Veraart Jelle, Fieremans Els, Novikov Dmitry S
Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA.
Department of Physics, iMinds-Vision Lab, University of Antwerp, Antwerp, Belgium.
Magn Reson Med. 2016 Nov;76(5):1582-1593. doi: 10.1002/mrm.26059. Epub 2015 Nov 24.
To estimate the spatially varying noise map using a redundant series of magnitude MR images.
We exploit redundancy in non-Gaussian distributed multidirectional diffusion MRI data by identifying its noise-only principal components, based on the theory of noisy covariance matrices. The bulk of principal component analysis eigenvalues, arising due to noise, is described by the universal Marchenko-Pastur distribution, parameterized by the noise level. This allows us to estimate noise level in a local neighborhood based on the singular value decomposition of a matrix combining neighborhood voxels and diffusion directions.
We present a model-independent local noise mapping method capable of estimating the noise level down to about 1% error. In contrast to current state-of-the-art techniques, the resultant noise maps do not show artifactual anatomical features that often reflect physiological noise, the presence of sharp edges, or a lack of adequate a priori knowledge of the expected form of MR signal.
Simulations and experiments show that typical diffusion MRI data exhibit sufficient redundancy that enables accurate, precise, and robust estimation of the local noise level by interpreting the principal component analysis eigenspectrum in terms of the Marchenko-Pastur distribution. Magn Reson Med 76:1582-1593, 2016. © 2015 International Society for Magnetic Resonance in Medicine.
使用一系列冗余的磁共振（MR）幅值图像估计空间变化的噪声图。
基于噪声协方差矩阵理论，通过识别仅含噪声的主成分，我们利用了非高斯分布的多方向扩散MRI数据中的冗余信息。由于噪声产生的大部分主成分分析特征值由通用的马尔琴科 - 帕斯图尔分布描述，该分布由噪声水平参数化。这使我们能够基于结合邻域体素和扩散方向的矩阵的奇异值分解来估计局部邻域的噪声水平。
我们提出了一种与模型无关的局部噪声映射方法，能够将噪声水平估计到约1%的误差。与当前的先进技术相比，所得的噪声图不会显示出通常反映生理噪声、尖锐边缘的存在或对MR信号预期形式缺乏足够先验知识的伪解剖特征。
模拟和实验表明，典型的扩散MRI数据表现出足够的冗余性，通过根据马尔琴科 - 帕斯图尔分布解释主成分分析特征谱，能够准确、精确且稳健地估计局部噪声水平。《磁共振医学》76:1582 - 1593, 2016。© 2015国际磁共振医学学会。
