Image denoising using simulated bifurcation based Ising machine

Abstract Ising machines are computational systems designed to solve combinatorial optimization problems by mapping them onto the Ising model. Among these, quantum inspired Simulated Bifurcation Machines (SBMs) have gained attention for their ability to efficiently minimize energy in large-scale problems. This work explores, for the first time, the application of SBMs to image denoising. We frame the image denoising task as an optimization problem, aiming to minimize the energy of the system represented by the noisy image. The Ising machine optimizes pixel values to restore the original image quality. We implement an image denoising task using SBM and propose a novel method of training Hopfield Neural Networks (HNN) with the Hebbian learning rule to generate the coupling matrix for SBM. The performance of SBM is evaluated with two integration methods: Euler and Huen. Further, the results shows that the SBM with Huen’s integration method achieves faster energy convergence and provides significant improvements in denoising performance compared to SBM with Euler’s and conventional Hopfield networks. The methods are also validated across various noise levels, with the SBM with Heun’s method consistently outperforming alternative approaches.