In many clinical MRI applications, not one but a series of images is acquired. Techniques that promote intra-and inter-image sparsity have recently emerged as powerful strategies for accelerating MRI applications; however, sparsity alone cannot always describe the complex relationships that exist between images in these series. In this paper, we will discuss the modeling of higher-dimensional MRI signals as matrices and tensors, and why promoting these signals to be low-rank (and, specifically, locally low-rank) can effectively identify and exploit these complex relationships. Example applications including training-free dynamic and calibrationless parallel MRI will be demonstrated.
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