Ionospheric tomography is an emerging technique for two-dimensional reconstruction of the electron density distribution in the ionosphere. One of the fundamental difficulties with this technique, currently, is the limited resolving capability caused by the physical constraints of the data acquisition scheme. The angles of the signal propagation paths are restricted to a certain angular coverage because each ground station can only make observations over a limited range. As a result, the corresponding projection angles of the data are severely limited. This effect creates a cone-shaped region in the spatial-frequency domain, where spectral content is not available. Because of the incomplete information content of the data, uniqueness of the solution to the inverse problem does not exist. In this paper a new Fourier domain extrapolation technique is presented which utilizes the information contained in the known region of the spectrum to estimate the frequency samples in the missing cone area. Unlike conventional two-dimensional extrapolation techniques, this method uses bidirectional extrapolation to maximize the amount of known information in each extrapolation step. By fully utilizing the information of the measured data, the resulting image provides a more accurate estimation of the electron density distribution.