Extended contrast source inversion

We discuss the problem of the reconstruction of the profile of a bounded object from scattered field data. Inspired by the successful implementation of the minimization of total variation (TV) in the modified gradient method, we have explored the possibilities of this image-enhancement technique in the contrast source inversion (CSI) method. In order to he able to implement the additional regularizer in the CSI method, the updating of the contrast has been modified. We present a preconditioned conjugate gradient method to update the contrast, which introduces hardly any additional computation time, but achieves the same or even better results than the original CSI method. The addition of the minimization of the total variation to the cost functional has a very positive effect on the quality of the reconstructions for both 'blocky' and smooth profiles, but a drawback is the presence of an artificial weighting parameter in the cost functional, which can only be determined through considerable numerical experimentation. Therefore, we have introduced the TV as a multiplicative constraint. Numerical experiments demonstrate that the algorithm, based on this multiplicative regularization, seems to be robust, handling noisy as well as limited data very well, without the necessity of artificial parameters.