Microwave Tomography for Breast Cancer Detection Using Level Sets Natalia Irishina 1 , Miguel Moscoso 2 , and Oliver Dorn 3 Modeling and Numerical Simulation Group Universidad Carlos III de Madrid Avda. de la Universidad, 30 28911 Legan´ es-Madrid, Spain 1 nirishin@math.uc3m.es, 2 moscoso@math.uc3m.es, 3 odorn@math.uc3m.es Abstract: In this paper we analyze the potential of a shape-based model for the early detection of breast tumors from microwave data. The tumors are modeled using a level-set technique. The formulation as a shape-reconstruction problem offers several advantages compared to more traditional pixel-based schemes, to mention in particular well- defined boundaries and the incorporation of an intrinsic regularization that reduces the dimensionality of the inverse problem whereby at the same time stabilizing the reconstruction. We present in this paper a novel strategy that is able to detect very small tumors compared to the wavelength used for illuminating the breast. In addition, our algorithm is able to determine the sizes and the dielectric properties of the tumors with good accuracy. Numerical experiments are shown in 2D which demonstrate the performance of this new technique in realistic situations. Keywords: Microwave tomography, medical imaging, level sets, shape reconstruction. 1. Introduction Microwave tomographic imaging is showing significant promise as a new technique for the early detec- tion of breast cancer. Its physical basis is the high contrast between the dielectric properties of the healthy breast tissue and the malignant tumors at microwave frequencies [1, 2]. Making use of this characteristic, microwave imaging systems aim at detecting, localizing and characterizing tumors in the breast (see, for example, [3] and references therein). The mathematical reconstruction problem in microwave tomography typically is treated as a nonlinear inverse problem in which a given cost functional is minimized via an iterative algorithm. Traditional iterative algorithms, well suited for nonlinear inverse problems and based on pixel reconstruction techniques, turn out to suffer from several drawbacks in this application. We mention in particular the typical oversmoothing effect of the interfaces between the tumors and the surrounding tissue in the reconstruction which is due to the need of strong regularization, normally addressed by adding a Tikhonov-Philips term to the cost functional. Recently, a new family of iterative methods has been developed for the reconstruction of images in many different applications such as diffuse optical tomography, electrical impedance tomography or reservoir characterization. These approaches formulate the problems at hand as shape reconstruction problems and are based on a level set representation of these shapes (see [4] and references therein). Following this approach, we will assume here during the reconstruction that the dielectric properties in the breast are piecewise constant with only few possible values, namely one for the skin, one for the healthy tissue (both of them corresponding to positive values of the level set function) and another for the tumor (corresponding 23rd Annual Review of Progress in Applied Computational Electromagnetics March 19-23, 2007 - Verona, Italy '2007 ACES 1955