Total variation as a multiplicative constraint for solving inverse problems

The total variation minimization method for deblurring noise is shown to be effective in increasing the resolution in a contrast source inversion approach to index reconstruction from measured scattered field data. Main drawback is the presence of an artificial weighting parameter in the cost functional, which can only be determined through considerable experimentation. Therefore, we introduce the total variation as a multiplicative constraint. Numerical examples demonstrate that the algorithm based on this multiplicative regularization seems to be robust and handling noisy data very well without the necessity of the weighting parameter.