Optical tomography has recently witnessed a substantial increase in the size of the data sets used, mainly owing to the use of CCD cameras. Larger data sets render 3D reconstructions more robust, quantitative, and reproducible, but also significantly increase the computing time needed to generate the reconstructed data. Approaches working with spatial-frequencies instead of real space variables seem to be the method of choice in this case, and a direct inversion method that can produce three-dimensional images from very large detector numbers $\left(>{10}^5\right)$ using either very large source numbers $\left(>{10}^3\right)$ [ Phys. Rev. E 64, 035601 (2001) ] or structured illumination [ Opt. Lett. 34, 983 (2009) ] has been presented. However, most small animal imaging setups typically incur a practical upper limit of only $\sim {10}^2$ sources mainly due to imaging time constraints, and currently all relying on point source illumination. In this Letter, what we believe to be a new approach, which combines Fourier and real space functions, is shown, which fills the gap between traditional fiber-based small data sets that are solved in real space and the very large data sets solved entirely in spatial-frequency domain.