A Deep Learning Method for Optimal Undersampling Patterns and Image Recovery for MRI Exploiting Losses and Projections

Compressed Sensing was recently proposed to reduce the long acquisition time of Magnetic Resonance Imaging by undersampling the signal frequency content and then algorithmically reconstructing the original image. We propose a way to significantly improve the above method by exploiting a deep neural network to tackle both problems of frequency sub-sampling and image reconstruction simultaneously, thanks to the introduction of a new loss function to drive the training and the addition of a post-processing non-neural stage. Furthermore, we highlight how some of the quantities along the processing chain can be used as a proxy of the quality of the recovered image, thus allowing a self-assessment of the whole technique. All improvements hinge on the possibility of identifying constraints to which the final image must obey and suitably enforce them. The effectiveness of our approach is tested on real-world MRI acquisitions from the fastMRI public database and achieves an appreciable improvement in Peak Signal-to-Noise Ratio with respect to the original CS-based proposal with speed-up factors 4 and 8.