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 log2 average energyofthedetailwaveletcoefficientsasafunctionofthelevelofsignaldecomposition 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, creating a new estimator. We focus on the 2D case, making the method suitable for analyzing complex image data. 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.