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

Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

1.0K
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
1.0K
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

1.2K
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...
1.2K
Convolution Properties I01:20

Convolution Properties I

633
Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
633
Discrete Fourier Transform01:15

Discrete Fourier Transform

967
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...
967
Imaging Studies I: CT and MRI01:14

Imaging Studies I: CT and MRI

979
Introduction: MRI and CT scans are crucial advancements in medical imaging techniques, playing a vital role in diagnosing conditions related to the gastrointestinal (GI) system. Each scan serves distinct purposes, targets specific areas, and requires unique nursing duties.
Description of the Procedures
Computed Tomography (CT) scan:
Computed Tomography (CT) scans use X-ray technology to generate detailed images of bones, organs, and tissues. During the scan, the patient lies on a moving table...
979
Magnetic Resonance Imaging01:24

Magnetic Resonance Imaging

10.0K
Magnetic resonance imaging (MRI) is a noninvasive medical imaging technique based on a phenomenon of nuclear physics discovered in the 1930s, in which matter exposed to magnetic fields and radio waves was found to emit radio signals. In 1970, a physician and researcher named Raymond Damadian noticed that malignant (cancerous) tissue gave off different signals than normal body tissue. He applied for a patent for the first MRI scanning device in clinical use by the early 1980s. The early MRI...
10.0K

You might also read

Related Articles

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

Sort by
Same author

Image Reconstruction with Maclaurin Series Expansion.

International journal of biomedical research & practice·2026
Same author

A Higher-Order Ising Model with Gradient-Free Update.

Axioms·2026
Same author

Limited-Angle Tomography Using a Neural Network as the Objective Function.

International journal of biomedical research & practice·2026
Same author

Radon Inversion Reconstruction for Kooshball-Like Sampling Trajectory in Cine.

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference·2025
Same author

Mitigating the Drawbacks of the L<sub>0</sub> Norm and the Total Variation Norm.

Axioms·2025
Same author

One-Step Image Reconstruction for Cine MRI with a Quadratic Constraint.

International journal of biomedical research & practice·2024
Same journal

Microlocal analysis of non-linear operators arising in Compton CT.

Inverse problems·2026
Same journal

A PINN-driven game-theoretic framework in limited data photoacoustic tomography.

Inverse problems·2025
Same journal

An accelerated preconditioned proximal gradient algorithm with a generalized Nesterov momentum for PET image reconstruction.

Inverse problems·2025
Same journal

Method of moments for 3D single particle <i>ab initio</i> modeling with non-uniform distribution of viewing angles.

Inverse problems·2025
Same journal

Multi-target detection with application to cryo-electron microscopy.

Inverse problems·2025
Same journal

Linearized boundary control method for density reconstruction in acoustic wave equations.

Inverse problems·2024
See all related articles

Related Experiment Video

Updated: Feb 22, 2026

Author Spotlight: Methodologies and Advancements of Chronic Pain Management Research
08:33

Author Spotlight: Methodologies and Advancements of Chronic Pain Management Research

Published on: January 5, 2024

1.8K

A discrete convolution kernel for No-DC MRI.

Gengsheng L Zeng1,2, Ya Li3

  • 1Department of Engineering, Weber State University, Ogden, UT 84408, USA.

Inverse Problems
|September 23, 2017
PubMed
Summary
This summary is machine-generated.

This study presents a filtered back-projection algorithm for magnetic resonance imaging (MRI) reconstruction. It enables imaging with larger un-measured low-frequency regions in k-space than previously possible.

Keywords:
MRIfourier transformimage reconstructiontomography

More Related Videos

Neuroimaging-Guided TMS&#8211;EEG for Real-Time Cortical Network Mapping
09:55

Neuroimaging-Guided TMS–EEG for Real-Time Cortical Network Mapping

Published on: June 13, 2025

2.9K
Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging
17:06

Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging

Published on: November 8, 2012

27.1K

Related Experiment Videos

Last Updated: Feb 22, 2026

Author Spotlight: Methodologies and Advancements of Chronic Pain Management Research
08:33

Author Spotlight: Methodologies and Advancements of Chronic Pain Management Research

Published on: January 5, 2024

1.8K
Neuroimaging-Guided TMS&#8211;EEG for Real-Time Cortical Network Mapping
09:55

Neuroimaging-Guided TMS–EEG for Real-Time Cortical Network Mapping

Published on: June 13, 2025

2.9K
Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging
17:06

Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging

Published on: November 8, 2012

27.1K

Area of Science:

  • Medical Imaging
  • Applied Mathematics
  • Signal Processing

Background:

  • Previous analytical inversion formulas for the exponential Radon transform allowed for exact MRI reconstruction without low-frequency data.
  • However, the un-measured low-frequency region (ULFR) in k-space was constrained to be very small.

Purpose of the Study:

  • To derive a practical filtered back-projection (FBP) algorithm for MRI reconstruction based on You's formula.
  • To demonstrate that this FBP algorithm can accommodate a larger ULFR than prior methods.
  • To provide a closed-form reconstruction algorithm for a specific type of under-sampled MRI data.

Main Methods:

  • Development of a discrete convolution kernel for the FBP algorithm.
  • Derivation of a point spread function for the developed FBP algorithm.
  • Mathematical analysis of the ULFR capacity of the new algorithm.

Main Results:

  • A novel FBP algorithm for MRI reconstruction was derived.
  • The algorithm successfully accommodates a larger ULFR compared to the 2007 analytical inversion formula.
  • A closed-form reconstruction solution is presented for a special case of under-sampled MRI data.

Conclusions:

  • The derived FBP algorithm offers a practical analytical solution for reconstructing images from under-sampled MRI data.
  • This method expands the possibilities for MRI reconstruction, potentially reducing data acquisition requirements.
  • The findings challenge the conventional reliance on iterative algorithms for under-sampled MRI reconstruction.