Hemant Kumar Aggarwal1, Aniket Pramanik1, and Mathews Jacob1
1Electrical and Computer Engineering, University of Iowa, Iowa City, IA, United States
1Electrical and Computer Engineering, University of Iowa, Iowa City, IA, United States
We proposed ENsample SURE loss function for MR image reconstruction problem using unsupervised learning. We show that training a network using an ensemble of images, each acquired with a different sampling pattern, can closely approximate the mean square error.
Fig. 3: ENSURE results on experimental data at 6-fold acceleration factor. Here we show the comparison of unsupervised training using the proposed ENSURE approach with supervised training as well as an existing unsupervised training approach SSDU [5]. The noise variance of the measurements was estimated, followed by the use of the SURE loss for training. The second row shows the zoomed cerebellum region. The third row shows error maps at 3x-scaling for visualization purposes. We observe that the ENSURE results closely match the MSE results with minimal blurring.
Fig. 1: The implementation details of the data-term in the proposed ENSURE approach for unsupervised training. First, we do the regridding reconstruction $$$\boldsymbol u_s$$$, then pass it through the network to get the reconstruction. Here the weighted projection term $$$\mathbf W_s$$$ represents the weighting of the k-space sample together with projection onto range space of $$$\mathcal A_s^H$$$. We note that this data-term does not require the ground truth image.
