Undersampled Magnetic Resonance Image Reconstructions Based on a Combination of U-Nets and L1, L2, and TV Optimizations

Magnetic Resonance Imaging (MRI) plays a major role in the diagnosis of several diseases. However, the acquisition of measurements in the k-space domain, which is the basis for image reconstruction, takes a long time compared to other imaging modalities and is comparatively costly. In this context, undersampled MRI reconstruction is an approach for decreasing the acquisition duration and the exam's final cost. With this objective, both Compressed Sensing (CS) and Deep Learning (DL) provide techniques for generating good quality MRI images from undersampled measurements. In this paper, we combine CS and DL methods in order to investigate the potential increase in image quality over each isolated approach. We use reconstructions from from highly undersampled MRI signals using two CS approaches, the L1 and total minimizations, as inputs to a U-Net. We also use, for comparison, the reconstructions from the same undersampled signals using L2 minimization, and also test them as inputs to a U-net. The goal is to evaluate whether the the U-Net can improve the results of the CS reconstructions after learning from degraded and original image pairs. Our experimental results suggest that the combination of L1 or TV minimization with U-Nets can improve reconstruction, in terms of objective image quality, over each technique used in isolation.