Input Layer Regularization and Automated Regularization Hyperparameter Tuning for Myelin Water Estimation Using Deep Learning

We present a deep learning framework that combines classical regularization and data preprocessing to improve estimation of the myelin water fraction (MWF) in the brain from magnetic resonance relaxometry data. The proposed method is developed within the context of biexponential signal modeling, a standard approach for quantifying MWF. Building on prior work on input layer regularization (ILR), we introduce several key extensions. First, we incorporate optimal regularization hyperparameter selection using either a dedicated neural network or generalized cross-validation (GCV), applied on a signal-by-signal (or pixel-by-pixel) basis to generate concatenated input features. Second, we extend the framework to directly estimate MWF in addition to exponential time constants. On synthetic data, the proposed architecture outperforms both conventional regularized fitting methods and standard multilayer perceptrons. When applied to in vivo brain data, it again yields superior accuracy, with GCV-based parameter selection performing slightly better than the neural network alternative. These findings demonstrate that ILR enhances MWF estimation within the biexponential model and that classical regularization techniques, when integrated with deep learning, can substantially improve quantitative estimation of myelin content.