In this communication we propose to solve the problem of reconstruction from limited data using a statistical regularization method based on a Bayesian information criterion. The minimization of the Bayesian information criterion, which is used here as an objective index to measure the goodness of an estimate, gives the optimum value of the smoothing parameter. By doing so, we could reduce the inversion problem to a simple minimization of a one-variable nonlinear function. The application of such a technique overcomes the nonuniqueness of the solution of the ill-posed problem and all shortcomings of many iterative methods. In the light of simulation and application to real data, we propose a slight modification to the Bayesian information criterion to reconstruct the wave energy distribution at the ionospheric base from the observation of radio wave electromagnetic field on the ground. The achieved results in both the inversion problem and the wave direction finding are very promising and may support other works so far suggested the use of Bayesian methods in the inversion of ill-posed problems to benefit from the valuable information brought by the a priori knowledge.