Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging

Physics-driven deep learning methods have emerged as a powerful tool for computational magnetic resonance imaging (MRI) problems, pushing reconstruction performance to new limits. This article provides an overview of the recent developments in incorporating physics information into learningbased MRI reconstruction. We consider inverse problems with both linear and non-linear forward models for computational MRI, and review the classical approaches for solving these. We then focus on physics-driven deep learning approaches, covering physics-driven loss functions, plug-and-play methods, generative models, and unrolled networks. We highlight domain-specific challenges such as real-and complex-valued building blocks of neural networks, and translational applications in MRI with linear and non-linear forward models. Finally, we discuss common issues and open challenges, and draw connections to the importance of physics-driven learning when combined with other downstream tasks in the medical imaging pipeline. K. Hammernik and D. Rueckert are with the Institute of AI and Informatics in Medicine, Technical University of Munich and the Department of Computing, Imperial College London. T. Küstner is with the Department of Diagnostic and Interventional Radiology, University Hospital of Tuebingen. B. Yaman and M. Akçakaya are with the Department of Electrical and Computer Engineering, and Center for Magnetic Resonance Research, University of Minnesota, USA. Z. Huang is with the Center for Biomedical Imaging, Department of Radiology, New York University. F. Knoll is with the Department Artificial Intelligence in Biomedical Engineering, Friedrich-Alexander University Erlangen. Magnetic resonance imaging (MRI) is a non-invasive radiation-free imaging modality with a plethora of clinical applications and extensively-studied physics underpinnings. The relationship between the acquired MRI data and the underlying magnetization is characterized by Bloch equations, and depends on a number of parameters, including the magnetic fields (e.g. the static B These intricate dependencies are encoded in the so-called k-space, corresponding to the spatial Fourier transform of the object's magnetization. It depends on the imaging sequence and reflects physiological, functional or hardware characteristics. For many applications, an analytical expression can be derived (e.g. via hard pulse approximation from the Bloch equations) for which a few examples are summarized in Table I (linear and non-linear models).