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General: 663 |
P6: Introduction of Regularization into Bi-exponential Magnetic Resonance Relaxometry Modeling to Break the CRLB Barrier in Parameter Estimation
Author: Zezheng Song , Advisor: Richard G. Spencer (NIH - NIA)
Problem Statement Presentation
Abstract
In this project, we consider inverse problems and study the stability and regular- ization in the process of parameter estimation in important magnetic resonance (MR) models. In the literature of MR and nonlinear least squares analysis, the Cramer-Rao lower bound (CRLB) provides a bound for the variance of parameters to be estimated. However, controlling variance to be small while making a huge bias is not desirable, and vice versa. Therefore, it is preferable to introduce the mean squared error (MSE), which is a metrics combining the variance and bias, to study the performance of the estimators. We will calculate the bias, variance and MSE by solving a regularized non-linear least squares problem using Monte Carlo simulations, and check if it is possible to adjust the range of regularization parameter to reduce MSE below the theoretical CRLB. We then propose a strategy to provide optimal regularization parameter to reduce the MSE below CRLB for a prior range of model parameters.
Final Presentation ,
Final Report
