An Efficient Statistical Method for Image Noise Level Estimation

In this paper, we address the problem of estimating noise level from a single image contaminated by additive zero-mean Gaussian noise. We first provide rigorous analysis on the statistical relationship between the noise variance and the eigenvalues of the covariance matrix of patches within an image, which shows that many state-of-the-art noise estimation methods underestimate the noise level of an image. To this end, we derive a new nonparametric algorithm for efficient noise level estimation based on the observation that patches decomposed from a clean image often lie around a low-dimensional subspace. The performance of our method has been guaranteed both theoretically and empirically. Specifically, our method outperforms existing state-of-the-art algorithms on estimating noise level with the least executing time in our experiments. We further demonstrate that the denoising algorithm BM3D algorithm achieves optimal performance using noise variance estimated by our algorithm.