Optimal preconditioning for interpolation of missing data in a band-limited sequence

In this paper, we propose optimal methods for preconditioning an ill-conditioned linear system of equations, obtained when interpolating missing data in a band-limited sequence. The optimal preconditioning weights are obtained by solving an eigenvalue optimization problem via semidefinite programming. The so-obtained optimal weights are compared with a commonly used set of heuristic weights in terms of the condition numbers of resulting systems, with and without the knowledge of noise.