The Dual Wavelet Spectra: An Alternative Perspective on Hurst Exponent Estimation with Application to Mammogram Classification

TL;DR

This paper introduces a novel wavelet-based estimator for the Hurst exponent using dual spectra, demonstrating its effectiveness through simulations and applying it to mammogram classification with significant results.

Contribution

It proposes a new dual wavelet spectra method for Hurst exponent estimation and applies it to breast cancer detection in mammograms.

Findings

New dual wavelet spectra estimator for Hurst exponent.

Effective in simulation studies.

Significant impact on mammogram classification.

Abstract

The wavelet spectra is a common starting point for estimating the Hurst exponent of a self-similar signal using wavelet-based techniques. The decay of the $\log_2$ average energy of the detail wavelet coefficients as a function of the level of signal decomposition can be used to construct estimators for this parameter. In this paper, we expand on previous work which introduced the ``dual" wavelet spectra, where decomposition levels are instead treated as a function of energy values, and propose a relationship between its slope and the Hurst exponent by inverting the standard wavelet spectra, thereby creating a new estimator. The effectiveness of this estimator and its sensitivity to several settings are demonstrated through a simulation study. Finally, we show how the technique performs as a feature extraction method by applying it to the task of detecting the presence of breast cancer in mammogram images. Dual spectra wavelet features had a statistically significant effect on the log-odds of Cancer.