This project was the second of three aims completed during my PhD.

Background: Long scan times remain a big issue in MRI, especially when one wants to do any sort of quantitative analysis by collecting specialized acquisitions, like T1-mapping. There are many deep learning approaches that aim to reconstruct high quality images from highly accelerated data, but what can you do if you don't have substantial training data for supervised training? One approach is to apply untrained methods (see Darestani et al.), which circumvent the need for training data, but methods prior to this work did not incorporate the signal model as a constraint in the reconstruction.

Objective:  Our aim was to implement physics-based regularization, based on the spoiled gradient echo (SPGR) equation, in tuning an untrained deep neural network for reconstruction multi-contrast MRIs from accelerated data. We call our method CD+r.

Methods: We collected fully-sampled variable flip angle (VFA) data for T1-mapping from a few volunteers and retrospectively undersampled the data by varying acceleration factors. Using Python (PyTorch), we implemented a generative neural network, optimized using a cost function in an untrained optimization scheme with a data consistency term and a regularization term incorporating the VFA signal model. We evaluated the quality of the reconstructed images compared to the fully-sampled using the normalized root mean square error (NRMSE) and the structural similarity index measure (SSIM). Our method also simultaneously computed the corresponding T1 maps at each training step, so we evaluated the agreement between the reconstruction-based T1 maps and the ground truth maps using the concordance correlation coefficient. All details are presented in the associated publication below. We also compared our method to more traditional methods, like locally low rank (LR) reconstruction. 

Results: Our method, CD+r, yielded reconstructions with SSIM>0.90 for acceleration factors as high as 12, bringing down the effective acquisition time from 50 minutes to approximately 4 minutes. We also found high agreement (CCC>0.90) between ground truth T1 maps and reconstruction-based T1 maps for the same acceleration factor.