Non-linear inverse resistivity profiling using wavelets

A quadratic approach is used to find the unknown resistivity of a conducting body. The resistivity variation are supposed to be spatially localized. The multiresolution analysis is discussed in order to obtain a good estimate of the resistivity profile with a limited number of unknown parameters. The method allows to identify the regions where the perturbations may be localized and to retrieve the unknowns parameters only in those regions. Some numerical results show the main features of the proposed approach.