  Magnetic resonance imaging (MRI) has revolutionized medical imaging,
providing a non-invasive and highly detailed look into the human body. However,
the long acquisition times of MRI present challenges, causing patient
discomfort, motion artifacts, and limiting real-time applications. To address
these challenges, researchers are exploring various techniques to reduce
acquisition time and improve the overall efficiency of MRI. One such technique
is compressed sensing (CS), which reduces data acquisition by leveraging image
sparsity in transformed spaces. In recent years, deep learning (DL) has been
integrated with CS-MRI, leading to a new framework that has seen remarkable
growth. DL-based CS-MRI approaches are proving to be highly effective in
accelerating MR imaging without compromising image quality. This review
comprehensively examines DL-based CS-MRI techniques, focusing on their role in
increasing MR imaging speed. We provide a detailed analysis of each category of
DL-based CS-MRI including end-to-end, unroll optimization, self-supervised, and
federated learning. Our systematic review highlights significant contributions
and underscores the exciting potential of DL in CS-MRI. Additionally, our
systematic review efficiently summarizes key results and trends in DL-based
CS-MRI including quantitative metrics, the dataset used, acceleration factors,
and the progress of and research interest in DL techniques over time. Finally,
we discuss potential future directions and the importance of DL-based CS-MRI in
the advancement of medical imaging. To facilitate further research in this
area, we provide a GitHub repository that includes up-to-date DL-based CS-MRI
publications and publicly available datasets -
https://github.com/mosaf/Awesome-DL-based-CS-MRI.
