  The classical $\overline \partial$-method has been generalized recently
[lnv], [lnv2] to be used in the presence of exceptional points. We apply this
generalization to solve Dirac inverse scattering problem with weak assumptions
on smoothness of potentials. As a consequence, this provides an effective
method of reconstruction of complex-valued one time differentiable
conductivities in the inverse impedance tomography problem.
