Image transmission through a multimode fibre in reflection mode with physics-guided deep learning towards ultrathin endoscopy

Ultrathin endoscopy is highly attractive for real-time tissue imaging in narrow and hard-to-reach regions of the body. A single multimode fibre (MMF) is an attractive probe because of its small diameter, flexibility, and diffraction-limited spatial resolution enabled by the large number of transverse modes guided within a single core. Because the distal fibre tip is inaccessible during endoscopy, reflection-mode imaging, in which the same fibre delivers illumination and collects backscattered light, is more practical than transmission-mode imaging. However, image recovery from the resulting speckle pattern is challenging because light undergoes double-pass propagation through the MMF, with mode coupling and dispersion; the backscattered signal is weak, and the camera records intensity only, without phase information. Here, we propose a single-shot reflection-mode MMF imaging framework that combines a reflected real-valued intensity transmission matrix (reflected-RVITM) with an image restoration network. The reflected-RVITM is calibrated using intensity-only measurements, without interferometry or phase retrieval, and provides a physics-guided initial reconstruction from a single backscattered speckle frame. A restoration network then refines this initial reconstruction instead of inverting the raw speckle. Four restoration backbones are evaluated: HPM-Attention-UNet, GAM, MambaIRv2, and CICPNet. On matched datasets, hybrid models outperformed corresponding networks trained to map raw speckle directly to images. For example, HPM-Attention-UNet on MNIST improved mean PCC from 0.572 to 0.944 (+65.1%). Under domain shift, with training only on Fashion-MNIST and tested on unseen CIFAR scenes, hybrid models achieved mean PCC of 0.61-0.65, compared with 0.36-0.50 for direct learning. This framework is further demonstrated using physical objects at the distal fibre tip. These results demonstrate that a reflected-RVITM physics prior combined with a restoration network enables single-shot image recovery after intensity-only calibration, offering a phase-retrieval-free and generalisable route towards minimally invasive reflection-mode MMF endoscopy.