Deep Equilibrium Unfolding Learning for Noise Estimation and Removal in Optical Molecular Imaging

Abstract

In clinical optical molecular imaging, the need for real-time high frame rates and low excitation doses to ensure patient safety inherently increases susceptibility to detection noise. Faced with the challenge of image degradation caused by severe noise, image denoising is essential for mitigating the trade-off between acquisition cost and image quality. However, prevailing deep learning methods exhibit uncontrollable and suboptimal performance with limited interpretability, primarily due to neglecting underlying physical model and frequency information. In this work, we introduce an end-to-end model-driven Deep Equilibrium Unfolding Mamba (DEQ-UMamba) that integrates proximal gradient descent technique and learnt spatial-frequency characteristics to decouple complex noise structures into statistical distributions, enabling effective noise estimation and suppression in fluorescent images. Moreover, to address the computational limitations of unfolding networks, DEQ-UMamba trains an implicit mapping by directly differentiating the equilibrium point of the convergent solution, thereby ensuring stability and avoiding non-convergent behavior. With each network module aligned to a corresponding operation in the iterative optimization process, the proposed method achieves clear structural interpretability and strong performance. Comprehensive experiments conducted on both clinical and in vivo datasets demonstrate that DEQ-UMamba outperforms current state-of-the-art alternatives while utilizing fewer parameters, facilitating the advancement of cost-effective and high-quality clinical molecular imaging.