Tomographic reconstruction from limited-angle projection data, also know as a sinogram, is required in many fields, including medical imaging, sonar, and radar. We present a sinogram restoration technique that restores a complete sinogram from the available incomplete sinogram. Using two-dimensional sampling theory and the result of Rattey and Lindgen, which shows that the spectral support of a sinogram is bowtie-shaped, a matrix formulation is developed. Restoration of the complete sonogram is then posed as a least-squares minimization problem, which is solved by a novel iterative algorithm. Our technique does not require any a priori knowledge of the underlying object and can be applied to any incomplete sinogram. The algorithm can also be regarded as a variation of the well-known projectiononto- convex-set method with improved computational efficiency. Computer simulation results are presented to demonstrate the efficacy of the proposed technique.