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

Maza-Quiroga, Rosa; Thurnhofer‐Hemsi, Karl; López-Rodríguez, Domingo; López‐Rubio, Ezequiel

doi:10.1007/978-3-030-87231-1_33

Cited by 2 publications

(5 citation statements)

References 25 publications

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“…It determines M4 as the best metric (see Figure 2). On the other hand, the M1 option is positioned at the bottom of the score, indicating that the metrics used in this analysis outperform the previous results in [30]. With good precision, R 2 = 0.98 determines SVR as the best model for the MMRR repository (see Table S6).…”

Section: Mindbogglementioning

confidence: 74%

“…In a previous work [30], we explored only M1 and M3 as separate inputs for the regression of the Rician noise level, obtaining the best results in the PR model with the HLN repository. Now, we propose new metrics as inputs and new regressors to estimate the Rician noise.…”

Section: Resultsmentioning

confidence: 99%

“…In general, the score of the best performing metrics does not include the single M1 or single M4 metrics. Therefore, we greatly outperform the prior proposal [30].…”

Section: Discussionmentioning

confidence: 95%

“…It is shown how regression techniques can be applied to accurately predict the noise level of an image. Note that, in a previous work [30], the authors have explored the regression of the noise level from the fitting of the Fourier coefficients to Benford's law. Now, we provide a deeper study to assess if other different transforms (such as the discrete cosine transform and the discrete sine transform) present the same first-digit distribution.…”

Section: Introductionmentioning

confidence: 99%

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

Maza-Quiroga,

Thurnhofer-Hemsi,

López-Rodríguez

et al. 2023

Axioms

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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.

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Section: Mindbogglementioning

confidence: 74%

Section: Resultsmentioning

confidence: 99%

“…In general, the score of the best performing metrics does not include the single M1 or single M4 metrics. Therefore, we greatly outperform the prior proposal [30].…”

Section: Discussionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Maza-Quiroga,

Thurnhofer-Hemsi,

López-Rodríguez

et al. 2023

Axioms

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show abstract

“…The researchers introduced different methods for the Rician noise distribution where a low signal-to-noise ratio (SNR) exists in MRI applications. [19][20][21] The paper 22 used a neural network as a probabilistic model to remove the noise in MRI. Recently, an author applied the denoising diffusion probabilistic model to show better performance for noise reduction in MRI.…”

Section: Related Workmentioning

confidence: 99%

A powerful probabilistic model for noise analysis in medical images

Gürman

Bilgehan²,

Sabuncu³

et al. 2022

Int J Imaging Syst Tech

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The statistical properties in various medical images demonstrate uncorrelated noise fluctuations. The signal noise fluctuations are generally due to physical imaging processes and have nothing to do with the tissue textures. Adding the noise types (e.g., quantization, electronics, photon) usually degrade medical images. The noise variation is usually assumed to be additive with zero-mean, constant variance Gaussian distribution. However, close consideration of different medical images indicates the need for better model representation to minimise the noise that can be vital in decision-making. This research proposed a probabilistic method to represent all real-type noise in general medical images. The method aims to cover most classical statistical models such as Gaussian, lognormal, Rayleigh, Weibull, and Nakagami without a prior examination to test for fitness. The proposed model was applied to actual clinical images to test the performance of the noise originating from the physical processes. The noise is assumed to be additive white Gaussian type with a zero mean and constant variance. The theoretical literature indicates that a nonlinear function can better represent noise. This research helps to form a relationship between the image intensity and the noise variance that yields the fitting parameters in the introduced nonlinear function. The validity of the proposed method was proved mathematically and tested using the well know Kolmogorov-Smirnov (K-S) and Akaike Information Criteria (AIC) tests. The method was successfully applied to various clinical images such as magnetic resonance, x-ray, and panoramic images. The model's performance is compared with the classical models using root mean squared error (RMSE), relative error (RE), and R 2 as the evaluation matrices. The presented model has outperformed all classic models.

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

Cited by 2 publications

References 25 publications

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

A powerful probabilistic model for noise analysis in medical images

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