Improved Biexponential Decay Parameter Estimation from Input-Layer Regularization of a Neural Network

A biexponential decay model can be used to describe relaxation processes in magnetic resonance relaxometry (MRR) studies of biophysical systems. However, the inverse problem of biexponential signal parameter estimation is known to be ill-posed, with distinct parameter sets mapping to nearly identical biexponential decay curves. Recently, neural network (NN) approaches have been found to outperform the conventional method of nonlinear least squares (NLLS) for this problem. Several methods of regularization have been introduced into NN analysis to prevent overfitting; here, we further develop a NN architecture based on Tikhonov regularization at the input layer. We find that this input layer regularization (ILR) of noisy decay signals improves accuracy and precision over conventional NN approaches for two-parameter decay constant estimation, indicating the stabilization effect of ILR of a parameter estimation NN. Our main application of these results will be to MRR studies of macromolecular mapping in the brain. For these applications, we are developing a 3-parameter estimation procedure using ILR of a NN that, in addition to providing estimates of relaxation times, also defines values for component sizes in the biexponential. We make use of multiple CPU processors to parallelize dataset generation for more efficient dataset generation techniques to render these higher-dimensional analyses more tractable. We are also implementing a NN-guided selection of an optimal regularization parameter.