Robust Non-Stationary Blind Super-Resolution with Corrupted Measurements via Convex Demixing

This paper addresses the problem of robust nonstationary blind super-resolution in the presence of gross corruptions in the measurement data. By employing a subspace model for the modulated unknown waveforms and utilizing a lifting trick, we reformulate the original ill-posed and nonconvex inverse problem into a linear one. To solve the resulting optimization problem, we propose a convex program that minimizes a weighted combination of the atomic norm and ell-one norm. Furthermore, we construct a dual polynomial to certify the optimality of the atomic and sparse decomposition. Numerical simulations validate the effectiveness of our proposed approach, demonstrating that simultaneous blind super-resolution and demixing in the presence of outliers is achievable.