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

Uniform Depth Channel Flow01:27

Uniform Depth Channel Flow

876
Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant...
876
Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

709
To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
709
Rapidly Varying Flow01:24

Rapidly Varying Flow

731
Rapidly varying flow (RVF) in open channels is characterized by abrupt changes in flow depth over a short distance, with the rate of depth change relative to distance often approaching unity. These flows are inherently complex due to their transient and multi-dimensional nature, making exact analysis difficult. However, approximate solutions using simplified models provide valuable insights into their behavior.Key Features of Rapidly Varying FlowRVF is commonly observed in scenarios involving...
731
Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

3.9K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
3.9K
Divergence and Curl01:15

Divergence and Curl

3.3K
The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as the volume tends to zero. More practically, divergence measures how much a vector field spreads out or diverges from a given point. For an outgoing flux, conventionally, the divergence is positive. The diverging point is often called the "source" of the field. Meanwhile, the negative divergence of a vector field at a point means that the vector...
3.3K
Deconvolution01:20

Deconvolution

764
Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
764

You might also read

Related Articles

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

Sort by
Same author

Deep Learning for Assessment of Cardiac Chamber Enlargement on Anteroposterior Chest Radiographs.

Radiology. Cardiothoracic imaging·2026
Same author

Arc-ZTE: Continuously-Slewed Zero-TE Imaging With Incoherent Temporal Sampling for Near-Silent Dynamic MRI.

Magnetic resonance in medicine·2026
Same author

BART Streams: Real-Time Reconstruction Using a Modular Framework for Pipeline Processing.

Magnetic resonance in medicine·2026
Same author

Corrigendum to "4D Flow cardiovascular magnetic resonance consensus statement: 2023 update" [Journal of Cardiovascular Magnetic Resonance 25 (2023) 40].

Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance·2026
Same author

Fast Real-Time Cardiac MRI: a Review of Current Techniques and Future Directions.

Investigative magnetic resonance imaging·2026
Same author

Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm.

Magnetic resonance in medicine·2026
Same journal

Suppression of Oscillation and Ghosting in RF-Spoiled Gradient-Echo-Based Dynamic Imaging.

Magnetic resonance in medicine·2026
Same journal

A Simple, Dynamic Geometric Phantom for MRI and CT Reconstruction Pipelines: Beyond Shepp-Logan.

Magnetic resonance in medicine·2026
Same journal

7T 3D-EPI PCASL With High SNR Efficiency and Robustness to Through-Plane B<sub>0</sub> Field Gradients.

Magnetic resonance in medicine·2026
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
See all related articles

Related Experiment Video

Updated: May 2, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

10.3K

Robust 4D flow denoising using divergence-free wavelet transform.

Frank Ong1, Martin Uecker, Umar Tariq

  • 1Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California, USA.

Magnetic Resonance in Medicine
|February 20, 2014
PubMed
Summary
This summary is machine-generated.

The divergence-free wavelet (DFW) transform effectively denoises four-dimensional flow MRI data, improving visualization and quantification. This method offers superior noise reduction compared to existing techniques.

Keywords:
divergence-freefour-dimensional flowwavelet denoising

More Related Videos

Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
08:42

Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method

Published on: September 3, 2021

2.9K
Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods
09:17

Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods

Published on: April 23, 2018

10.2K

Related Experiment Videos

Last Updated: May 2, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

10.3K
Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
08:42

Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method

Published on: September 3, 2021

2.9K
Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods
09:17

Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods

Published on: April 23, 2018

10.2K

Area of Science:

  • Medical Imaging
  • Fluid Dynamics
  • Signal Processing

Background:

  • Four-dimensional (4D) flow MRI generates complex spatiotemporal data.
  • Noise in 4D flow MRI can obscure important hemodynamic information.
  • Existing denoising methods may struggle with preserving quantitative accuracy.

Purpose of the Study:

  • To evaluate the divergence-free wavelet (DFW) transform for 4D flow MRI denoising.
  • To compare DFW denoising performance against current techniques.
  • To assess the impact of DFW on data visualization and quantification.

Main Methods:

  • The divergence-free wavelet (DFW) transform, a vector-wavelet, was employed.
  • DFW enforces soft divergence-free conditions to address numerical artifacts.
  • Denoising involved coefficient shrinkage, with SureShrink and cycle spinning explored for enhancement.

Main Results:

  • DFW demonstrated superior noise reduction on simulated and phantom data compared to existing methods.
  • The technique proved robust against segmentation errors.
  • Application to in vivo data improved visualization and maintained flow quantification accuracy.

Conclusions:

  • DFW denoising effectively reduces noise in 4D flow MRI data.
  • The method offers both quantitative and visual improvements.
  • DFW is a promising technique for enhancing 4D flow MRI analysis.