Optical refocusing through perturbed multimode fiber using Cake-Cutting Hadamard encoding algorithm to improve robustness

•A Cake-Cutting Hadamard encoding algorithm was first used to counteract the fiber's perturbation in multimode fiber imaging to help improve the robustness of the system.•The proposed method can have a fast convergence rate and high enhancement.•The proposed method does not require the adjustment of parameters.•The proposed method improves the robustness of multimode fiber imaging systems regardless of the intensity of noise and random fiber bending.