Two-dimensional non-linear microwave imaging with total variation regularization

Using an electric field integral equation formulation, we perform a comparative study between linear and nonlinear microwave imaging with adaptive total variation regularization. It is well known that linearized methods fail for higher values of dielectric contrasts. So, it is important to investigate nonlinear methods which are valid for higher contrasts. However, these methods have the challenge of dealing with computationally expensive computations of the cost-function gradients; in this paper, we propose a fast gradient computation using the conjugate-gradient fast Fourier transform. Further, we impose a total variation based regularization where the regularization parameter is adaptively estimated using a Bayesian approach, and minimize the cost function using a majorization-minimization algorithm. Finally, we compare the performance and computational costs of using the nonlinear optimization method.