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

Gradient Fields01:27

Gradient Fields

A gradient field is a vector field derived from a scalar field. A scalar field assigns a single numerical value to every point in space, such as temperature, pressure, or electric potential. The gradient field describes how that value changes from point to point. It gives both the direction of the fastest increase and the rate of change in that direction.For a scalar field f(x, y), the gradient is written as\begin{equation*}\nabla f=\left\langle \jfrac{\partial f}{\partial x},\jfrac{\partial...
Gradient Vectors and Their Applications01:19

Gradient Vectors and Their Applications

Every point on a topographical map corresponds to a particular elevation, so the landscape can be modeled as a surface whose height depends on horizontal position. From any given location, a hiker may face infinitely many directions, but only one direction produces the fastest possible increase in elevation. This unique route is called the direction of steepest ascent, and in multivariable calculus, it is represented by the gradient vector of the elevation function.The gradient vector points...
Significance of the Gradient Vector01:27

Significance of the Gradient Vector

A surface defined by a function of two variables can be understood by examining how it changes along specific directions. When one variable is held constant, the surface reduces to a curve that reflects variation in the other variable. For example, fixing one variable and moving parallel to a coordinate axis produces a cross-sectional curve. The slope of this curve at a given point represents how the function changes in that particular direction, providing a measure of local steepness.By...
Maximizing the Directional Derivative01:25

Maximizing the Directional Derivative

The directional derivative is a central concept in multivariable calculus that describes how a function changes at a given point when moving in a specified direction. This direction is represented by a unit vector, ensuring that only the orientation influences the rate of change. By varying the direction, different rates of change can be observed, demonstrating that the directional derivative depends strongly on the chosen direction.The directional derivative is computed using the gradient...
Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
Gradient and Del Operator01:14

Gradient and Del Operator

In mathematics and physics, the gradient and del operator are fundamental concepts used to describe the behavior of functions and fields in space. The gradient is a mathematical operator that gives both the magnitude and direction of the maximum spatial rate of change. Consider a person standing on a mountain. The slope of the mountain at any given point is not defined unless it is quantified in a particular direction. For this reason, a "directional derivative" is defined, which is a vector...

You might also read

Related Articles

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

Sort by
Same author

Speckle processing method for synthetic-aperture-radar phase correction.

Optics letters·2009
Same author

Interpolated spatially variant apodization in synthetic aperture radar imagery.

Applied optics·2008
Same author

A method for a fully automatic definition of coronary arterial edges from cineangiograms.

IEEE transactions on medical imaging·1988
Same author

Some practical aspects of moving object deblurring in a perspective plane.

Applied optics·1985
Same author

Computerized tomography using video recorded fluoroscopic images.

IEEE transactions on bio-medical engineering·1977
Same author

The capability of fluoroscopic systems for the production of computerized axial tomograms.

Investigative radiology·1976

Related Experiment Video

Updated: Jun 20, 2026

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Phase-gradient algorithm as an optimal estimator of the phase derivative.

P H Eichel, C V Jakowatz

    Optics Letters
    |September 16, 2009
    PubMed
    Summary
    This summary is machine-generated.

    A new phase-gradient algorithm enhances signal processing for aperture-synthesis imaging. This technique improves synthetic-aperture-radar phase correction and stellar image reconstruction by estimating phase derivatives.

    More Related Videos

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
    13:44

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

    Published on: August 30, 2013

    Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
    13:04

    Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

    Published on: January 18, 2022

    Related Experiment Videos

    Last Updated: Jun 20, 2026

    Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
    09:04

    Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

    Published on: February 23, 2018

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
    13:44

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

    Published on: August 30, 2013

    Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
    13:04

    Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

    Published on: January 18, 2022

    Area of Science:

    • Signal processing
    • Image reconstruction
    • Astronomy

    Background:

    • Aperture-synthesis imaging is crucial for high-resolution imaging.
    • Phase errors degrade the quality of reconstructed images.
    • Existing methods for phase correction can be computationally intensive.

    Purpose of the Study:

    • To introduce and validate a novel phase-gradient algorithm.
    • To demonstrate its effectiveness in aperture-synthesis imaging applications.
    • To establish the theoretical properties of the phase-derivative estimator.

    Main Methods:

    • The phase-gradient algorithm is developed to estimate phase derivatives from redundant data.
    • The algorithm's performance is analyzed in the context of synthetic-aperture-radar (SAR) phase correction.
    • Its application to stellar image reconstruction is also investigated.

    Main Results:

    • The phase-gradient algorithm effectively combines redundant information to estimate phase derivatives.
    • The developed estimator is proven to be a linear, minimum-variance estimator.
    • The technique shows promise for improving image quality in SAR and astronomical imaging.

    Conclusions:

    • The phase-gradient algorithm is a powerful new tool for signal processing in aperture-synthesis imaging.
    • It offers a robust method for phase correction and image reconstruction.
    • The algorithm's theoretical foundation as a minimum-variance estimator ensures optimal performance.