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 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...
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...
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...
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...
Lagrange Multipliers: Two Constraints01:28

Lagrange Multipliers: Two Constraints

The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.
Deconvolution01:20

Deconvolution

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...

You might also read

Related Articles

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

Sort by
Same author

On Multi-Layer Basis Pursuit, Efficient Algorithms and Convolutional Neural Networks.

IEEE transactions on pattern analysis and machine intelligence·2019
Same journal

Change-Prior-Guided Unsupervised Change Detection of Heterogeneous Remote Sensing Images.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

AgonicDreamer: Enhancing Multi-View Consistency in Text-to-3D Generation via Rectified Score Distillation.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

BiCM-Prompt: Bidirectional Cross-Modal Prompt Tuning for Class-Incremental Learning on Multisource Remote Sensing Images.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

GoP-based Quality Enhancement on Video Compression.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

Align then Tensorize: Multi-Level Consistent Anchor Graph Learning for Scalable Multi-View Clustering.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

Beyond Fidelity: Diverse Image Synthesis via Retrieval-Augmented Diffusion.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
See all related articles

Related Experiment Video

Updated: Jun 21, 2026

Deep Neural Networks for Image-Based Dietary Assessment
13:19

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems.

Amir Beck1, Marc Teboulle

  • 1Department of Industrial Engineering and Management, The Technion-Israel Institute of Technology, Haifa 32000, Israel. becka@ie.technion.ac.il

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|July 29, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a fast gradient-based algorithm for constrained image deblurring using total variation (TV) minimization. The method combines dual approaches and a novel FISTA algorithm for efficient and accurate image restoration.

Related Experiment Videos

Last Updated: Jun 21, 2026

Deep Neural Networks for Image-Based Dietary Assessment
13:19

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

Area of Science:

  • Applied Mathematics
  • Image Processing
  • Computer Vision

Background:

  • Image denoising and deblurring are crucial in image processing.
  • Total Variation (TV) minimization is a common model for these tasks.
  • Existing gradient-based methods can be computationally intensive.

Purpose of the Study:

  • To develop a fast gradient-based algorithm for constrained image deblurring.
  • To improve the efficiency and convergence rate of TV minimization methods.
  • To apply the algorithm to both anisotropic and isotropic TV functionals.

Main Methods:

  • Utilizing a discretized total variation (TV) minimization model with constraints.
  • Combining an accelerated dual approach for denoising.
  • Implementing a novel monotone version of the Fast Iterative Shrinkage/Thresholding Algorithm (FISTA).

Main Results:

  • A fast and simple gradient-based algorithm for constrained image deblurring.
  • A proven global convergence rate superior to existing gradient projection methods.
  • Demonstrated viability and efficiency on image deblurring problems with box constraints.

Conclusions:

  • The proposed algorithm offers a significant advancement in constrained image deblurring.
  • The method is applicable to various TV functionals (anisotropic and isotropic).
  • Numerical results confirm the algorithm's effectiveness and efficiency.