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