UTA Department of Mathematics

Mathematics and Statistics Colloquium

Date/Time/Room: Friday (4/13/2007) at 2:30pm in 304 Pickard Hall

Speaker: Dr. Matthew A. Lewis, Assistant Professor
Department of Radiology, University of Texas Southwestern Medical Center at Dallas


"The linear sampling and factorization inverse scattering methods: can they be translated to medical imaging?"

Abstract: In women under age 40, the breast may be too dense for mammographic screening and microcalcification detection. A non-ionizing method would be preferred for frequent screening in patients with significant risk factors for developing breast cancer. Ultrasonic detection of microcalcifications has been problematic since frequencies above 10 MHz suffer from appreciable attenuation in soft tissues. Transmission diffraction tomography is by construction a low-pass filter and insensitive to scattering caused by small, hard inhomogeneities. A more general form of acoustic inverse scattering is therefore needed for microcalcification detection and localization by ultrasound. An advanced scalar inverse scattering theory developed by Colton, Kirsch, and others [D. Colton, J. Coyle, and P. Monk. SIAM Review 42(3), 369-414 (2000)] in the electromagnetic inverse scattering community for determining the location and shape of scatterers with size on the order of the wavelength (the so-called resonance region) has been simulated in the context of breast microcalcification detection. This method was shown to be related to both Multiple Signal Classification and time-reversal algorithms [M. Cheney. Inverse Problems 17:581-585 (2001)] [S.K. Lehman and A.J. Devaney. JASA 113(5):2742-2753 (2003)]. Translation of this method to a heterogeneous soft tissue background is a significant challenge.