Hankel structured matrix rank minimization approach to signal declipping

This paper proposes a new algorithm for the restoration of the clipped signal based on the structured matrix rank minimization. We assume that the signal is modeled by deterministic autoregressive model with unknown model order and propose the matrix rank minimization approach to recover the clipped signal. The main result of this paper is to formulate the signal declipping problem as the Hankel structured matrix rank minimization problem with inequality constraint and to provide an algorithm to solve this problem by modifying the null space based alternating optimization (NSAO) algorithm. Numerical examples show that the proposed algorithm recovers the clipping signal efficiently.