Purpose: Previous quantitative MR imaging studies using self-supervised deep learning have reported biased parameter estimates at low SNR. Such systematic errors arise from the choice of Mean Squared Error (MSE) loss function for network training, which is incompatible with Rician-distributed MR magnitude signals. To address this issue, we introduce the negative log Rician likelihood (NLR) loss. Methods: A numerically stable and accurate implementation of the NLR loss was developed to estimate quantitative parameters of the apparent diffusion coefficient (ADC) model and intra-voxel incoherent motion (IVIM) model. Parameter estimation accuracy, precision and overall error were evaluated in terms of bias, variance and root mean squared error and compared against the MSE loss over a range of SNRs (5 - 30). Results: Networks trained with NLR loss show higher estimation accuracy than MSE for the ADC and IVIM diffusion coefficients as SNR decreases, with minimal loss of precision or total error. At high effective SNR (high SNR and small diffusion coefficients), both losses show comparable accuracy and precision for all parameters of both models. Conclusion: The proposed NLR loss is numerically stable and accurate across the full range of tested SNRs and improves parameter estimation accuracy of diffusion coefficients using self-supervised deep learning. We expect the development to benefit quantitative MR imaging techniques broadly, enabling more accurate parameter estimation from noisy data.

翻译：目的：以往采用自监督深度学习的定量磁共振成像研究在低信噪比下常报告有偏的参数估计。此类系统误差源于网络训练时选用均方误差损失函数，该损失与服从黎曼分布的磁共振幅值信号不兼容。为解决该问题，我们提出负对数黎曼似然损失。方法：开发了数值稳定且精确的负对数黎曼似然损失实现，用于估计表观扩散系数模型和体素内不相干运动模型的定量参数。通过偏差、方差和均方根误差评估参数估计的准确性、精密度和整体误差，并在信噪比范围（5-30）内与均方误差损失进行对比。结果：随着信噪比降低，采用负对数黎曼似然损失训练的网络对ADC和IVIM扩散系数的估计准确性均高于均方误差损失，且精密度或总误差的损失极小。在高有效信噪比（高信噪比且小扩散系数）下，两种损失对两模型所有参数的准确性和精密度均表现相当。结论：所提出的负对数黎曼似然损失在全部测试信噪比范围内均保持数值稳定性和准确性，并通过自监督深度学习提升了扩散系数的参数估计精度。我们预期该进展将广泛促进定量磁共振成像技术，实现从噪声数据中更精确的参数估计。