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Quantifying Intermembrane Distances with Serial Image Dilations
07:45

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Published on: September 28, 2018

Critically sampled wavelets with composite dilations.

Glenn R Easley1, Demetrio Labate

  • 1System Planning Corporation, Arlington, VA 22201, USA. geasley@sysplan.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|August 17, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces new critically sampled wavelets with composite dilations for efficient image coding. These advanced wavelets offer superior nonlinear approximation rates compared to traditional methods.

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Area of Science:

  • Signal Processing
  • Image Analysis
  • Applied Mathematics

Background:

  • Traditional wavelets analyze data at various scales and locations.
  • Composite dilations extend wavelets to include orientation and anisotropic scaling.
  • The shearlet system is an example of composite dilation wavelets for sparse image representation.

Purpose of the Study:

  • To develop critically sampled wavelets with composite dilations for image coding.
  • To improve the efficiency of analyzing geometric information in multidimensional data.
  • To achieve better nonlinear approximation rates in image representations.

Main Methods:

  • Investigating constructions from the composite dilation framework.
  • Developing new critically sampled discrete transforms.
  • Comparing performance against traditional discrete wavelet transforms and other multiscale transforms.

Main Results:

  • Demonstrating that many directional constructions fit within the composite dilation framework.
  • Introducing novel critically sampled discrete transforms.
  • Achieving significantly better nonlinear approximation rates for image coding.

Conclusions:

  • Wavelets with composite dilations offer a powerful framework for image analysis and coding.
  • The developed transforms outperform existing methods in nonlinear approximation.
  • This approach enhances the efficient representation of geometric image features.