Optimally sparse 3D approximations using shearlet representations
نویسندگان
چکیده
منابع مشابه
Optimally Sparse 3d Approximations Using Shearlet Representations
This paper introduces a new Parseval frame, based on the 3–D shearlet representation, which is especially designed to capture geometric features such as discontinuous boundaries with very high efficiency. We show that this approach exhibits essentially optimal approximation properties for 3–D functions f which are smooth away from discontinuities along C2 surfaces. In fact, the N term approxima...
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Abstract. We study efficient and reliable methods of capturing and sparsely representing anisotropic structures in 3D data. As a model class for multidimensional data with anisotropic features, we introduce generalized three-dimensional cartoon-like images. This function class will have two smoothness parameters: one parameter β controlling classical smoothness and one parameter α controlling a...
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In this paper, we introduce pyramid-adapted shearlet systems for the three-dimensional setting, and show how one can construct frames for L(R) with this particular shearlet structure. We then introduce a generalized three-dimensional cartoon-like image model class of piecewise C smooth functions with discontinuities on a C smooth surface with 1 < α ≤ 2 and show that pyramid-adapted shearlet sys...
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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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This paper introduces a Parseval frame of shearlets for the representation of 3D data, which is especially designed to handle geometric features such as discontinuous boundaries with very high efficiency. This system of 3D shearlets forms a multiscale pyramid of well-localized waveforms at various locations and orientations, which become increasingly thin and elongated at fine scales. We prove ...
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ژورنال
عنوان ژورنال: Electronic Research Announcements in Mathematical Sciences
سال: 2010
ISSN: 1935-9179
DOI: 10.3934/era.2010.17.125