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

A decaying biexponential model is used to describe relaxation processes in biophysical systems as disparate as drug pharmacokinetics, fluorescence imaging, and magnetic resonance relaxometry (MRR). However, estimation of biexponential signal parameters is well-known to be an ill-posed problem, with distinct parameter sets producing nearly identical decay curves. Recently introduced Neural network (NN) approaches out-perform non-linear least squares (NLLS) analysis. Regularization is an important component of NN design to prevent overfitting; here, we introduce a new type of NN regularization based on Tikhonov regularization at the input layer. We achieve robust performance in signals with limited SNR by incorporating a larger region of parameter space into the training set than in the testing set. We find improvements in accuracy and precision of decay constant estimation on the order of 15% over conventional advanced NN analyses, and of roughly 40% over NLLS, highlighting the additional content provided by regularization. Input layer regularization is compatible with more conventional methods of NN regularization, such as epoch analysis and weight drop-out. In our main application of MRR, these results will improve macromolecular mapping in the brain and other tissues.