Efficient Non-uniform Fast Fourier Transform (NuFFT) Implementation for MRI Processing on FPGA

Magnetic Resonance Imaging (MRI) is one of the most used technique in the medical field to image the human body thanks to its non invasive data acquisition procedure that can be used in numerous applications. The major challenge that the scientific community is facing with MRI is the acquisition time that could be really long. In that direction from Cartesian sampling trajectories, that are slow but guarantee easiness in data processing performing an Inverse Discrete Fourier Transform with fast algorithms, new more complex trajectories have been proposed. The saving in acquisition time requires more complexity in performing the IDFT on non-Cartesian data. A fast algorithm that embed all the necessary steps for the reconstruction of non-uniform sampled data is called Non-uniform Fast Fourier Transform (NuFFT). This document devises and implements an efficient NuFFT algorithm on FPGA using OpenCL, investigating the functionality and performance of the design. This document is focusing on different techniques to implement the density compensation step, proposing and comparing different algorithms in terms of performance, accuracy of the reconstructed image and hardware utilization. An efficient, low power and scalable architecture is then proposed, achieving a marking improvement with respet to previously published papers. A fixed point implementation of the architecture is, then, proposed, achieving a reduction in hardware utilization suitable for 3D applications. Furthermore, new techniques exploiting the symmetric property of the k-space is presented, potentially achiving large improvements in performance and memory utilization at a minor cost in terms of accuracy of the image reconstruction.