A single-pixel imaging method for multimode fibers with low sampling rates

Multimode fibers (MMFs), due to their microscopic dimensions and high flexibility, hold significant potential for applications in complex scenarios such as flexible endoscopy and biomedical imaging. However, existing fiber-based single-pixel imaging (SPI) techniques typically rely on random speckle modulation, which introduces redundancy in the sensing matrix and exhibit poor reconstruction fidelity under low sampling rates when using traditional sparse optimization algorithms. To address these challenges, this study proposes a novel SPI reconstruction framework that integrates sparse basis optimization with an interpretable neural network. Specifically, a low-correlation speckle basis is constructed through correlation analysis and a greedy selection algorithm, thereby enhancing the efficiency of compressive sensing. For image reconstruction, a modified ISTA-net architecture incorporating a "Speckle Mode" module is designed, which leverages both physical priors and neural network capabilities, eliminating the need for manual parameter tuning and enabling robust adaptation to fiber speckle illumination. Simulation results demonstrate that, under low sampling rates, the proposed method significantly outperforms the conventional TVAL3 algorithm, achieving a 2.82-fold improvement in SSIM and a 2.54-fold enhancement in PSNR. The proposed approach offers strong generalization ability and practical applicability, providing a new pathway for the deployment of flexible fiber-based imaging systems.