Regression of the Rician Noise Level in 3D Magnetic Resonance Images from the Distribution of the First Significant Digit

Regression of the Rician Noise Level in 3D Magnetic Resonance Images from the Distribution of the First Significant Digit

Neuroimage
Authors
Rosa María Maza-Quiroga , Karl Thurnhofer-Hemsi , Domingo López-Rodríguez , Ezequiel López-Rubio
Published
13 December 2023
Publication details
Axioms, 12(12), 1117
Links
DOI PDF

 

Abstract

This paper investigates the distribution characteristics of Fourier, discrete cosine, and discrete sine transform coefficients in T1 MRI images. This paper reveals their adherence to Benford’s law, characterized by a logarithmic distribution of first digits. The impact of Rician noise on the first digit distribution is examined, which causes deviations from the ideal distribution. A novel methodology is proposed for noise level estimation, employing metrics such as the Bhattacharyya distance, Kullback–Leibler divergence, total variation distance, Hellinger distance, and Jensen–Shannon divergence. Supervised learning techniques utilize these metrics as regressors. Evaluations on MRI scans from several datasets coming from a wide range of different acquisition devices of 1.5 T and 3 T, comprising hundreds of patients, validate the adherence of noiseless T1 MRI frequency domain coefficients to Benford’s law. Through rigorous experimentation, our methodology has demonstrated competitiveness with established noise estimation techniques, even surpassing them in numerous conducted experiments. This research empirically supports the application of Benford’s law in transforms, offering a reliable approach for noise estimation in denoising algorithms and advancing image quality assessment.

Citation

How to cite

R. Maza-Quiroga, K. Thurnhofer-Hemsi, D. López-Rodríguez, et al. “Regression of the Rician Noise Level in 3D Magnetic Resonance Images from the Distribution of the First Significant Digit”. In: Axioms 12.12 (2023). ISSN: 2075-1680. DOI: 10.3390/axioms12121117. URL: https://www.mdpi.com/2075-1680/12/12/1117.

BibTeX 
<pre><code>
@Article{axioms12121117, AUTHOR = {Maza-Quiroga, Rosa and Thurnhofer-Hemsi, Karl and López-Rodríguez, Domingo and López-Rubio, Ezequiel}, TITLE = {Regression of the Rician Noise Level in 3D Magnetic Resonance Images from the Distribution of the First Significant Digit}, JOURNAL = {Axioms}, VOLUME = {12}, YEAR = {2023}, NUMBER = {12}, ARTICLE-NUMBER = {1117}, URL = {https://www.mdpi.com/2075-1680/12/12/1117}, ISSN = {2075-1680}, ABSTRACT = {This paper investigates the distribution characteristics of Fourier, discrete cosine, and discrete sine transform coefficients in T1 MRI images. This paper reveals their adherence to Benford’s law, characterized by a logarithmic distribution of first digits. The impact of Rician noise on the first digit distribution is examined, which causes deviations from the ideal distribution. A novel methodology is proposed for noise level estimation, employing metrics such as the Bhattacharyya distance, Kullback–Leibler divergence, total variation distance, Hellinger distance, and Jensen–Shannon divergence. Supervised learning techniques utilize these metrics as regressors. Evaluations on MRI scans from several datasets coming from a wide range of different acquisition devices of 1.5 T and 3 T, comprising hundreds of patients, validate the adherence of noiseless T1 MRI frequency domain coefficients to Benford’s law. Through rigorous experimentation, our methodology has demonstrated competitiveness with established noise estimation techniques, even surpassing them in numerous conducted experiments. This research empirically supports the application of Benford’s law in transforms, offering a reliable approach for noise estimation in denoising algorithms and advancing image quality assessment.}, DOI = {10.3390/axioms12121117} } 
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Regression of the Rician Noise Level in 3D Magnetic Resonance Images from the Distribution of the First Significant Digit

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Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

  1. Bogdan-Vasile Ileanu, Adrian Pană (2026). Auditing primary diagnostic coding using the First Digit Law of Benford. Journal of Management Analytics DOI
  2. Hyoyoung Jang, Sangmin LEE (2026). Diffusion model with Rician–Gaussian priors for robust MR image synthesis. Neural Networks DOI