Reconstruction from samples on linear and expanding spiral scans

The problem of reconstructing a two-dimensional function from a set of spiral samples is addressed. This problem is of practical interest in magnetic resonance imaging (MRI). A theorem that enables exact interpolation from linear spiral samples to a Cartesian lattice is presented, dealing with nonlinear, expanding spirals. These kinds of spirals have a potential advantage in a situation for which the data collection time is limited. In general, there is no exact reconstruction procedure from nonlinear spiral samples. Two practical methods are furnished to reconstruct an image from a set of spiral samples of its Fourier transform and examples are shown of reconstructions obtained through both methods