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

Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Boundary Conditions: Lossless Lines01:21

Boundary Conditions: Lossless Lines

Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
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...
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
Reducing Line Loss01:18

Reducing Line Loss

In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
With a step-up transformer at the source, the voltage is increased, thereby reducing the current in the transmission lines since power loss in...

You might also read

Related Articles

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

Sort by
Same author

Vibrational and structural properties of tetramethyltin under pressure.

The Journal of chemical physics·2013
Same author

[Risk factors on the unintentional injuries among rural children aged 0-12 in Shaanxi province].

Zhonghua liu xing bing xue za zhi = Zhonghua liuxingbingxue zazhi·2013
Same author

Adcyap1r1 genotype, posttraumatic stress disorder, and depression among women exposed to childhood maltreatment.

Depression and anxiety·2013
Same author

Current status and challenge of Human Parasitology teaching in China.

Pathogens and global health·2012
Same author

Molecular characterization of heterogeneous mesenchymal stem cells with single-cell transcriptomes.

Biotechnology advances·2012
Same author

Surgical treatment of ossification of the ligamentum flavum associated with dural ossification in the thoracic spine.

Journal of clinical neuroscience : official journal of the Neurosurgical Society of Australasia·2012

Related Experiment Video

Updated: May 18, 2026

Measuring the Shape and Size of Activated Sludge Particles Immobilized in Agar with an Open Source Software Pipeline
09:27

Measuring the Shape and Size of Activated Sludge Particles Immobilized in Agar with an Open Source Software Pipeline

Published on: January 30, 2019

Non-Lipschitz lp-regularization and box constrained model for image restoration.

Xiaojun Chen1, Michael K Ng, Chao Zhang

  • 1Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong. maxjchen@polyu.edu.hk

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|September 26, 2012
PubMed
Summary

This study introduces a new method for image restoration using nonsmooth nonconvex regularization with box constraints. The method ensures recovered images have constant regions separated by edges, improving restoration quality.

Related Experiment Videos

Last Updated: May 18, 2026

Measuring the Shape and Size of Activated Sludge Particles Immobilized in Agar with an Open Source Software Pipeline
09:27

Measuring the Shape and Size of Activated Sludge Particles Immobilized in Agar with an Open Source Software Pipeline

Published on: January 30, 2019

Area of Science:

  • Image processing and computer vision
  • Applied mathematics and optimization

Background:

  • Nonsmooth nonconvex regularization is effective for piecewise constant image restoration.
  • Constrained optimization enhances image restoration by incorporating prior information.

Purpose of the Study:

  • To investigate regularized nonsmooth nonconvex minimization with box constraints for image restoration.
  • To present a computable constant θ for nonconvex nonsmooth regularization and analyze its properties.

Main Methods:

  • Development of a box-constrained image restoration model using non-Lipschitz nonconvex l(p)-norm regularization.
  • Theoretical analysis to determine the properties of local minimizers.

Main Results:

  • A computable positive constant θ is presented for nonconvex nonsmooth regularization.
  • Demonstration that pixel differences in restored images are either 0 or greater than θ.
  • Theoretical proof that local minimizers consist of constant regions bounded by contours and edges.

Conclusions:

  • The proposed model effectively restores images by ensuring piecewise constant regions.
  • Theoretical findings are validated by numerical examples, confirming the model's performance.