  We investigate a framework for binary image denoising via restricted
Boltzmann machines (RBMs) that introduces a denoising objective in quadratic
unconstrained binary optimization (QUBO) form and is well-suited for quantum
annealing. The denoising objective is attained by balancing the distribution
learned by a trained RBM with a penalty term for derivations from the noisy
image. We derive the statistically optimal choice of the penalty parameter
assuming the target distribution has been well-approximated, and further
suggest an empirically supported modification to make the method robust to that
idealistic assumption. We also show under additional assumptions that the
denoised images attained by our method are, in expectation, strictly closer to
the noise-free images than the noisy images are. While we frame the model as an
image denoising model, it can be applied to any binary data. As the QUBO
formulation is well-suited for implementation on quantum annealers, we test the
model on a D-Wave Advantage machine, and also test on data too large for
current quantum annealers by approximating QUBO solutions through classical
heuristics.
