Nelson, JDB;
(2014)
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.
IEEE Transactions on Signal Processing
, 62
(20)
5270 - 5281.
10.1109/TSP.2014.2345346.
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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.
| Type: | Article |
|---|---|
| Title: | 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 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/TSP.2014.2345346 |
| Publisher version: | http://dx.doi.org/10.1109/TSP.2014.2345346 |
| Additional information: | © Copyright 2014 IEEE. This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/ |
| Keywords: | Riesz bases, basis constr uction, Fourier series, $ell_p$ regularization, sparsity basis selection |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1465835 |
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