We consider computational aspects of a 3D inverse scattering problem f
or the Helmholtz equation. An algorithm based on the regularized quasi
-reversibility method is presented. The performance of this algorithm
for the identification of general 3D non-symmetric dielectric function
s is analysed for the scattering from a homogeneous ball. The numerica
l results show that a reasonable identification can be achieved within
a short time frame, which is the first result of this kind in the com
putational ISP.