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

Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from 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.
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...
Time-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...

You might also read

Related Articles

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

Sort by
Same author

Dynamic reconfiguration of subunits from the hippocampal-amygdala complex indicate patterns of psychosis vulnerability in 22q11.2 deletion syndrome.

Scientific reports·2026
Same author

Shared and Individual Resting-State MEG Network Signatures of Tinnitus Revealed by Holistic Graph Learning.

IEEE open journal of engineering in medicine and biology·2026
Same author

The microstructure-weighted human connectome: network properties and structure-function correlations across spatial scales.

bioRxiv : the preprint server for biology·2026
Same author

Revisiting deep information propagation: Fractal frontier and finite-size effects.

Neural networks : the official journal of the International Neural Network Society·2026
Same author

A diffusion MRI-derived perivascular metric related to glymphatic-associated processes in bipolar disorder vulnerability: Multimodal correlates across emotion dysregulation patients and offspring.

Psychiatry research·2026
Same author

Spinal cord structural and functional architecture and its shared organization with the brain across the adult lifespan.

Nature communications·2026
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 2, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Steerable pyramids and tight wavelet frames in L2(R(d)).

Michael Unser1, Nicolas Chenouard, Dimitri Van de Ville

  • 1Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|April 12, 2011
PubMed
Summary
This summary is machine-generated.

We developed a new framework for designing steerable wavelet frames, offering more flexibility than existing methods. Optimized wavelet designs, like equalized principal component analysis, show superior performance in signal denoising tasks.

Related Experiment Videos

Last Updated: Jun 2, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Area of Science:

  • Signal Processing
  • Image Analysis
  • Applied Mathematics

Background:

  • Traditional steerable pyramids offer limited wavelet customization.
  • Existing methods lack a generalized framework for multi-dimensional steerable wavelet design.

Purpose of the Study:

  • To introduce a flexible functional framework for designing tight steerable wavelet frames in any dimension.
  • To generalize Simoncelli's steerable pyramid with a broader range of steerable wavelets.
  • To enable arbitrary shaping of steerable wavelets through unitary matrix parametrization.

Main Methods:

  • Construction of a primal isotropic wavelet frame for multiresolution decomposition.
  • Generation of steerable wavelets via Nth-order generalized Riesz transform.
  • Application of an M×M unitary matrix for controlling wavelet shaping.
  • Development of a Fast Fourier Transform-based decomposition algorithm.
  • Proposal of a principal-component-based method for signal-adapted wavelet design.

Main Results:

  • A complete functional description and steering equations for generalized wavelet transforms.
  • Demonstration of concrete transform examples, including Mallat-type multiresolution analysis.
  • Comparison of denoising performance across different steerable transform designs.
  • Identification of optimized wavelet designs, specifically equalized principal component analysis, as top performers.

Conclusions:

  • The proposed framework provides a powerful and flexible tool for designing steerable wavelet frames.
  • Arbitrary shaping via unitary matrices significantly expands the palette of steerable wavelets.
  • Signal-adapted wavelet design, particularly equalized principal component analysis, yields superior denoising results.