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On the Equivalence Between a Minimal Codomain Cardinality Riesz Basis Construction, a System of Hadamard–Sylvester Operators, and a Class of Sparse, Binary Optimization Problems
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Material Type |
Article
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Author(s) |
Nelson, J.D.B. (Author)
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Source Journal Info. |
Title:
IEEE Transactions on Signal Processing
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Volume/ Issue No.: 2014/SEP-OCT V.62 N.17-20
Call No.:621.3805 ITS Location: Periodicals & References Hall - 2nd floor
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Physical Description |
p 5270 - 5281
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Subject Area/ Descriptors |
Engineering
(39711)
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Abstract |
Piecewise, low-order polynomial, Riesz basis families are constructed such that they share the same coefficient functionals of smoother, orthonormal bases in a localized indexing subset. It is shown that a minimal cardinality basis codomain can be realized by inducing sparsity, via l1 regularization, in the distributional derivatives of the basis functions and that the optimal construction can be found numerically by constrained binary optimization over a suitably large dictionary. Furthermore, it is shown that a subset of these solutions are equivalent to a specific, constrained analytical solution, derived via Sylvester-type Hadamard operators....
Full Abstract
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Journal:
IEEE Transactions on Signal Processing
(2889)
Issu: 2014/SEP-OCT V.62 N.17-20
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