Nelson, JDB;
Nafornita, C;
Isar, A;
(2016)
Semi-local scaling exponent estimation with box-penalty constraints and total-variation regularisation.
IEEE Transactions on Signal Processing
, 25
(7)
pp. 3167-3181.
10.1109/TIP.2016.2551365.
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Abstract
We here establish and exploit the result that 2-D isotropic self-similar fields beget quasi-decorrelated wavelet coefficients and that the resulting localised log sample second moment statistic is asymptotically normal. This leads to the development of a semi-local scaling exponent estimation framework with optimally modified weights. Furthermore, recent interest in penalty methods for least squares problems and generalised Lasso for scaling exponent estimation inspires the simultaneous incorporation of both bounding box constraints and total variation smoothing into an iteratively reweighted least-squares estimator framework. Numerical results on fractional Brownian fields with global and piecewise constant, semi-local Hurst parameters illustrate the benefits of the new estimators.
| Type: | Article |
|---|---|
| Title: | Semi-local scaling exponent estimation with box-penalty constraints and total-variation regularisation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/TIP.2016.2551365 |
| Publisher version: | https://doi.org/10.1109/TIP.2016.2551365 |
| Language: | English |
| Additional information: | Copyright © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
| Keywords: | Wavelets, scaling exponent, Hurst parameter, self-similar processes, scaling processes |
| 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/1477549 |
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