Compactly supported shearlets are optimally sparse
نویسندگان
چکیده
منابع مشابه
Compactly supported shearlets are optimally sparse
Cartoon-like images, i.e., C functions which are smooth apart from a C discontinuity curve, have by now become a standard model for measuring sparse (non-linear) approximation properties of directional representation systems. It was already shown that curvelets, contourlets, as well as shearlets do exhibit (almost) optimally sparse approximations within this model. However, all those results ar...
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Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation operators applied to it, in much the same way wavelet systems are dyadic scalings and translations of a single function, but including a precise control of directio...
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Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model cl...
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In this paper we show that the shearlets, an affine-like system of functions recently introduced by the authors and their collaborators, are essentially optimal in representing 2–dimensional functions f that are C2 except for discontinuities along C2 curves. More specifically, if fS N is the N–term reconstruction of f obtained by using the N largest coefficients in the shearlet representation, ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2011
ISSN: 0021-9045
DOI: 10.1016/j.jat.2011.06.005