Introduction to Shearlets
نویسندگان
چکیده
Shearlets emerged in recent years among the most successful frameworks for the efficient representation of multidimensional data. Indeed, after it was recognized that traditional multiscale methods are not very efficient at capturing edges and other anisotropic features which frequently dominate multidimensional phenomena, several methods were introduced to overcome their limitations. The shearlet representation stands out since it offers a unique combinations of some highly desirable properties: it has a single or finite set of generating functions, it provides optimally sparse representations for a large class of multidimensional data, it is possible to use compactly supported analyzing functions, it has fast algorithmic implementations and it allows a unified treatment of the continuum and digital realms. In this chapter, we present a self-contained overview of the main results concerning the theory and applications of shearlets.
منابع مشابه
A Shearlets-based Edge Identification Algorithem for Infrared Image
A shearlets-based edge identification algorithem for infrared image is proposed. The algorithem demonstrates the performance of edge detection based on shearlets, combines with the edge hysteresis thresholding, designs steps of edge detection, which is proper to use in infrared images.Simultaneously, with the advantage of edge geometric features provided by the shearlets, infrared image were ex...
متن کاملParabolic Molecules
Anisotropic decompositions using representation systems based on parabolic scaling such as curvelets or shearlets have recently attracted significantly increased attention due to the fact that they were shown to provide optimally sparse approximations of functions exhibiting singularities on lower dimensional embedded manifolds. The literature now contains various direct proofs of this fact and...
متن کاملDigital Shearlet Transforms
Over the past years, various representation systems which sparsely approximate functions governed by anisotropic features such as edges in images have been proposed. We exemplarily mention the systems of contourlets, curvelets, and shearlets. Alongside the theoretical development of these systems, algorithmic realizations of the associated transforms were provided. However, one of the most comm...
متن کاملApplied Harmonic Analysis meets Sparse Regularization of Operator Equations
Sparse regularization of operator equations has already shown its effectiveness both theoretically and practically. The area of applied harmonic analysis offers a variety of systems such as wavelet systems which provide sparse approximations within certain model situations which then allows to apply this general approach provided that the solution belongs to this model class. However, many impo...
متن کاملLinearized Riesz transform and quasi-monogenic shearlets
The only quadrature operator of order two on L2(R) which covaries with orthogonal transforms, in particular rotations is (up to the sign) the Riesz transform. This property was used for the construction of monogenic wavelets and curvelets. Recently, shearlets were applied for various signal processing tasks. Unfortunately, the Riesz transform does not correspond with the shear operation. In thi...
متن کامل