Extended contrast source inversion

We discuss the problem of the reconstruction of the profile of a bounded ob ject from scattered field data. Inspired by the successful implementation o f 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 implemen t the additional regularizer in the CSI method, the updating of the contras t 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 me thod. The addition of the minimization of the total variation to the cost functio nal has a very positive effect on the quality of the reconstructions for bo th 'blocky' and smooth profiles, but a drawback is the presence of an artif icial weighting parameter in the cost functional, which can only be determi ned through considerable numerical experimentation. Therefore, we have intr oduced the TV as a multiplicative constraint. Numerical experiments demonst rate that the algorithm, based on this multiplicative regularization, seems to be robust, handling noisy as well as limited data very well, without th e necessity of artificial parameters.