Department of Radiology and Biomedical Research Imaging Center (BRIC) University of North Carolina, Chapel Hill, United States of America.
School of Information and Electrical Engineering, Hunan University of Science & Technology, Xiangtan, China.
PLoS One. 2019 Feb 6;14(2):e0211621. doi: 10.1371/journal.pone.0211621. eCollection 2019.
Diffusion MRI derives its contrast from MR signal attenuation induced by the movement of water molecules in microstructural environments. Associated with the signal attenuation is the reduction of signal-to-noise ratio (SNR). Methods based on total variation (TV) have shown superior performance in image noise reduction. However, TV denoising can result in stair-casing effects due to the inherent piecewise-constant assumption. In this paper, we propose a tight wavelet frame based approach for edge-preserving denoising of diffusion-weighted (DW) images. Specifically, we employ the unitary extension principle (UEP) to generate frames that are discrete analogues to differential operators of various orders, which will help avoid stair-casing effects. Instead of denoising each DW image separately, we collaboratively denoise groups of DW images acquired with adjacent gradient directions. In addition, we introduce a very efficient method for solving an ℓ0 denoising problem that involves only thresholding and solving a trivial inverse problem. We demonstrate the effectiveness of our method qualitatively and quantitatively using synthetic and real data.
扩散 MRI 从微观结构环境中水分子的运动引起的磁共振信号衰减中获得对比。与信号衰减相关的是信噪比 (SNR) 的降低。基于全变差 (TV) 的方法在图像降噪方面表现出了优异的性能。然而，由于固有的分段常数假设，TV 去噪可能会导致阶梯效应。在本文中，我们提出了一种基于紧小波框架的方法，用于保留扩散加权 (DW) 图像的边缘进行去噪。具体来说，我们利用酉延拓原理 (UEP) 生成与各种阶微分算子离散相似的框架，这将有助于避免阶梯效应。我们不是分别对每个 DW 图像进行去噪，而是对具有相邻梯度方向的 DW 图像组进行协作去噪。此外，我们引入了一种非常有效的方法来解决仅涉及阈值处理和求解一个简单逆问题的 ℓ0 去噪问题。我们使用合成数据和真实数据定性和定量地证明了我们方法的有效性。
