We propose a series expansion method of image reconstruction from projections which is equivalent to the Fourier transform method. By using the method we find a subspace within which we can strictly reconstruct images from a finite number of sampled values of a finite number of projections. We get two reconstruction formulae. One is effective to whole angle projection data and the other is applicable to any limited angle projection data. It is also proved that the back-projection operator is the adjoint operator of the Radon transform.