Compressed sensing (CS) aims to reconstruct signals and images from significantly fewer measurements than were traditionally thought necessary. Magnetic Resonance Imaging (MRI) is an essentialedical imaging tool burdened by an inherently slow data acquisition process. The application of CS to MRI has the potential for significant scan time reductions, with benefits for patients and health care economics.

MRI obeys two key requirements for successful application of CS: (1) medical imagery is naturally compressible by sparse coding in an appropriate transform domain (e.g., by wavelet transform); (2) MRI scanners naturally acquire samples of the encoded image in spatial frequency, rather than direct pixel samples.

In this paper we review the requirements for successful CS, describe their natural fit to MRI, and then give examples of four interesting applications of CS in MRI. We emphasize an intuitive understanding of CS by describing the CS reconstruction as a process of interference cancellation. We also emphasize an understanding of the driving factors in applications, including limitations posed by MRI hardware, the characteristics of different types of images, and clinical concerns.

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