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 $0.9532\pm 0.3315$. 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.

中文翻译：

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磁共振图像噪声估计的模糊模型

背景和目标

噪声是破坏磁共振（MR）图像视觉清晰度的关键因素。在用于MR图像的许多降噪方案中，降噪的深度是根据噪声的强度决定的，并且其操作参数与噪声的标准偏差（SD）成比例地进行调整。大多数最新的噪声模型都根据所选择的标准概率密度函数（拟合在图像直方图上）间接估计噪声统计量。在这项工作中，提出了一种数学模型，用于根据图像的模糊性来估计磁共振（MR）图像中的噪声统计量。

材料与方法

噪点会显着影响图像的灰度，梯度和模糊性的随机性。基于此原理，提出了一种直接计算噪声方差的方法。通过使用多项式模型，可以直接从噪声图像的模糊性中估计图像的噪声方差。每个像素的模糊隶属度值与归一化局部梯度成比例设置。

结果

在幻像研究中，观察到模糊的二次指数与噪声的标准偏差具有良好的相关性，相关性为 $0.9532\pm 0.3315$。提出的多项式模型表现出良好的拟合度，r = 0.9996。发现该模型在均方根误差（RMSE）方面优于现有模型。

结论

在对MR体模的仿真研究中，发现噪声方差与图像模糊性密切相关。所提出的模型表现出很高的拟合度。发现该模型在均方根误差（RMSE）方面优于文献中提供的噪声模型。与使用图像直方图的间接噪声模型相比，所提出的基于模糊性的噪声模型的原理很简单。