Mammogram Diagnostics Using Robust Wavelet-Based Estimator of Hurst Exponent

  • Chen FengEmail author
  • Yajun Mei
  • Brani Vidakovic
Part of the ICSA Book Series in Statistics book series (ICSABSS)


Breast cancer is one of the leading causes of death in women. Mammography is an effective method for early detection of breast cancer. Like other medical images, mammograms demonstrate a certain degree of self-similarity over a range of scales, which can be used in classifying individuals as cancerous or non-cancerous. In this paper, we study the robust estimation of Hurst exponent (self-similarity measure) in two-dimensional images based on non-decimated wavelet transforms (NDWT). The robustness is achieved by applying a general trimean estimator on non-decimated wavelet detail coefficients of the transformed data, and the general trimean estimator is derived as a weighted average of the distribution’s median and quantiles, combining the median’s emphasis on central values with the quantiles’ attention to the extremes. The properties of the proposed estimators are studied both theoretically and numerically. Compared with other standard wavelet-based methods (Veitch and Abry (VA) method, Soltani, Simard, and Boichu (SSB) method, median based estimators MEDL and MEDLA, and Theil-type (TT) weighted regression method), our methods reduce the variance of the estimators and increase the prediction precision in most cases. We apply proposed methods to digitized mammogram images, estimate Hurst exponent, and then use it as a discriminatory descriptor to classify mammograms to benign and malignant. Our methods yield the highest classification accuracy around 65%.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.H. Milton Stewart School of Industrial and Systems Engineering and Wallace H. Coulter Department of Biomedical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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