Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Fast Fourier Transform01:10

Fast Fourier Transform

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
Discrete Fourier Transform01:15

Discrete Fourier Transform

The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
Convergence of Fourier Series01:21

Convergence of Fourier Series

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Mechanisms behind protein-protein interactions in a β-lg-legumin co-precipitate.

Food chemistry·2021
Same author

Ground-truth-free deep learning for artefacts reduction in 2D radial cardiac cine MRI using a synthetically generated dataset.

Physics in medicine and biology·2021
Same author

Morphological and molecular characterization of Cystoisospora laidlawi oocysts (Apicomplexa: Eimeriidae) in farmed American mink (Neovison vison) in Denmark.

Parasitology research·2020
Same author

Health assessment of harbour porpoises (PHOCOENA PHOCOENA) from Baltic area of Denmark, Germany, Poland and Latvia.

Environment international·2020
Same author

Neural networks-based regularization for large-scale medical image reconstruction.

Physics in medicine and biology·2020
Same author

Responsiveness of different dynamic contrast-enhanced magnetic resonance imaging approaches: a post-hoc analysis of a randomized controlled trial of certolizumab pegol in rheumatoid arthritis.

Scandinavian journal of rheumatology·2019

Related Experiment Video

Updated: Jul 6, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:48

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

Accelerating the nonequispaced fast Fourier transform on commodity graphics hardware.

T S Sorensen1, T Schaeffter, K O Noe

  • 1Division of Imaging Sciences at King's College London, London WC2R 2LS, UK. sangild@cavi.dk

IEEE Transactions on Medical Imaging
|April 9, 2008
PubMed
Summary
This summary is machine-generated.

We developed a fast GPU algorithm for the nonequispaced fast Fourier transform, significantly speeding up medical imaging reconstruction. This GPU-accelerated method is up to 85x faster than CPU-based approaches for non-Cartesian MRI.

More Related Videos

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
11:34

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

Published on: December 3, 2013

Blood Flow Imaging with Ultrafast Doppler
05:57

Blood Flow Imaging with Ultrafast Doppler

Published on: October 14, 2020

Related Experiment Videos

Last Updated: Jul 6, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:48

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
11:34

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

Published on: December 3, 2013

Blood Flow Imaging with Ultrafast Doppler
05:57

Blood Flow Imaging with Ultrafast Doppler

Published on: October 14, 2020

Area of Science:

  • Computer Science
  • Medical Imaging
  • Signal Processing

Background:

  • The nonequispaced fast Fourier transform (NFFT) is crucial for reconstructing images from non-Cartesian data in medical imaging.
  • The convolution step in NFFT has historically been computationally intensive, limiting reconstruction speed.
  • Graphics Processing Units (GPUs) offer parallel processing capabilities that can accelerate such computations.

Purpose of the Study:

  • To develop and evaluate a fast parallel algorithm for the nonequispaced fast Fourier transform (NFFT) utilizing commodity graphics hardware (GPU).
  • To specifically optimize the convolution step within the NFFT, addressing its previous performance bottleneck.
  • To demonstrate the algorithm's applicability and performance in medical imaging, particularly for non-Cartesian magnetic resonance imaging (MRI).

Main Methods:

  • A novel parallel algorithm for NFFT was implemented on GPU hardware.
  • The convolution step was re-engineered for GPU acceleration.
  • Performance was assessed using radial and spiral trajectories and various convolution kernels.
  • Accuracy was quantitatively evaluated across different settings.
  • The algorithm was applied to reconstruct a numerical phantom and an in vivo cardiac MRI dataset.

Main Results:

  • The GPU-accelerated NFFT convolution achieved speedups of up to 85 times compared to the open-source NFFT library on a high-performance CPU.
  • Performance was analyzed for different sampling distributions (radial, spiral) and convolution kernels.
  • The accuracy of the GPU implementation was validated.
  • Successful reconstruction of non-Cartesian MRI data, including a numerical phantom and a cardiac image, was demonstrated.

Conclusions:

  • The proposed GPU-based NFFT algorithm offers a significant speed improvement for non-Cartesian MRI reconstruction.
  • This acceleration is primarily driven by the optimized GPU convolution implementation.
  • The method is accurate and applicable to real-world medical imaging scenarios, enhancing the efficiency of gridding techniques.