06078417

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06078417 Sauer, Tomas Shearlet multiresolution and multiple refinement. Kutyniok, Gitta (ed.) et al., Shearlets. Multiscale analysis for multivariate data. Boston, MA: Birkh\"auser (ISBN 978-0-8176-8315-3/hbk; 978-0-8176-8316-0/ebook). Applied and Numerical Harmonic Analysis, 199-237 (2012). 2012 Boston, MA: Birkh\"auser EN filterbank multiresolution analysis multiple MRA shearlet MRA subdivision

doi:10.1007/978-0-8176-8316-0_6

Summary: 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.