Optimally Sparse Approximations of Multivariate Functions Using Compactly Supported Shearlet Frames
نویسندگان
چکیده
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 systems provide a nearly optimally sparse approximation error rate within this model class measured by means of non-linear, best n-term approximations. Keywords— Anisotropic Features, Shearlets, Cartoon-like Images, Non-linear Approximations, Sparse Approximations
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