Semi-Local Scaling Exponent Estimation With Box-Penalty Constraints and Total-Variation Regularization

We here establish and exploit the result that 2D 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 framewo...

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Bibliographic Details
Published inIEEE transactions on image processing Vol. 25; no. 7; pp. 3167 - 3181
Main Authors Nelson, J. D. B., Nafornita, C., Isar, A.
Format Journal Article
LanguageEnglish
Published United States IEEE 01.07.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Asymptotic properties
Constants
Estimation
Estimators
Exponents
Image reconstruction
Least squares method
Mathematical models
Noise reduction
Robustness
Self-similarity
Statistical methods
Wavelet domain
Wavelet transforms
Wavelet transforms
statistical analysis
stochastic processes
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Summary:We here establish and exploit the result that 2D 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 square problems and generalized Lasso for scaling exponent estimation inspires the simultaneous incorporation of both bounding box constraints and total variation smoothing into an iteratively reweighted least-square estimator framework. Numerical results on fractional Brownian fields with global and piecewise constant, semi-local Hurst parameters illustrate the benefits of the new estimators.
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ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2016.2551365