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The articles in this special section focus on computational magnetic resonance imaging (MRI) using compressed sensing applications. Presents recent developments in computational MRI. These developments are pushing the frontier of computational imaging beyond CS. Similar to CS, most of these algorithms rely on image representation in one form or another. However, the common recent thread is the departure from handcrafted image representations to learning-based image representations. These learned representations are seamlessly combined with clever measurement strategies to significantly advance the state of the art in a number of areas. Several exciting applications including significantly improved spatial and temporal resolution, a considerable reduction in scan time, measurement of biophysical parameters directly from highly undersampled data, and direct measurement of very high-dimensional data are reviewed in this special issue of SPM. This issue describes key ideas underlying the computational approaches used in MRI. These approaches range from CS algorithms that rely on fixed transforms or dictionaries, to adaptive or shallow-learning algorithms that adapt the image representation to the data to recent deep-learning methods that learn a highly nonlinear representation from exemplar data. The articles provide insight into the capabilities of the current algorithms, their limitations, and their utility in challenging MRI problems.
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