W-LDMM: A Wasserstein driven low-dimensional manifold model for noisy image restoration

Abstract The Wasserstein distance originated from the optimal transport theory is a general and flexible statistical metric in a variety of image processing problems. In this paper, we propose a novel Wasserstein driven low-dimensional manifold model (W-LDMM), which tactfully embrace the Wasserstein distance between two noise histograms and low-dimensional manifold regularization for noisy image restoration. Specifically, with the Wasserstein distance, the discrepancy between the estimated noise histogram and the reference noise histogram is minimized to improve the noise estimation accuracy. Moreover, based on the fact that the patch manifold structures of many natural images are low dimensional, the dimension of the image patch maniflod is utilized as regularization constraint. The key idea of W-LDMM is that the Wasserstein distance for noise constraint and the low-dimensional manifold for image regularization are complementary to each other, rather than isolated and uncorrelated. Together, they promote the W-LDMM to exhibit excellent restored results in Gaussian denoising and noisy image inpainting. Finally, extensive experiments confirm that our W-LDMM can greatly improve visual and quantitative performance compared to several popular image restoration models.