Wavelet-based 3-D multifractal spectrum with applications in breast MRI images

Breast cancer is the second leading cause of death in women in the United States. Breast Magnetic Resonance Imaging (BMRI) is an emerging tool in breast cancer diagnostics and research, and it is becoming routine in clinical practice. Recently, the American Cancer Society (ACS) recommended that women at very high risk of developing breast cancer have annual BMRI exams, in addition to annual mammograms, to increase the likelihood of early detection. (Saslow et al. [20] ). Many medical images demonstrate a certain degree of self-similarity over a range of scales. The multifractal spectrum (MFS) summarizes possibly variable degrees of scaling in one dimensional signals and has been widely used in fractal analysis. In this work, we develop a generalization of MFS to three dimensions and use dynamics of the scaling as discriminatory descriptors for the classification of BMRI images to benign and malignant. Methodology we propose was tested using breast MRI images for four anonymous subjects (two cancer, and two cancer-free cases). The dataset consists of BMRI scans obtained on a 1.5T GE Signa MR (with VIBRANT) scanner at Emory University. We demonstrate that meaningful descriptors show potential for classifying inference.