A generalization of the two-dimensional prolate spheroidal wave function method for nonrectilinear MRI data acquisition methods

The two-dimensional (2-D) prolate spheroidal wave function (2-D PSWF) method was previously introduced as an efficient method for trading off between spatial and temporal resolution in magnetic resonance imaging (MRI), with minimal penalty due to truncation and partial volume effects. In the 2-D PSWF method, the k-space sampling area and a matching 2-D PSWF filter, with optimal signal concentration and minimal truncation artifacts, are determined by the shape and size of a given convex region of interest (ROI). The spatial information in the reduced k-space data is used to calculate the total image intensity over a nonsquare ROI instead of producing a low-resolution image. This method can be used for tracking dynamic signals from non-square ROIs using a reduced k-space sampling area, while achieving minimal signal leakage. However, the previous theory is limited to the case of rectilinear sampling. In order to make the 2-D PSWF method more suitable for dynamic studies, this paper presents a generalized version of the 2-D PSWF theory that can be applied to nonrectilinear data acquisition methods. The method is applied to an fMRI study using a spiral trajectory, which illustrates the methods efficiency at tracking hemodynamic signals with high temporal resolution.