A principle of the line-scan Compton backscatter imaging based on the scattered photon energy spectra is presented. This imaging equation is concluded as a large-scale system of nonlinear equations. In view of the neural network with multi-criteria optimization
a solution of image reconstruction is worked out accordingly. Results of data simulations illustrate the fact that it is feasible to adopt the method of constructing neural network for the sake of multi-criteria Compton backscatter imaging
which is applicable to solving the ill-posed reconstruction problems.