  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. To date,
reconstruction algorithms have focused on FOVs with simple geometries: a
rectangle or a hexagon. This yields sampling patterns that are more burdensome
than necessary. Due to the reduced area of imaging possible with an arbitrary
(e.g., non-rectangular) FOV, the number of samples required for a high-quality
images is reduced. However, when an arbitrary FOV has been considered, the
reconstruction algorithm is computationally expensive. In this manuscript, we
present a method to reduce the sampling pattern for an arbitrary FOV with an
accompanying direct (non-iterative) reconstruction algorithm. We also present a
method to decrease the computational cost of the (iterative) model-based
reconstruction (MBR) algorithm. We present results using MRI data of an ankle,
a pineapple, and a brain.
