Convergence of the solver and the regularization are two important issues concerning an ill-posed inverse problem. The intrinsic regularization of the conjugate gradient method along iteration makes the method superior for solving an ill-posed problem. The solutions along iteration converge fast to an optimal solution. If the termination criterion is not satisfied, the solution will diverge to a solution which dominated by the noise. Reformulation of an ill-posed problem as an eigenvalue formulation gives a very convenient formula since it is possible to estimate an optimal regularization parameter and an optimal solution at once. For very large problems, the fast Fourier transformation could be implemented in the circulant matrix-vector multiplication. The developed method is applied to some inverse problems of elasto-dynamic and the accurate estimation was achieved.