A Longitudinal Study of Mammograms Utilizing the Automated Wavelet Transform Modulus Maxima Method

Breast cancer is a disease which predominatly affects women. About 1 in 8 women are diagnosed with breast cancer during their lifetime. Early detection is key to increasing the survival rate of breast cancer patients since the longer the tumor goes undetected, the more deadly it can become. The modern approach for diagnosing breast cancer relies on a combination of self-breast exams and mammography to detect the formation of tumors. However, this approach only accounts for tumors which are either detectable by touch or are large enough to be observed during a screening mammogram. For some individuals, by the time a tumor is detected, it has already progressed to a deadly stage. Unlike previous research, this paper focuses on the predetection of tumorous tissue. This novel approach sets out to examine changes in the breast microenvironment instead of locating and identifying tumors. The purpose of this paper is to explore whether it is possible to discover changes in the breast tissue microenvironment which later develop into breast cancer. We hypothesized that changes in the breast tissue would be detected by analyzing mammograms from the years prior to the discovery of tumorous tissue by a radiologist. We analyzed a set of time-series digital mammograms corresponding to 26 longitudinal cancer cases, obtained through a collaboration with Eastern Maine Medical Center (EMMC) in Bangor, Maine. We automated the Wavelet Transform Modulus Maxima (WTMM) method, a mathematical formalism that we used to perform a multifractal analysis. In particular, this automated WTMM (AWTMM) was used to calculate the Hurst exponent, a metric that is correlated with breast tissue density. The AWTMM allowed us to see with greater detail the changes in mammogram tissue, specifically concerning breast density. The results suggest that signs of malignancy can be observed as early as two years before standard radiological procedures. In this research, we identify a set of variables that show significance when classifying precancerous tissue

2D wavelet-based spectra with applications

A wavelet-based spectral method for estimating the (directional) Hurst parameter in isotropic and anisotropic non-stationary fractional Gaussian fields is proposed. The method can be applied to self-similar images and, in general, to d-dimensional data which scale. In the application part, the problems of denoising 2D fractional Brownian fields and classification of digital mammograms to benign and malignant are considered. In the first application, a Bayesian inference calibrated by information from the wavelet-spectral domain is used to separate the signal from the noise. In the second application, digital mammograms are classified into benign and malignant based on the directional Hurst exponents which prove to be discriminatory summaries.Scaling Wavelets Self-similarity 2D wavelet spectra