Theory and applications of shearlets - Demetrio Labate (University of Houston - Texas)
Seminario di Analisi Numerica
Dettagli dell'evento
Quando
15/12/2015
dalle 11:30 alle 13:00
dalle 11:30 alle 13:00
Dove
Dipartimento di Matematica e Informatica
Persona di riferimento
Theory and applications of shearlets - Demetrio Labate (University of Houston - Texas)
Abstract
Several advanced multiscale representations, most notably curvelets and shearlets, were introduced during the last decade to overcome known limitations of wavelets and other traditional methods. In fact, even though wavelets are very efficient to handle signals with point singularities, they are suboptimal when dealing with edges and those distributed singularities which typically dominate multidimensional data. Shearlets, in particular, are specially designed to combine the power of multiscale analysis with ability to handle directional information efficiently. As a result, they offer very useful microlocal properties and optimally efficient representations, in a precise sense, for a large class of multivariate functions.
In this talk, I will illustrate the construction of shearlet frames and give a brief overview of their sparse approximation properties. Next, I will present and discuss several results illustrating the unique ability of the shearlet transform to provide a precise geometric characterization of singularities. These properties provide the theoretical underpinning for several state-of-the-art applications from signal processing and inverse problems, including data restoration, edge detection and feature extraction.
In this talk, I will illustrate the construction of shearlet frames and give a brief overview of their sparse approximation properties. Next, I will present and discuss several results illustrating the unique ability of the shearlet transform to provide a precise geometric characterization of singularities. These properties provide the theoretical underpinning for several state-of-the-art applications from signal processing and inverse problems, including data restoration, edge detection and feature extraction.
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Il seminario, pur di ambito applicativo, include argomenti trasversali di analisi armonica e teoria dell'approssimazione.
