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Related Concept Videos

Propagation of Waves01:07

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Reflection of Waves01:07

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...
Wave Parameters01:10

Wave Parameters

The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...
Interference and Superposition of Waves01:07

Interference and Superposition of Waves

When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect of the waves is the sum of the individual waves' effects. However, it does not imply that the individual waves affect the propagation of other waves.
Interference occurs in mechanical waves, such as sound waves, waves on a string, and surface water waves. Mechanical waves correspond to the physical displacement of particles. Hence,...
Steady Flow of a Fluid Stream01:27

Steady Flow of a Fluid Stream

Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
During this process, the momentum of the fluid within the control volume remains constant over the time interval dt. By applying the...

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Related Experiment Video

Updated: May 20, 2026

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

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Published on: July 19, 2016

3D steerable wavelets in practice.

Nicolas Chenouard1, Michael Unser

  • 1Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland. nicolas.chenouard@gmail.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|July 4, 2012
PubMed
Summary
This summary is machine-generated.

We developed steerable wavelet frames for 3D image analysis. These novel wavelets enable efficient directional pattern characterization and image reconstruction, proving useful in biomedical data processing.

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Last Updated: May 20, 2026

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Area of Science:

  • Signal Processing
  • Image Analysis
  • Applied Mathematics

Background:

  • Wavelet frames are crucial for signal and image analysis.
  • Existing methods often lack efficient steerability in 3D.
  • Need for adaptive and directional analysis tools in 3D data.

Purpose of the Study:

  • To introduce a systematic and practical design for steerable wavelet frames in 3D.
  • To enable efficient rotation and adaptation of wavelet basis functions.
  • To demonstrate applications in 3D biomedical data processing and inverse problems.

Main Methods:

  • Applying a 3D generalized Riesz transform to an isotropic wavelet frame.
  • Utilizing linear combinations of Riesz wavelets for directional rotation.
  • Developing a 3D monogenic analysis for edge detection and pattern characterization.
  • Proposing an inverse-problem formalism for image reconstruction.

Main Results:

  • The proposed transform is self-reversible, forming a tight frame.
  • Elementary constituents (Riesz wavelets) can be efficiently rotated in any 3D direction.
  • Demonstrated high-quality 3D image reconstructions from sparse wavelet-domain edges.
  • Showcased feature-reduction ability and potential for solving inverse problems.

Conclusions:

  • The developed steerable wavelet frames offer a practical and systematic approach for 3D data analysis.
  • These wavelets are effective for characterizing directional patterns and detecting edges in 3D.
  • The proposed inverse-problem formalism facilitates high-quality image reconstruction, highlighting the utility of steerable wavelets.