Accelerating the Nonuniform Fast Fourier Transform Using FPGAs

Abstract

We present an FPGA accelerator for the Nonuniform Fast Fourier Transform, which is a technique to reconstruct images from arbitrarily sampled data. We accelerate the compute-intensive interpolation step of the NuFFT Gridding algorithm by implementing it on an FPGA. In order to ensure efficient memory performance, we present a novel FPGA implementation for Geometric Tiling based sorting of the arbitrary samples. The convolution is then performed by a novel Data Translation architecture which is composed of a multi-port local memory, dynamic coordinate-generator and a plug-and-play kernel pipeline. Our implementation is in single-precision floating point and has been ported onto the BEE3 platform. Experimental results show that our FPGA implementation can generate fairly high performance without sacrificing flexibility for various data-sizes and kernel functions. We demonstrate up to 8X speedup and up to 27 times higher performance-per-watt over a comparable CPU implementation and up to 20% higher performance-per-watt when compared to a relevant GPU implementation.

Power-efficient re-gridding architecture for accelerating Non-uniform Fast Fourier Transform

“…Other works like [6], [10], [5] also use the same gridding algorithm for re-gridding and employ various techniques to improve the efficiency of computation.…”

“…High performance implementations for computing NuFFT have been pursued on various platforms including multi-core CPU's, [3], [1], [2], General Purpose Graphics Processing Units (GPGPU's) [3] and FPGAs [5]. Since the lack of locality in memory accesses is the major bottleneck in the re-gridding process, most of the techniques are based on efficient utilization of memory bandwidth.…”

“…Non-Uniform Fast Fourier Transform (NuFFT) helps computing NuDFT with some approximation in O(M + N log N ) complexity [5]. It uses the Fast Fourier Transform (FFT) in combination with an approximation scheme.…”

“…Since the source points are read in random order with respect to coordinates, accesses to T for updating corresponding target points lack data-locality. This incurs significant delays due to repeated memory accesses and hence re-gridding is known to be the most time consuming step (over 90%) of the whole NUFFT computation [5].…”

Gpu-Based ω-K Tomographic Processing by 1d Non-Uniform FFTS

“…Throughout the literature, processing algorithms based on parallel NUFFT implementations, on CPU [28], GPU [29][30][31][32][33] or Field Programmable Gate Arrays (FPGAs) [34], have been developed, mainly for applications of Magnetic Resonance Imaging (MRI), antenna fast analysis or Optical Coherence Tomography (OCT). In these instances, transformation of 2D signals from non-uniform to uniform grids or vice versa is necessary, thus requiring 2D NonEquispaced Data (NED) or Non-Equispaced Results (NER) NUFFT routines, depending on the application of interest.…”