Showing papers on "Non-uniform discrete Fourier transform published in 2021"

Generalized Image Reconstruction in Optical Coherence Tomography Using Redundant and Non-Uniformly-Spaced Samples.

Abstract: In this paper, we use Frame Theory to develop a generalized OCT image reconstruction method using redundant and non-uniformly spaced frequency domain samples that includes using non-redundant and uniformly spaced samples as special cases. We also correct an important theoretical error in the previously reported results related to OCT image reconstruction using the Non-uniform Discrete Fourier Transform (NDFT). Moreover, we describe an efficient method to compute our corrected reconstruction transform, i.e., a scaled NDFT, using the Fast Fourier Transform (FFT). Finally, we demonstrate different advantages of our generalized OCT image reconstruction method by achieving (1) theoretically corrected OCT image reconstruction directly from non-uniformly spaced frequency domain samples; (2) a novel OCT image reconstruction method with a higher signal-to-noise ratio (SNR) using redundant frequency domain samples. Our new image reconstruction method is an improvement of OCT technology, so it could benefit all OCT applications.

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.

Least Squares Optimal Density Compensation for the Gridding Non-uniform Discrete Fourier Transform

Abstract: The Gridding algorithm has shown great utility for reconstructing images from non-uniformly spaced samples in the Fourier domain in several imaging modalities. Due to the non-uniform spacing, some correction for the variable density of the samples must be made. Existing methods for generating density compensation values are either sub-optimal or only consider a finite set of points (a set of measure 0) in the optimization. This manuscript presents the first density compensation algorithm for a general trajectory that takes into account the point spread function over a set of non-zero measure. We show that the images reconstructed with Gridding using the density compensation values of this method are of superior quality when compared to density compensation weights determined in other ways. Results are shown with a numerical phantom and with magnetic resonance images of the abdomen and the knee.