Han, Bin; Kutyniok, Gitta; Shen, Zuowei Adaptive multiresolution analysis structures and shearlet systems. (English) Zbl 1283.42053 SIAM J. Numer. Anal. 49, No. 5, 1921-1946 (2011). The authors introduce the concept of an adaptive multiresolution analysis (AMRA). This concept is a variant of the classical multiresolution analysis (MRA) and is motivated by the desire to design a fast and flexible decomposition algorithm that adapts to the data at each level of decomposition. This new concept is studied within the framework of affine-like systems and for filter design purposes a unitary extension principle is derived. Based on their theoretical results, the authors then present a comprehensive theory of shearlet systems that includes tight shearlet frames with spatially compactly supported generators. The underlying fast adaptive decomposition and reconstruction algorithms are explicitly described and illustrated by hand of an example. Reviewer: Peter Massopust (München) Cited in 17 Documents MSC: 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 42C15 General harmonic expansions, frames 65T60 Numerical methods for wavelets 65T99 Numerical methods in Fourier analysis 94A08 Image processing (compression, reconstruction, etc.) in information and communication theory Keywords:adaptive multiresolution analysis; affine systems; fast decomposition algorithm; shearlets; tight frames Software:ShearLab PDFBibTeX XMLCite \textit{B. Han} et al., SIAM J. Numer. Anal. 49, No. 5, 1921--1946 (2011; Zbl 1283.42053) Full Text: DOI