Shearlets pp 199-237 | Cite as

Shearlet Multiresolution and Multiple Refinement

Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Starting from the concept of filterbanks and subband coding, we present an entirely digital approach to shearlet multiresolution which is not a discretization of the continuous transform but is naturally connected to the filtering of discrete data, the usual procedure in digital signal processing. It will be shown that a full analogy of multiresolution analysis (MRA) can be derived also for shearlets as a special instance of multiple MRA (MMRA) based on cascading a finite number of filterbanks. In this discrete shearlet transform, the MMRA concept goes hand in hand with shear-based scaling matrices of a particularly appealing and simple geometry. Finally, also some application issues of such discrete transformations will be considered briefly.

Key words

Filterbank Multiresolution analysis Multiple MRA Shearlet MRA Subdivision 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Lehrstuhl für Numerische MathematikJustus-Liebig-Universität GießenGießenGermany

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