Multiple region MRI.

Traditional Fourier MR imaging (FT MRI) utilizes the Whittaker-Kotel'nikov-Shannon (WKS) sampling theorem. This theorem specifies the spatial frequency components which need to be measured to reconstruct an image with a known field of view (FOV). In this paper, we generalize this result in order to find the optimal k-space sampling for images that vanish except in multiple, possibly non-adjacent regions within the FOV. This provides the basis for "multiple region MRI" (mrMRI), a method of producing such images from a traction of the k-space samples required by the WKS theorem. Image reconstruction does not suffer from noise amplification and can be performed rapidly with fast Fourier transforms, just as in conventional FT MRI. The mrMRI method can also be used to reconstruct images that have low spatial-frequency components throughout the entire FOV and high spatial frequencies (i.e. edges) confined to multiple small regions. The greater efficiency of mrMRI sampling can be parlayed into increased temporal or spatial resolution whenever the imaged objects have signal or "edge" intensity confined to multiple small portions of the FOV. Possible areas of application include MR angiography (MRA), interventional MRI, functional MRI, and spectroscopic MRI. The technique is demonstrated by using it to acquire Gd-enhanced first-pass 3D MRA images of the carotid arteries without the use of bolus-timing techniques.