Sparse signal reconstruction for nonlinear models via piecewise rational optimization

We propose a method to reconstruct sparse signals degraded by nonlinear distortion and acquired at limited sampling rate. Our formulates the reconstruction problem as nonconvex minimization of sum data fitting term penalization term. In contrast with most previous works which settle for approximated local solutions, we seek global solution obtained challenging problem. approach relies on so-called Lasserre relaxation polynomial optimization. here specifically include in our case piecewise rational functions, makes it possible address wide class exact continuous relaxations ?0 function. Additionally, study complexity optimization It is shown how use structure lighten computational burden efficiently. Finally, numerical simulations illustrate benefits terms both optimality signal reconstruction.