A semi-analytical approach to the ill-posed inverse problem of reconstructing the dielectric constant of dielectric objects placed in free space or in a waveguide is proposed. It is shown that the advantage of an experiment, performed at huge frequency array, is the possibility of formulating a well-posed vector problem with attainable experimental parameters. The method substantiates the analysis of the operators of forward scattering problems, which makes it possible to justify the unique solvability of the studied inverse problem. It is proved that a solution to the problem can be found by the least squares method from the measurement data obtained in an imperfect experiment; it converges to the desired parameter of the test material while improving the quality of the experimental setup and reducing noise; the convergence rate grows with an increase in the number of frequencies used in the measurement.