论文标题
高维MRI数据的张量
Tensor denoising of high-dimensional MRI data
论文作者
论文摘要
信号与噪声比（SNR）从根本上限制了通过磁共振成像（MRI）访问的信息。最近的一系列剥离技术已经解决了这一局限性，最近包括所谓的MPPCA：信号的主成分分析（PCA），然后进行自动等级估计，从而利用了Marchenko-Pastur（MP）的噪声单数值分布。这种流行的方法在由数据斑组成的矩阵上操作，客观地识别噪声组件，理想情况下，可以删除噪声，而无需引入诸如图像模糊或非本地平均的伪影。但是，MPPCA等级估计依赖于相对于信号成分数量的大量噪声奇异值以避免这种不良影响。当数据绘制时，不太可能满足这种情况，因此矩阵很小，例如由于空间变化的噪声。在这里，我们介绍了张量MPPCA（TMPPCA），以降低多维数据，例如从多对比度采集中。 TMPPCA不是在矩阵中结合尺寸，而是利用多维数据固有的张量结构的每个维度来更好地表征噪声，并递归估计信号成分。相对于基于矩阵的MPPCA，TMPPCA不需要其他假设，并且比较了数值幻影中的两者和多TE-TE扩散MRI数据集，TMPPCA极大地改善了DeNOSIS的性能。对于小型数据绘制，尤其如此，我们认为在空间变化的噪声情况下，这将改善DeNo的状态。
The signal to noise ratio (SNR) fundamentally limits the information accessible by magnetic resonance imaging (MRI). This limitation has been addressed by a host of denoising techniques, recently including so-called MPPCA: Principal component analysis (PCA) of the signal followed by automated rank estimation, exploiting the Marchenko-Pastur (MP) distribution of noise singular values. Operating on matrices comprised by data-patches, this popular approach objectively identifies noise components and, ideally, allows noise to be removed without introducing artifacts such as image blurring or non-local averaging. The MPPCA rank estimation, however, relies on a large number of noise singular values relative to the number of signal components to avoid such ill effects. This condition is unlikely to be met when data-patches and therefore matrices are small, for example due to spatially varying noise. Here, we introduce tensor MPPCA (tMPPCA) for the purpose of denoising multidimensional data, for example from multi-contrast acquisitions. Rather than combining dimensions in matrices, tMPPCA utilizes each dimension of the multidimensional data's inherent tensor-structure to better characterize noise, and to recursively estimate signal components. Relative to matrix-based MPPCA, tMPPCA requires no additional assumptions, and comparing the two in a numerical phantom and a multi-TE diffusion MRI dataset, tMPPCA dramatically improves denoising performance. This is particularly true for small data-patches, which we believe will improve denoising in cases of spatially varying noise.
