Optimally Sparse Frames
نویسندگان
چکیده
منابع مشابه
Optimally Sparse Fusion Frames: Existence and Construction
Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. In this paper, we introduce the notion of a sparse fusion frame, that is, a fusion frame whose subspaces are generated by orthonormal basis vectors that are sparse in a ‘uniform basis’ over all subspaces, thereby enabling low-complexity fusion frame decomposition...
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We here prove a lower bound on the number of support vectors to achieve generalization bounds of the form which we consider. Importantly, this result holds not only for linear classifiers, but also for randomized classifiers of a more general form than those by our sparsification procedure (Section 4). Lemma 3.1. Let R,L∗, ≥ 0 be given, with L∗ + ≤ 1/4 and with R being an integer. There exists ...
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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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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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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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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2011
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2011.2160521