Shearlets
Multiscale Analysis for Multivariate Data
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Beschreibung
Over the last 20 years, multiscale methods and wavelets have revolutionized the field of applied mathematics by providing efficient means for encoding isotropic phenomena. Directional multiscale systems, particularly shearlets, are currently having the same dramatic impact on the encoding of multivariate signals, which are usually dominated by anisotropic features. Since its introduction about six years ago, the theory of shearlets has rapidly developed and gained wide recognition as the superior approach for multiscale analysis of multivariate signals, providing a truly unified treatment of both the continuum and the digital setting. By now, this research field has reached full maturity, with deep mathematical results, efficient numerical methods, and a variety of high-impact applications.
Edited by the topic's two main pioneers, this volume systematically surveys the theory and applications of shearlets. Following a general survey of the subject, carefully selected contributions explore the current state of the field in greater detail. Specific areas covered include:
* analysis of anisotropic features;
* sparse approximations of multivariate data;
* shearlet smoothness spaces;
* numerical implementations;
* applications to image processing.
Shearlets is aimed at graduate students and researchers in the areas of applied mathematics, computer science, engineering, and any other field dealing with the development and applications of highly efficient methodologies for processing multivariate data. As the first monograph in the literature to survey shearlets, this volume offers both a unique state-of-the-art resource for scientists dealing with advanced multiscale methodsand 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.
The first book published on the topic of shearlets or geometric multiscale analysis Unified notation used throughout Comprehensive presentation of shearlet theory and applications Valuable for an interdisciplinary audience of graduate students and researchers in applied mathematics, computer science, and engineering Includes supplementary material: sn.pub/extras
Autor*in
Gitta Kutyniok
Themen in »Shearlets«
anisotropic data representation directional multiscale analysis image processing multivariate data shearlets sparsity wavelets