Inversion Algorithm for Microwave Breast Cancer Detection Using Level Sets

Abstract

This work focuses on the application of breast cancer detection from microwave data. We present a novel shape-based reconstruction algorithm that makes use of level set tech- niques. Our reconstruction algorithm consists of several stages of increasing complexity in which more details of the anatomical structure of the breast interior are incorporated successively. In particular, the algorithm approximates flrst the flbroglandular and fatty regions, and then deter- mines the presence and characteristics of the tumor, such as its size and dielectric properties. The shape-based approach implies an implicit regularization of the inverse problem that creates the images, in the form of prior knowledge regarding the types of tissues present in the breast. This reduces the dimensionality of the inverse problem helping to stabilize the reconstruction process. In addition, it provides well deflned interfaces between the tissues. Our results demostrate the potential and feasibility of this approach to detect, locate, and characterize tumors in their early stages of development. 1. INTRODUCTION Lately, there has been increased interest in the use of microwaves for the early detection of breast cancer. The high contrast of electromagnetic parameters of malignant tissue with respect to healthy tissue makes this technique a very promising alternative to the more traditional technique of X-ray imaging which sufiers from low contrast images and a potential health risk due to the ionizing nature of the probing radiation. Despite of the relative simplicity of the microwave imaging technique, there is still many di-- culties to overcome. This is at least due in part to the high level of heterogeneity of breast tissue which is composed, among others, of flbroglandular and fatty tissues giving rise to complicated internal structures. These two type of tissue have very difierent dielectric properties (1,2) that lead to signiflcant clutter. Imaging in clutter with broadband array imaging techniques that syntheti- cally focus the recorded signals at each point of the domain (see (3), and references therein) may lead to unstable images that cannot be used for practical purposes. We mention, though, that new broadband imaging techniques specially designed for imaging in noisy environments are currently under investigation (4,5). On the other hand, tomographic reconstruction techniques that use a 'classical' shape-based approach sufier from similar drawbacks when the data is acquired in very noisy environments, and the commonly used homogeneous interior assumption is adopted during the reconstruction. In 'classical' shape-based approaches, one assumes during the reconstruction that the dielectric properties are piecewise constant over the domain with only two possible values: one for the healthy tissue and other for the tumor (6). In other words, the very complicated interior structure is not taken into account when inverting the data. Figure 1(a) shows that the homogeneous interior assumption breaks down and that a more complicated algorithm is needed to detect the tumor. The top left and top right images represent the reference and reconstructed permittivity proflles, respectively. The level set function, which deflne the tumor shape, and a cross section through the tumor location, are shown in the bottom images. Therefore, there are still several fundamental problems to be resolved before microwave data can be used for the early diagnosis of breast cancer in clinical situations. We belive that the current work is an attempt to provide one signiflcant step toward this direction. Indeed, we consider MRI- derived breast models that capture the real heterogeneity, and show that a good estimate of the internal breast structure is essential prior to the detection of small tumors. For this purpose, we present a four stage algorithm where we also invert for the internal structure of the breast (7). In our algorithm, the complexity of the permittivity map increases at each new stage of the algorithm, until arriving at the complete breast model. In this way, we incorporate our flndings to the subsequent stages in the form of prior knowledge about the internal structure. In other words, we use submodels of increasing complexity at each new stage of the reconstruction