Abstract
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.
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Notes
- 1.
The source code with scripts and sample data is available in: https://github.com/icai-uma/RicianNoiseEst_3DMRI_BenfordsLaw.git.
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Acknowledgements
This work is partially supported by the following Spanish grants: TIN2016-75097-P, PIT.UMA.B1.2017, RTI2018-094645-B-I00 and UMA18-FEDERJA-084. All of them include funds from the European Regional Development Fund (ERDF). The authors thankfully acknowledge the computer resources, technical expertise and assistance provided by the SCBI (Supercomputing and Bioinformatics) center of the University of Málaga. They also gratefully acknowledge the support of NVIDIA Corporation with the donation of two Titan X GPUs. The authors acknowledge the funding from the Universidad de Málaga. Rosa Maza-Quiroga is funded by a Ph.D. grant from the Instituto de Salud Carlos III (ISCIII) of Spain under the i-PFIS program (IFI19/00009). Karl Thurnhofer-Hemsi is funded by a Ph.D. scholarship from the Spanish Ministry of Education, Culture and Sport under the FPU program (FPU15/06512).
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Maza-Quiroga, R., Thurnhofer-Hemsi, K., López-Rodríguez, D., López-Rubio, E. (2021). Rician Noise Estimation for 3D Magnetic Resonance Images Based on Benford’s Law. In: de Bruijne, M., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2021. MICCAI 2021. Lecture Notes in Computer Science(), vol 12906. Springer, Cham. https://doi.org/10.1007/978-3-030-87231-1_33
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