A Fuzzy Model for Noise Estimation in Magnetic Resonance Images

Background and objectives: Noise is a critical factor which destroys the visual clarity of Magnetic Resonance (MR) images. In many of the denoising schemes used on MR images, the depth of denoising is decided based on the strength of noise and their operational parameters are tuned in proportion to the Standard Deviation (SD) of noise. Most of the state-of-the-art noise models estimate noise statistics indirectly from the standard probability density function of choice, fitted on the image histogram. A mathematical model to estimate the noise statistics in Magnetic Resonance (MR) images, from the image fuzziness is proposed in this work. Material and methods: Noise significantly affects the randomness of gray levels, gradient and fuzziness of the image. Based on this principle, a direct method for computing the noise variance is proposed in this paper. Noise variance of the image is directly estimated from the fuzziness of the noisy image by using the polynomial model. The fuzzy membership values at each pixel are set in proportion to the normalized local gradient. Results: On phantom studies, quadratic index of fuzziness is observed to be well-correlated with standard deviation of noise with a correlation of 0.9532 +/- 0.3315. The proposed polynomial model exhibited a goodness of fit, r = 0.9996. The model is found to be superior to the existing models with regard to Root Mean Squared Error (RMSE). Conclusion: On simulation studies on MR phantom, noise variance is found to be well-correlated with image fuzziness. The proposed model exhibited high goodness of fit. The model is found to be superior to the noise models available in literature in terms of Root Mean Square Error (RMSE). The principle of the proposed fuzziness based noise model is straightforward compared to indirect noise models which make use of image histogram. (C) 2019 AGBM. Published by Elsevier Masson SAS. All rights reserved.