Compressed Sensing: From Research to Clinical Practice With Deep Neural Networks: Shortening Scan Times for Magnetic Resonance Imaging Compressed sensing (CS) reconstruction methods leverage sparse structure in underlying signals to recover highresolution images from highly undersampled measurements. When applied to magnetic resonance imaging (MRI), CS has the potential to dramatically shorten MRI scan times, increase diagnostic value, and improve the overall patient experience. However, CS has several shortcomings that limit its clinical translation. These include 1) artifacts arising from inaccurate sparse modeling assumptions, 2) extensive parameter tuning required for each clinical application, and 3) clinically infeasible reconstruction times. Recently, CS has been extended to incorporate deep neural networks as a way of learning complex image priors from historical exam data. Commonly referred to as unrolled neural networks, these techniques have proven to be a compelling and practical approach to address the challenges of sparse CS. In this tutorial, we review the classical CS formulation and outline steps needed to transform this formulation into a deeplearningbased reconstruction framework. Supplementary opensource code in Python is used to demonstrate this approach with open databases. Further, we discuss considerations in applying unrolled neural networks in the clinical setting.

Deep Magnetic Resonance Image Reconstruction: Inverse Problems Meet Neural Networks Image reconstruction from undersampled kspace data has been playing an important role in fast magnetic resonance imaging (MRI). Recently, deep learning has demonstrated tremendous success in various fields and also shown potential in significantly accelerating MRI reconstruction with fewer measurements. This article provides an overview of deeplearningbased image reconstruction methods for MRI. Two types of deeplearningbased approaches are reviewed, those that are based on unrolled algorithms and those that are not, and the main structures of both are explained. Several signal processing issues for maximizing the potential of deep reconstruction in fast MRI are discussed, which may facilitate further development of the networks and performance analysis from a theoretical point of view.