Hyperbolic shearlets

Glenn R. Easley, Demetrio Labate, Vishal M. Patel

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Wavelets with composite dilations extend the traditional wavelet approach by allowing for the construction of waveforms defined not only at various scales and locations but also according to various orthogonal transformations. The shearlets, which yield optimally sparse representations for a large class of 2D and 3D data is the most widely known example of wavelets with composite dilations. However, many other useful constructions are obtained within this framework. In this paper, we examine the hyperbolic shearlets, a variant of the shearlet construction obtained as a system of well localized waveforms defined at various scales, locations and orientations, where the directionality is controlled by orthogonal transformations producing a sort of shearing along hyperbolic curves. The effectiveness of this new representation is illustrated by applications to image denoising. Our results compare favorably against similar denoising algorithms based on wavelets, curvelets and other sophisticated multiscale representations.

Original languageEnglish (US)
Title of host publication2012 IEEE International Conference on Image Processing, ICIP 2012 - Proceedings
Number of pages4
StatePublished - 2012
Event2012 19th IEEE International Conference on Image Processing, ICIP 2012 - Lake Buena Vista, FL, United States
Duration: Sep 30 2012Oct 3 2012

Publication series

NameProceedings - International Conference on Image Processing, ICIP
ISSN (Print)1522-4880


Other2012 19th IEEE International Conference on Image Processing, ICIP 2012
Country/TerritoryUnited States
CityLake Buena Vista, FL

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems


  • Wavelets with composite dilations
  • contourlets
  • directional wavelets
  • multiresolution analysis
  • shearlets


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