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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2512.00996 |
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| _version_ | 1866912739844161536 |
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| author | Hinton, Jr., Raymond J. Cobo, Pepa Ramírez Vidakovic, Brani |
| author_facet | Hinton, Jr., Raymond J. Cobo, Pepa Ramírez Vidakovic, Brani |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00996 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Dual Wavelet Spectra: An Alternative Perspective on Hurst Exponent Estimation with Application to Mammogram Classification Hinton, Jr., Raymond J. Cobo, Pepa Ramírez Vidakovic, Brani Methodology 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. |
| title | The Dual Wavelet Spectra: An Alternative Perspective on Hurst Exponent Estimation with Application to Mammogram Classification |
| topic | Methodology |
| url | https://arxiv.org/abs/2512.00996 |