Undersampled radial MR acquisition and highly constrained back projection (HYPR) reconstruction: potential medical imaging applications in the post-Nyquist era.

During the past several years there has been extensive study of alternative MR acquisition strategies such as spiral and radial. Vastly undersampled imaging with projections (VIPR) is a three-dimensional (3D) radial acquisition that provides acceptable images while violating the Nyquist theorem by factors of up to several hundred. For applications like magnetic resonance angiography (MRA), VIPR provides sparse data sets with incoherent artifacts that satisfy the requirements of emerging reconstruction approaches like iterative image norm minimization (compressed sensing) and highly constrained back projection (HYPR). All of these tools can be used in combination with parallel imaging to provide extremely high acceleration factors in MRI. In this review we do not attempt to do justice to the many exciting developments in the general field of constrained reconstruction but focus on preliminary results using VIPR and HYPR for non-Cartesian, Nyquist-violating MRI and the extension of HYPR processing to a broad range of medical imaging applications in which the acquisitions satisfy the Nyquist theorem but lack sufficient signal-to-noise ratio (SNR), leading to the possibility of radiation reduction, increased ultrasound resolution and field-of-view, and improved dynamic display of radiotracers.