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Related Concept Videos

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...
Shearing Stress01:18

Shearing Stress

Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
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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...
Shear Diagram01:27

Shear Diagram

In the study of beam mechanics, shear diagrams play a crucial role in understanding the distribution of shear forces along the length of a beam. Consider a beam AB that is supported at both ends and subjected to perpendicular loads.
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Singularity Functions for Shear01:26

Singularity Functions for Shear

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Related Experiment Video

Updated: Jun 27, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Shearlet-based total variation diffusion for denoising.

Glenn R Easley1, Demetrio Labate, Flavia Colonna

  • 1System Planning Corporation, Arlington, VA 22209, USA.geasley@sysplan.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|December 20, 2008
PubMed
Summary
This summary is machine-generated.

This study introduces a novel shearlet-based total variation (TV) method for image denoising. The new shearlet-TV approach significantly enhances image quality and requires fewer iterations than competing methods.

Related Experiment Videos

Last Updated: Jun 27, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Area of Science:

  • Image processing
  • Computational imaging
  • Applied mathematics

Background:

  • Traditional wavelets struggle to represent image discontinuities effectively.
  • Existing methods combining wavelets with Total Variation (TV) or diffusion can introduce artifacts.
  • Shearlets offer superior representation of image edges and discontinuities.

Purpose of the Study:

  • To develop a shearlet formulation of the Total Variation (TV) method for image denoising.
  • To improve image estimation by constraining residual coefficients in the shearlet domain.
  • To analyze the performance of shearlet-based diffusion methods for image denoising.

Main Methods:

  • A projected adaptive Total Variation (TV) scheme was applied in the shearlet domain.
  • Shearlet transform was utilized for superior edge characterization and discontinuity representation.
  • A shearlet-based diffusion method was analyzed for its denoising capabilities.

Main Results:

  • The proposed shearlet-TV scheme yields significantly better image estimates compared to existing methods.
  • Numerical examples show high effectiveness in denoising complex images.
  • The shearlet-TV method outperforms curvelet transform-based approaches and requires fewer iterations.

Conclusions:

  • Shearlet-based Total Variation (TV) formulation provides a powerful tool for image denoising.
  • The method effectively handles image discontinuities and reduces artifacts.
  • This approach offers a more efficient and effective solution for complex image denoising tasks.