Shearlets Multiscale Analysis for Multivariate Data - Kutyniok, Gitta; Labate, Demetrio (Applied and Numerical Harmonic Analysis, 2012)
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 methods and a supplemental textbook for graduate courses in applied harmonic analysis.