Two dimensional microwave imaging using a divide and unite algorithm

Quantitative microwave imaging using inverse scattering is a promising technique for biomedical imaging. Given the ill-posed nature of the inverse problem, the use of efficient regularization techniques is essential in order to come up with meaningful solutions to the imaging problem. In this paper, we propose a novel regularization technique that is based on an iterative divide-and-unite algorithm of the imaged domain. Multi-scaling procedures have been proposed earlier, where the object domain is iteratively divided based on heuristic criteria. We take a different route, where, starting from a single coarse pixel, the domain is divided into finer pixels based on heterogeneity in the gradient of the cost function. An inexpensive algebraic reconstruction technique is then applied to estimate the values of the finer pixels. Subsequently, an unite step is performed to combine pixels with similar values of dielectric contrast. The power of this method is that it keeps the number of reconstructed pixels at a minimum and allows for nonlocal pixels, as also seen in level-set based reconstructions. Implementation of the algorithm shows a significant reduction in converging time, the cost function and the total shape error.