Diffusion kurtosis imaging (DKI) has been shown to be valuable in a wide range of neuroscientific and clinical applications. However, reliable estimation of DKI tensors is often compromised by noise, especially for the kurtosis tensor (KT). Here, we propose a joint denoising and estimating framework that integrates multiple sources of prior information, including nonlocal structural self-similarity (NSS), local spatial smoothness (LSS), physical relevance (PR) of the DKI model, and noise characteristics of magnitude diffusion MRI (dMRI) images for improved estimation of DKI tensors. The local and nonlocal spatial smoothing constraints are complementary to each other, making the proposed framework highly effective in reducing the noise fluctuations on DKI tensors, especially KT. As an additional refinement, we propose to impose a physically relevant constraint within our joint denoising and estimation framework. We further adopt the first-moment noise-corrected fitting model (M ¹ NCM) to remove the noncentral ${\chi }$ -distribution noise bias. The effectiveness of integrating multiple sources of priors into the joint framework is verified by comparing the proposed M ¹ NCM-NSS-LSS-PR method with various versions of M ¹ NCM-based estimators and two state-of-the-art methods. Results show that the proposed method outperformed the compared methods in simulations and in-vivo dMRI datasets of both spatially stationary and nonstationary noise distributions. The in-vivo experiments also show that the proposed M ¹ NCM-NSS-LSS-PR method was robust to the number of diffusion directions.

中文翻译：

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使用多个先验信息去噪和估计扩散峰度张量的联合框架

扩散峰度成像 (DKI) 已被证明在广泛的神经科学和临床应用中具有价值。然而，DKI 张量的可靠估计通常会受到噪声的影响，尤其是对于峰态张量 (KT)。在这里，我们提出了一个联合去噪和估计框架，该框架集成了多个先验信息源，包括非局部结构自相似性 (NSS)、局部空间平滑度 (LSS)、DKI 模型的物理相关性 (PR) 和幅度噪声特征用于改进 DKI 张量估计的扩散 MRI (dMRI) 图像。局部和非局部空间平滑约束相互补充，使得所提出的框架在减少 DKI 张量，尤其是 KT 上的噪声波动方面非常有效。作为额外的改进，我们建议在我们的联合去噪和估计框架中施加物理相关的约束。我们进一步采用一阶噪声校正拟合模型（M ¹ NCM）去除非中心 ${\chi}$ -分布噪声偏差。^{通过将提出的 M 1} NCM-NSS-LSS-PR 方法与各种版本的 M ¹ NCM 估计器和两种最先进的方法进行比较，验证了将多个先验源集成到联合框架中的有效性 。结果表明，所提出的方法在空间静止和非静止噪声分布的模拟和体内 dMRI 数据集中优于比较方法。体内实验还表明，所提出的 M ¹ NCM-NSS-LSS-PR 方法对扩散方向的数量具有鲁棒性。