Reducing the sampling burden of Fourier sensing with a non-rectangular field-of-view

Fourier sensing devices collect data in the frequency domain. For example, Magnetic Resonance Imaging (MRI) is a Fourier sensing modality where the user has the freedom to choose which spatial frequencies are sampled. With Fourier sensing, it is commonly the case that the field-of-view (FOV), the area of space to be imaged, is known prior to reconstruction. Most commonly, reconstruction algorithms have focused on FOVs with simple geometries. This leads to sampling patterns that are more burdensome (with more samples) than necessary. Due to the reduced area of imaging possible with an arbitrary (e.g., non-rectangular and non-convex) FOV, the number of samples required for a high-quality image is reduced. However, when an arbitrary FOV has been considered, the reconstruction algorithm has been computationally expensive. In this manuscript, we present a method to reduce the sampling burden for an arbitrary FOV with an accompanying direct (non-iterative) and computationally efficient reconstruction algorithm. We also present a method to decrease the computational cost of the iterative POCSENSE algorithm used with a non-rectangular FOV. We present results using MRI data of an ankle, a pineapple, and a brain.