Rician Noise Estimation for 3D Magnetic Resonance Images Based on Benford's Law.

In this paper, a novel method to estimate the level of Rician noise in magnetic resonance images is presented. We hypothesize that noiseless images follow Benford’s law, that is, the probability distribution of the first digit of the image values is logarithmic. We show that this is true when we consider the raw acquired image in the frequency domain. Two measures are then used to quantify the (dis)similarity between the actual distribution of the first digits and the more theoretical Benford’s law: the Bhattacharyya coefficient and the Kullback-Leibler divergence. By means of these measures, we show that the amount of noise directly affects the distribution of the first digits, thereby making it deviate from Benford’s law. In addition, in this work, these findings are used to design a method to estimate the amount of Rician noise in an image. The utilization of supervised machine learning techniques (linear regression, polynomial regression, and random forest) allows predicting the parameters of the Rician noise distribution using the dissimilarity between the measured distribution and Benford’s law as the input variable for the regression. In our experiments, testing over magnetic resonance images of 75 individuals from four different repositories, we empirically show that these techniques are able to precisely estimate the noise level present in the test T1 images.