Shearlets

This volume surveys the theory and applications of shearlets. It serves as a unique state-of-the-art resource for scientists interested in advanced multiscale methods as well as a supplemental textbook for graduate courses in applied harmonic analysis.

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.

Introduction. - Shearlets and Microlocal Analysis. - Analysis and Identification of Multidimensional Singularities using the Continuous Shearlet Transform. - Multivariate Shearlet Transform, Shearlet Coorbit Spaces and their Structural Properties. - Shearlets and Optimally Sparse Approximations. - Shearlet Multiresolution and Multiple Refinement. - Digital Shearlet Transforms. - Imaging Applications.