| Breast cancer continues to be a significant public health problem in the United States: It is the second leading cause of female mortality, and, disturbingly, one out of eight women in the United States will be diagnosed with breast cancer in her life time. Until the cause of this disease is fully understood, early detection remains the only hope to improve prognosis and treatment.;In this thesis, the tumor detection problem in breast images is formulated as a hypothesis testing problem, where the signal of interest is the tumor and the noise refers to the healthy tissue in the breast. In communication engineering, it is known that the optimal detector of a known signal in noise is the North filter. However, the tumor characteristics (size, shape, location, etc) vary between patients and stages of the disease. We show that, for an unknown signal of interest, the optimal filter is given by the Wiener filter. We apply and compare both filters to cancerous and healthy ultrasound breast images. We show that the North filter provides 83% accuracy, and the Wiener filter achieves 91% accuracy. |
