Two-dimensional ARMA modeling for breast cancer detection and classification

Computer aided diagnosis (CAD) paradigms have gained currency for discriminating malignant from benign lesions in ultrasound breast images. But even the most sophisticated investigators often rely on one-dimensional representations of the image in terms of its scanlines. Such vector representations are convenient because of the mathematical tractability of one-dimensional time-series. However, they fail to take into account the spatial correlations between the pixels, which is crucial in tumor detection and classification in breast images. In this paper, we propose a CAD system for tumor detection and classification (cancerous v.s. benign) in ultrasound breast images based on a two-dimensional Auto-Regressive-Moving-Average (ARMA) model of the breast image. First, we show, using the Wold decomposition theorem, that ultrasound breast images can be accurately modeled by two-dimensional ARMA random fields. As in the 1D case, the 2D ARMA parameter estimation problem is much more difficult than its 2D AR counterpart, due to the non-linearity in estimating the 2D moving average (MA) parameters. We propose to estimate the 2D ARMA parameters using a two-stage Yule-Walker Least-Squares algorithm. The estimated parameters are then used as the basis for statistical inference and biophysical interpretation of the breast image. We evaluate the performance of the 2D ARMA vector features in real ultrasound images using a k-means classifier. Our results suggest that the proposed CAD system based on a two-dimensional ARMA model leads to parameters that can accurately segment the ultrasound breast image into three regions: healthy tissue, benign tumor, and cancerous tumor. Moreover, the specificity and sensitivity of the proposed two-dimensional CAD system is superior to its one-dimensional homologue.