Scalable Noisy Image Restoration using Quantum Markov Random Field

Abstract

We propose an algorithm for binary image denoising, which uses a Markovian Random Field based energy optimization approach to remove Gaussian and salt and pepper noise. It is a two-stage algorithm. In the first stage, the image is processed pixel by pixel to generate a relation graph for each pixel using its neighbor's in an Ising model. In the Second stage, the relation graph with its initial state is embedded into the D-Wave quantum annealer. The solution is one state among 2n states (n = number of pixels) that minimizes the Ising model. The minimized solution is reprocessed and converted back as a denoised image. We use a fixed size window to convolve a large image. The visual and quantitative results show that the Mean Squared Error was reduced by 39 % and the Peak Signal Noise Ratio was reduced by 8.5 %, for the Gaussian noise. Similar results were obtained for the Salt and pepper noise. Also shown was the MRF restoration of a de-noised image was comparable to that obtained with classical approaches. The proposed de-noising MRF algorithm implemented on the D-Wave quantum annealer implies the method can be extended to image segmentation problems.