Blind Super-resolution via Projected Gradient Descent

Abstract: Blind super-resolution can be cast as low rank matrix recovery problem by exploiting the inherent simplicity of the signal. In this paper, we develop a simple yet efficient nonconvex method for this problem based on the low rank structure of the vectorized Hankel matrix associated with the target matrix. Theoretical guarantees have been established under the similar conditions as convex approaches. Numerical experiments are also conducted to demonstrate its performance.