Fast convex optimization method for frequency estimation with prior knowledge in all dimensions

This paper investigates the frequency estimation problem in all dimensions within the recent gridless-sparse-method framework. The frequencies of interest are assumed to follow a prior probability distribution. To effectively and efficiently exploit the prior knowledge, a weighted atomic norm approach is proposed in both the 1-D and the multi-dimensional cases. Like the standard atomic norm approach, the resulting optimization problem is formulated as convex programming using the theory of trigonometric polynomials and shares the same computational complexity. Numerical simulations are provided to demonstrate the superior performance of the proposed approach in accuracy and speed compared to the state-of-the-art.