Optimal Non-Linear Models for Sparsity and Sampling
نویسندگان
چکیده
منابع مشابه
Optimal Non-linear Models for Sparsity and Sampling
Given a set of vectors (the data) in a Hilbert space H, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This collection of subspaces gives the best sparse representation for the given data, in a sense defined in the paper, and provides an optimal model for sampling in u...
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This paper is a survey about recent results on sparse representations and optimal models in different settings. Given a set of functions, we show that there exists an optimal collection of subspaces minimizing the sum of the square of the distances between each function and its closest subspace in the collection. Further, this collection of subspaces gives the best sparse representation for the...
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15 صفحه اولSampling and Reconstruction driven by Sparsity Models: Theory and Applications
It has been shown recently that it is possible to sample classes of non-bandlimited signals which we call signals with Finite Rate of Innovation (FRI). Perfect reconstruction is possible based on a set of suitable measurements and this provides a sharp result on the sampling and reconstruction of sparse continuous-time signals. In this paper, we first review the basic theory and results on samp...
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2008
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-008-9040-2