  Multimode fibres offer the advantages of high resolution and miniaturization
over single mode fibers in the field of optical imaging. However, multimode
fibre's imaging is susceptible to perturbations of MMF that can lead to
secondary spatial distortions in the transmitted image. Perturbations include
random disturbances in the fiber as well as environmental noise. Here, we
exploit the fast focusing capability of the Cake-Cutting Hadamard coding
algorithm to counteract the effects of perturbations and improve the system's
robustness. Simulation shows that it can approach the theoretical enhancement
at 2000 measurements. Experimental results show that the algorithm can help the
system to refocus in a short time when MMFs are perturbed. This research will
further contribute to using multimode fibres in medicine, communication, and
detection.
