-based techniques with the expressive power of deep learning-enabling sophisticated non-linear and data-driven priors that enhance reconstruction quality. This synergy yields a framework that is interpretable, robust, generalizable, and produces higher-quality images, effectively addressing key limitations of model-based and learning-based approaches in isolation. First, we show there exists a simple approach to generalize and accelerate Expectation Maximization algorithms which can adaptively speedup convergence based on individual voxel values. We then introduce a key re-parametrization that enables viewing multiple reconstruction algorithms as special cases of a general mapping function between iterations. Building on these insights, we propose a novel model-based deep neural network architecture that effectively is a generalized deep unrolling of a family of algorithms. The proposed method learns to reconstruct high-quality images by systematically performing the required trade-off across the represented algorithms, or it can learn a specific algorithm through training without compromising its robustness and generalization. Furthermore, to address the scarcity of PET imaging data the proposed method can be trained both in supervised and self-supervised regime. Our approach demonstrates superior adaptation with limited training data across varying noise levels, scan duration and out-of-distribution data. Experimental results show significant improvements in image quality compared to both existing iterative methods and deep learning approaches, while maintaining computational efficiency and theoretical interpretability. The associated code is publicly available online.