Jigsaw: A Slice-and-Dice Approach to Non-uniform FFT Acceleration for MRI Image Reconstruction

Abstract

The Fast Fourier Transform (FFT) is a fundamental algorithm in signal processing; significant efforts have been made to improve its performance using software optimizations and specialized hardware accelerators. Computational imaging modalities, such as MRI, often rely on the Non-uniform Fast Fourier Transform (NuFFT), a variant of the FFT for processing data acquired from non-uniform sampling patterns. The most time-consuming step of the NuFFT algorithm is “gridding;” wherein non-uniform samples are interpolated to allow a uniform FFT to be computed over the data. Each non-uniform sample affects a window of non-contiguous memory locations, resulting in poor cache and memory bandwidth utilization. As a result, gridding can account for more than 99.6% of the NuFFT computation time, while the FFT requires less than 0.4%. We present Slice-and-Dice, a novel approach to the NuFFT's gridding step that eliminates the presorting operations required by prior methods and maps more efficiently to hardware. Our GPU implementation achieves gridding speedups of over 250× and 16× vs prior state-of-the-art CPU and GPU implementations, respectively. We achieve further speedup and energy efficiency gains by implementing Slice-and-Dice in hardware with JIGSAW, a streaming hardware accelerator for non-uniform data gridding. JIGSAW uses stall-free fixed-point pipelines to process M non-uniform samples in approximately M cycles, irrespective of sampling pattern-yielding speedups of over 1500× the CPU baseline and 36× the state-of-the-art GPU implementation, consuming $\sim 200\mathrm{m}\mathrm{W}$ power and $\sim 12\mathrm{m}\mathrm{m}^{2}$ area in 16 nm technology. Slice-and-Dice GPU and JIGSAW ASIC implementations achieve unprecedented end-to-end NuFFT speedups of 8× and 36× compared to the state-of-the-art GPU implementation, respectively.