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

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...
Sampling Distribution01:12

Sampling Distribution

Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
Sampling Methods: Overview01:06

Sampling Methods: Overview

A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of sampling...
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...

You might also read

Related Articles

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

Sort by
Same author

Exact, time-dependent analytical equations for spiral trajectories and matching gradient and density-correction waveforms.

Magnetic resonance in medicine·2025
Same author

Time-efficient simultaneous fat and water cardiac cine imaging using spiral magnetic resonance imaging.

Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance·2025
Same author

High-quality FLORET UTE imaging for clinical translation.

Magnetic resonance in medicine·2024
Same author

Retinal peri-arteriolar versus peri-venular amyloidosis, hippocampal atrophy, and cognitive impairment: exploratory trial.

Acta neuropathologica communications·2024
Same author

Simultaneous brain and neck time-of-flight MRA using spiral multiband with localized quadratic encoding.

Magnetic resonance in medicine·2024
Same author

A 3D dual-echo spiral sequence for simultaneous dynamic susceptibility contrast and dynamic contrast-enhanced MRI with single bolus injection.

Magnetic resonance in medicine·2024
Same journal

A Comparison of Tissue Property Values Estimated Using Conventional Cardiac MRF and MT-Cardiac MRF.

Magnetic resonance in medicine·2026
Same journal

Dependence of the Extra-Cellular Diffusion Coefficient on the Fractions of Neurites and Cell Bodies in Gray Matter.

Magnetic resonance in medicine·2026
Same journal

Triple-Pulse <sup>23</sup>Na MRI Sequence (TriNa) for Simultaneous Acquisition of Spin-Density-Weighted and Fluid-Attenuated Images.

Magnetic resonance in medicine·2026
Same journal

Evaluation of Phantom Doping Materials in Quantitative Susceptibility Mapping.

Magnetic resonance in medicine·2026
Same journal

Design of an 8-Channel Transmit 32-Channel Receive 11.7T Head Coil and Evaluation of SNR Gains.

Magnetic resonance in medicine·2026
Same journal

The Potential for Absolute Temperature Imaging Based on Brain Metabolites Using an FID-Shifting Approach in Gradient Echo Planar Spectroscopic Imaging (GREPSI).

Magnetic resonance in medicine·2026
See all related articles

Related Experiment Video

Updated: Jun 26, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Convolution kernel design and efficient algorithm for sampling density correction.

Kenneth O Johnson1, James G Pipe

  • 1Keller Center for Imaging Innovation, Barrow Neurological Institute, Phoenix, Arizona 85013, USA. ken.johnson@asu.edu

Magnetic Resonance in Medicine
|January 24, 2009
PubMed
Summary
This summary is machine-generated.

A novel convolution kernel and efficient algorithm improve non-Cartesian image reconstruction by reducing sampling density errors. This method enhances image quality and is applicable in both 2D and 3D imaging.

Related Experiment Videos

Last Updated: Jun 26, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Area of Science:

  • Medical Imaging
  • Image Reconstruction
  • Signal Processing

Background:

  • Non-Cartesian imaging requires sampling density compensation for accurate image reconstruction.
  • Convolution-based methods are commonly used to determine compensation weights.
  • Existing methods may introduce reconstruction errors.

Purpose of the Study:

  • To develop a new convolution kernel for more accurate sampling density compensation.
  • To create a computationally efficient algorithm for kernel convolution.
  • To evaluate the performance of the new method in reducing reconstruction error.

Main Methods:

  • Design of a novel convolution kernel to minimize image reconstruction error.
  • Development of an efficient algorithm for finite kernel convolution calculation.
  • Extension of the kernel and algorithm to three-dimensional (3D) imaging.

Main Results:

  • The new kernel significantly reduces reconstruction error compared to previous methods.
  • The efficient algorithm facilitates practical implementation of the convolution.
  • The approach demonstrates effectiveness in both 2D and 3D non-Cartesian image reconstruction.

Conclusions:

  • The proposed convolution kernel and algorithm offer improved accuracy and efficiency for sampling density compensation.
  • This advancement can lead to higher quality non-Cartesian magnetic resonance imaging (MRI) and other applications.
  • The 3D extension broadens the applicability of the technique.