Two dimensional prolate spheroidal wave functions for MRI

The tradeoff between spatial and temporal resolution is often used to increase data acquisition speed for dynamic MR imaging. Reduction of the k-space sampling area, however, leads to stronger partial volume and truncation effects. A two dimensional prolate spheroidal wave function (2D-PSWF) method is developed to address these problems. Utilizing prior knowledge of a given region of interest (ROI) and the spatial resolution requirement as constraints, this method tailors the k-space sampling area with a matching 2D-PSWF filter so that optimal signal concentration and minimal truncation artifacts are achieved. The k-space sampling area is reduced because the shape and size of the sampling area match the resolution posed by the non-rectangular shape of a convex ROI. The 2D-PSWF method offers an efficient way for spatial and temporal tradeoff with minimal penalty due to truncation, and thus, it promises a wide range of applications in MRI research.