Physics-Driven Autoregressive State Space Models for Medical Image Reconstruction

Medical image reconstruction from undersampled acquisitions is an ill-posed inverse problem requiring accurate recovery of anatomical structures from incomplete measurements. Physics-driven (PD) network models have gained prominence for this task by integrating data-consistency mechanisms with learned priors, enabling improved performance over purely data-driven approaches. However, reconstruction quality still hinges on the network's ability to disentangle artifacts from true anatomical signals-both of which exhibit complex, multi-scale contextual structure. Convolutional neural networks (CNNs) capture local correlations but often struggle with non-local dependencies. While transformers aim to alleviate this limitation, practical implementations involve design compromises to reduce computational cost by balancing local and non-local sensitivity, occasionally resulting in performance comparable to CNNs. To address these challenges, we propose MambaRoll, a novel physics-driven autoregressive state space model (SSM) for high-fidelity and efficient image reconstruction. MambaRoll employs an unrolled architecture where each cascade autoregressively predicts finer-scale feature maps conditioned on coarser-scale representations, enabling consistent multi-scale context propagation. Each stage is built on a hierarchy of scale-specific PD-SSM modules that capture spatial dependencies while enforcing data consistency through residual correction. To further improve scale-aware learning, we introduce a Deep Multi-Scale Decoding (DMSD) loss, which provides supervision at intermediate spatial scales in alignment with the autoregressive design. Demonstrations on accelerated MRI and sparse-view CT reconstructions show that MambaRoll consistently outperforms state-of-the-art CNN-, transformer-, and SSM-based methods.