biostudies-literatureRozowski MIntramural NIH HHSNIA NIH HHSDivision of Mathematical SciencesNational Science Foundation of Sri LankaNational Institute on Aging1076-1086https://www.ebi.ac.uk/biostudies/studies/S-EPMC10185331biostudies-literatureUnknown60(11)Many methods have been developed for estimating the parameters of biexponential decay signals, which arise throughout magnetic resonance relaxometry (MRR) and the physical sciences. This is an intrinsically ill-posed problem so that estimates can depend strongly on noise and underlying parameter values. Regularization has proven to be a remarkably efficient procedure for providing more reliable solutions to ill-posed problems, while, more recently, neural networks have been used for parameter estimation. We re-address the problem of parameter estimation in biexponential models by introducing a novel form of neural network regularization which we call input layer regularization (ILR). Here, inputs to the neural network are composed of a biexponential decay signal augmented by signals constructed from parameters obtained from a regularized nonlinear least-squares estimate of the two decay time constants. We find that ILR results in a reduction in the error of time constant estimates on the order of 15%-50% or more, depending on the metric used and signal-to-noise level, with greater improvement seen for the time constant of the more rapidly decaying component. ILR is compatible with existing regularization techniques and should be applicable to a wide range of parameter estimation problems.Magnetic resonance in chemistry : MRCInput layer regularization for magnetic resonance relaxometry biexponential parameter estimation.PMC10185331DMS 17380031738003Intramural Research ProgramZ99 AG999999Palumbo JCzaja WBisen JRozowski MBi CBouhrara MSpencer RGfalseInput layer regularization for magnetic resonance relaxometry biexponential parameter estimation.Many methods have been developed for estimating the parameters of biexponential decay signals, which arise throughout magnetic resonance relaxometry (MRR) and the physical sciences. This is an intrinsically ill-posed problem so that estimates can depend strongly on noise and underlying parameter values. Regularization has proven to be a remarkably efficient procedure for providing more reliable solutions to ill-posed problems, while, more recently, neural networks have been used for parameter estimation. We re-address the problem of parameter estimation in biexponential models by introducing a novel form of neural network regularization which we call input layer regularization (ILR). Here, inputs to the neural network are composed of a biexponential decay signal augmented by signals constructed from parameters obtained from a regularized nonlinear least-squares estimate of the two decay time constants. We find that ILR results in a reduction in the error of time constant estimates on the order of 15%-50% or more, depending on the metric used and signal-to-noise level, with greater improvement seen for the time constant of the more rapidly decaying component. ILR is compatible with existing regularization techniques and should be applicable to a wide range of parameter estimation problems.2022-01-01T00:00:00Z2022 Nov2025-04-05T16:14:37.638Z2025-04-05T16:14:37.638ZS-EPMC101853313559338510.1002/mrc.5289