UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

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

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. Green open access

[img]
Preview
PDF
Nelson.06870501.pdf
Available under License : See the attached licence file.

Download (2MB)

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 > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1465835
Downloads since deposit
118Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item