We propose a novel deep learning method which combines classical regularization with data augmentation for estimating myelin water fraction (MWF) in the brain via biexponential analysis. Our aim is to design an accurate deep learning technique for analysis of signals arising in magnetic resonance relaxometry. In particular, we study the biexponential model, one of the signal models used for MWF estimation. We greatly extend our previous work on \emph{input layer regularization (ILR)} in several ways. We now incorporate optimal regularization parameter selection via a dedicated neural network or generalized cross validation (GCV) on a signal-by-signal, or pixel-by-pixel, basis to form the augmented input signal, and now incorporate estimation of MWF, rather than just exponential time constants, into the analysis. On synthetically generated data, our proposed deep learning architecture outperformed both classical methods and a conventional multi-layer perceptron. On in vivo brain data, our architecture again outperformed other comparison methods, with GCV proving to be somewhat superior to a NN for regularization parameter selection. Thus, ILR improves estimation of MWF within the biexponential model. In addition, classical methods such as GCV may be combined with deep learning to optimize MWF imaging in the human brain.

翻译：我们提出了一种新颖的深度学习方法，该方法将经典正则化与数据增强相结合，通过双指数分析来估计大脑中的髓鞘水分数（MWF）。我们的目标是设计一种精确的深度学习技术，用于分析磁共振弛豫测量中产生的信号。具体而言，我们研究了双指数模型，这是用于MWF估计的信号模型之一。我们从多个方面极大地扩展了先前关于*输入层正则化（ILR）*的工作。我们现在通过专用神经网络或基于逐信号（或逐像素）的广义交叉验证（GCV）来纳入最优正则化参数选择，以形成增强的输入信号，并且现在将MWF的估计（而不仅仅是指数时间常数）纳入分析。在合成生成的数据上，我们提出的深度学习架构优于经典方法和传统的多层感知机。在活体大脑数据上，我们的架构再次优于其他比较方法，其中GCV在正则化参数选择方面被证明略优于神经网络。因此，ILR改善了双指数模型内MWF的估计。此外，经典方法如GCV可以与深度学习相结合，以优化人脑中的MWF成像。