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Related Concept Videos

Downsampling01:20

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
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Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...
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¹H NMR: Interpreting Distorted and Overlapping Signals

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Related Experiment Video

Updated: Jul 11, 2026

Diffusion Imaging in the Rat Cervical Spinal Cord
10:46

Diffusion Imaging in the Rat Cervical Spinal Cord

Published on: April 7, 2015

Fractional-order anisotropic diffusion for image denoising.

Jian Bai1, Xiang-Chu Feng

  • 1Department of Applied Mathematics, Xidian University, Xi'an 710071, China. keywhite26@126.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|October 12, 2007
PubMed
Summary

This study presents novel fractional-order anisotropic diffusion equations for image noise removal. These advanced methods offer improved visual quality and signal-to-noise ratio in denoising applications.

Related Experiment Videos

Last Updated: Jul 11, 2026

Diffusion Imaging in the Rat Cervical Spinal Cord
10:46

Diffusion Imaging in the Rat Cervical Spinal Cord

Published on: April 7, 2015

Area of Science:

  • Image processing
  • Partial differential equations
  • Numerical analysis

Background:

  • Anisotropic diffusion equations are widely used for image denoising.
  • Existing methods often rely on second-order or fourth-order derivatives.
  • Fractional calculus offers potential for more sophisticated image processing techniques.

Purpose of the Study:

  • Introduce a new class of fractional-order anisotropic diffusion equations.
  • Generalize existing diffusion models for enhanced noise removal.
  • Develop an efficient numerical algorithm for practical application.

Main Methods:

  • Formulated equations as Euler-Lagrange equations of a specific cost functional.
  • Utilized fractional derivatives of image intensity.
  • Implemented a numerical algorithm using the discrete Fourier transform in the frequency domain.
  • Employed a folded algorithm for handling image border effects.

Main Results:

  • Demonstrated effective noise removal on real images.
  • Achieved good visual effects in denoised images.
  • Showcased a significant improvement in signal-to-noise ratio.

Conclusions:

  • The proposed fractional-order anisotropic diffusion equations are effective for image denoising.
  • The numerical scheme provides a practical and efficient solution.
  • This work extends the capabilities of anisotropic diffusion for image restoration.