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

Area of Science:

• * Statistical analysis of random fields.
• * Wavelet analysis and signal processing.
• * Fractional Brownian motion and scaling exponents.

Background:

• * Understanding the statistical properties of 2D isotropic self-similar fields is crucial.
• * Wavelet coefficients of such fields exhibit quasi-decorrelation.
• * Accurate estimation of scaling exponents is vital in various scientific domains.

Purpose of the Study:

• * To establish and exploit the quasi-decorrelation of wavelet coefficients for 2D isotropic self-similar fields.
• * To develop a novel semi-local scaling exponent estimation framework.
• * To incorporate bounding box constraints and total variation smoothing into the estimation framework.

Main Methods:

• * Establishing the asymptotic normality of the localized log sample second moment statistic.
• * Developing a semi-local scaling exponent estimation framework with optimally modified weights.
• * Implementing an iteratively reweighted least-square estimator incorporating bounding box constraints and total variation smoothing.

Main Results:

• * Demonstrated that 2D isotropic self-similar fields produce quasi-decorrelated wavelet coefficients.
• * Developed and validated a semi-local scaling exponent estimation framework.
• * Showcased the benefits of the new estimators on fractional Brownian fields with diverse Hurst parameters.

Conclusions:

• * The developed framework provides an effective method for estimating scaling exponents.
• * The incorporation of constraints and smoothing enhances the robustness of the estimators.
• * The findings have implications for the analysis of complex random fields.