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Compressed Sensing and HYPR

The desire to achieve high spatial and/or temporal resolution in MRI coupled with limited scan time has led to the necessity to reconstruct images from incomplete datasets. Mathematically this amounts to solving an underdetermined system of equations, that is, the number of unknowns (image pixel values) is larger than the number of equations (acquired measurements). Underdetermined systems of equations generally have an infinite number of possible solutions. A standard approach to isolate a single feasible solution is to incorporate additional prior information about the problem in order to regularize reconstruction and to account for unsampled data points. A number of methods to accelerate MR imaging have been proposed, including parallel imaging [1-3], UNFOLD [4], k-t BLAST/SENSE [5], and, more recently, compressed sensing [6-8] and HYPR [9, 10]. We will discuss several different ways to regularize image reconstruction from incomplete data, using both theoretical assumptions and image-specific constraints.