Algebraic reconstruction techniques for inverse imaging

Inverse microwave imaging has the potential to provide low cost solutions for medical imaging applications, such as in breast cancer detection. The mathematical challenges in the solution of inverse problems, namely non-linearity, ill-posedness and non-uniqueness, are well known and cause optimization algorithms to get stuck at local minima(s). In this regard, the initial guess is very crucial in guiding the inversion algorithm to an acceptable solution. We investigate the role of algebraic reconstruction techniques along with box constraints in providing a good initial guess. We propose an inversion algorithm that combines these techniques with a regularization that maximises entropy (using a Gaussian a priori law) and show good reconstructions for contrasts up to 2.