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 appr oach to index reconstruction from measured scattered field data. Main drawb ack is the presence of an artificial weighting parameter in the cost functi onal, which can only be determined through considerable experimentation. Th erefore, we introduce the total variation as a multiplicative constraint. N umerical examples demonstrate that the algorithm based on this multiplicati ve regularization seems to be robust and handling noisy data very well with out the necessity of the weighting parameter.