Shearlets: Multiscale Analysis for Multivariate Data

✍ Scribed by Gitta Kutyniok, Demetrio Labate (auth.), Gitta Kutyniok, Demetrio Labate (eds.)

• Publisher: Birkhäuser Basel
• Year: 2012
• Tongue: English
• Leaves: 346
• Series: Applied and numerical harmonic analysis
• Edition: 1
• Category: Library

✦ Synopsis

Over the last 20 years, multiscale methods and wavelets have revolutionized the field of applied mathematics by providing an efficient means of encoding isotropic phenomena. Directional multiscale systems, particularly shearlets, are now having the same dramatic impact on the encoding of multidimensional signals. Since its introduction about five years ago, the theory of shearlets has rapidly developed and gained wide recognition as the superior way of achieving a truly unified treatment in both a continuous and a digital setting. By now, it has reached maturity as a research field, with rich mathematics, efficient numerical methods, and various important applications.

✦ Table of Contents

Front Matter....Pages i-xix
Introduction to Shearlets....Pages 1-38
Shearlets and Microlocal Analysis....Pages 39-67
Analysis and Identification of Multidimensional Singularities Using the Continuous Shearlet Transform....Pages 69-103
Multivariate Shearlet Transform, Shearlet Coorbit Spaces and Their Structural Properties....Pages 105-144
Shearlets and Optimally Sparse Approximations....Pages 145-197
Shearlet Multiresolution and Multiple Refinement....Pages 199-237
Digital Shearlet Transforms....Pages 239-282
Image Processing Using Shearlets....Pages 283-325
Back Matter....Pages 327-328

✦ Subjects

Fourier Analysis; Signal, Image and Speech Processing; Numerical Analysis; Data Storage Representation; Applications of Mathematics