Wavelet-enhanced residual optimal transport for Mamba-based image restoration in photoacoustic tomography

Photoacoustic tomography (PAT) combines the high contrast of optical imaging with deep tissue penetration via ultrasound detection. However, hardware limitations often cause sparse sampling during image acquisition, resulting in disruptive streak artifacts that many current deep-learning methods fail to remove effectively. In this paper, we introduce Residual Condition Optimal Transport Mamba (RCMamba)-a novel framework that enhances residual optimal transport by integrating wavelet-based analysis with a hybrid multi-scale state space model backbone, specifically designed for sparse PAT image restoration. Our approach makes two primary contributions. First, we propose a wavelet residual-enhanced transport plan that leverages multi-resolution analysis and a novel wavelet coherence penalty to accurately capture the complex, scale-dependent sparsity patterns characteristic of sparse acquisitions. Second, we develop a hybrid multi-scale mamba architecture that uniquely combines window-based and global state space scanning to preserve both fine anatomical details and long-range structural information. Extensive experiments on vessel phantoms and <i>in vivo</i> mouse models across various sampling densities (16, 32, and 64 projections) demonstrate that RCMamba consistently outperforms state-of-the-art techniques in terms of artifact suppression and structural fidelity. RCMamba holds great promise in advancing the clinical potential of sparse-sampling PAT systems for diagnostic imaging and interventional procedures.