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

- The frequency estimation problem is studied in all dimensions with prior knowledge;
- A convex optimization approach is proposed based on the weighted atomic norm in both the 1-D and the multi-dimensional cases;
- To the best of our knowledge, the proposed method is the only convex optimization method for multi-dimensional frequency estimation that can exploit the prior knowledge and work in the continuous domain;
- The proposed method shares the same computational cost as the standard atomic norm method;
- Numerical simulations show that the proposed method can improve the estimation accuracy compared to the standard atomic norm method;
- Numerical simulations show that the proposed method can be an order of magnitude faster than an existing method with comparable accuracy in the 1-D case.

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.