Noise estimation using statistics of natural images

We develop a framework for estimating noises of natural images using two important properties of natural image statistics: high kurtosis and scale invariance of natural images in certain transform domains. We examine the effects of additive independent noise on the third and fourth moments of the transformed image signal (skewness and kurtosis). By exploring the said priors of high kurtosis and scale invariance of natural image statistics in 2D discrete cosine transform domain and random unitary transform domain, we derive constrained nonlinear optimization algorithms for accurate estimation of noise variance. Simulation and comparative study show that the proposed approach is capable of estimating the variance of Gaussian additive noise with a relative error as low as one percent. Moreover, the new estimation approach is shown to be effective on multiplicative-additive compound noises as well. This work can significantly improve the performance of existing denoising techniques that require the noise variance as a critical parameter.