  Convolutional Gridding is a technique (algorithm) extensively used in Radio
Interferometric Image Synthesis for fast inversion of functions sampled with
irregular intervals on the Fourier plane. In this thesis, we propose some
modifications to the technique to execute faster on a GPU. These modifications
give rise to \textit{Hybrid Gridding} and \textit{Pruned NN Interpolation},
which take advantage of the oversampling of the Gridding Convolutional Function
in Convolutional Gridding to try to make gridding faster with no reduction in
the quality of the output. Our experiments showed that given the right
conditions, Hybrid Gridding executes up to $6.8\times$ faster than
Convolutional Gridding, and Pruned NN Interpolation is generally slower than
Hybrid Gridding.
  The two new techniques feature the downsampling of an oversampled grid
through convolution to accelerate the Fourier inversion. It is a well-known
approximate technique which suffers from aliasing. In this thesis, we are
re-proposing the technique as a \textit{Convolution-Based FFT Pruning}
algorithm able to suppress aliasing below arithmetic noise. The algorithm uses
the recently discovered least-misfit gridding functions, which through our
experiments gave promising results, although not as good as expected from the
related published work on the stated gridding functions. Nevertheless, our
experiments showed that, given the right conditions, Convolutional-Based
Pruning reduces the Fourier inversion execution time on a GPU by approximately
a factor of $8\times$.
