andrewwmao/biasreducednetworks

Bias Reduced Neural Networks for Parameter Estimation in Quantitative MRi

This repository aims to partially reproduce the results in the paper https://arxiv.org/abs/2312.11468. These neural networks have reduced bias compared to those trained with the typical mean-squared error loss, and a variance that is close to the Cramér-Rao Bound.

sim.jl and sim.sh are an example Julia script to calculate the training data using the MRIgeneralizedBloch.jl package, and a corresponding bash script to submit it as a job to a computational cluster managed by Slurm.

td.jl and td.sh are used to calculate the training data, td.mat, from the simulated fingerprints, compressed to a low-rank space. In this case, a precomputed basis basis.mat is provided, calculated using the method described in the paper https://arxiv.org/abs/2305.00326 and by the corresponding repository https://github.com/andrewwmao/CRBBasis.

train.jl and train.sh are example scripts for training the Bias-Reduced networks.

plot_fig1.jl, plot_fig2.jl, and plot_fig4.jl partially reproduce Figs. 1, 2, and 4 in the Bias-Reduced networks paper. The parts that require non-linear least squares fitting can be reproduced using code already provided in MRIgeneralizedBloch.jl.

Our preprint is currently under revision at Magnetic Resonance in Medicine. This repository will be finalized when the paper is published.