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

Fast Fourier Transform01:10

Fast Fourier Transform

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
Reconstruction of Signal using Interpolation01:10

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...
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
Convolution Properties I01:20

Convolution Properties I

Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

You might also read

Related Articles

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

Sort by
Same author

Clinical Course and Predictors of Heart Failure in Asymptomatic Obstructive Hypertrophic Cardiomyopathy.

Journal of the American Heart Association·2026
Same author

Clinical Spectrum and Outcomes in Hypertrophic Cardiomyopathy With Apical Aneurysms: A Large Multicenter International Cohort.

JACC. Advances·2026
Same author

Midventricular Obstruction in Hypertrophic Cardiomyopathy: Clinical Outcomes in a Multicenter Cohort.

Journal of the American College of Cardiology·2026
Same author

Non-invasive evaluation of left ventricular hemodynamic force abnormalities in hypertrophic cardiomyopathy: Implications for myosin inhibition.

International journal of cardiology·2026
Same author

Effect of continuous positive airway pressure on ventricular remodeling of patients with combined diabetes mellitus and obstructive sleep apnea: a cross-sectional study and follow-on randomized clinical trial.

International journal of cardiology·2025
Same author

High-Quality CEST Mapping With Lorentzian-Model Informed Neural Representation.

IEEE transactions on bio-medical engineering·2025

Related Experiment Video

Updated: Jun 22, 2026

Meso-Scale Particle Image Velocimetry Studies of Neurovascular Flows In Vitro
08:00

Meso-Scale Particle Image Velocimetry Studies of Neurovascular Flows In Vitro

Published on: December 3, 2018

A fast optimization transfer algorithm for image inpainting in wavelet domains.

Raymond H Chan1, You-Wei Wen, Andy M Yip

  • 1Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong. rchan@math.cuhk.edu.hk

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

This study introduces an optimization transfer technique for wavelet inpainting, improving image restoration. The new method efficiently fills missing wavelet coefficients, outperforming previous approaches.

Related Experiment Videos

Last Updated: Jun 22, 2026

Meso-Scale Particle Image Velocimetry Studies of Neurovascular Flows In Vitro
08:00

Meso-Scale Particle Image Velocimetry Studies of Neurovascular Flows In Vitro

Published on: December 3, 2018

Area of Science:

  • Image processing and computer vision
  • Applied mathematics and optimization

Background:

  • Wavelet inpainting addresses missing image data by reconstructing wavelet coefficients.
  • Variational methods, like Chan et al.'s, use gradient descent for minimization.
  • Existing methods face challenges in efficiency and convergence.

Purpose of the Study:

  • To develop a more efficient and robust algorithm for wavelet inpainting.
  • To improve upon the variational approach for filling missing wavelet coefficients.
  • To introduce an optimization transfer technique for image restoration.

Main Methods:

  • Replaced the univariate functional with an equivalent bivariate functional using an auxiliary variable.
  • Employed alternating minimization to solve the bivariate functional.
  • Formulated the original variable minimization as a total variation (TV) denoising problem, solved via dual formulation.

Main Results:

  • The proposed bivariate functional is mathematically equivalent to the original univariate functional.
  • The alternating minimization process is proven to be convergent.
  • Numerical experiments demonstrate superior efficiency and performance compared to Chan et al.'s method.

Conclusions:

  • The optimization transfer technique provides an efficient and convergent solution for wavelet inpainting.
  • The proposed algorithm significantly outperforms existing variational methods.
  • This advancement offers improved image restoration capabilities.