Shearlet Multiresolution and Multiple Refinement
Tomas Sauer · Applied and numerical harmonic analysis · 2012
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.