Efficient Super-Resolution Two-Dimensional Harmonic Retrieval With Multiple Measurement Vectors

This paper develops an efficient solution for super-resolution two-dimensional (2D) harmonic retrieval from multiple measurement vectors (MMV). Given the sample covariance matrix constructed from the MMV, a gridless compressed sensing approach is proposed based on the atomic norm minimization (ANM). In the approach, our key step is to perform a redundancy reduction (RR) transformation that effectively reduces the large problem size at hand, without loss of useful frequency information. For uncorrelated sources, the transformed 2D covariance matrices in the RR domain retain a salient structure, which permits a sparse representation over a matrix-form atom set with decoupled 1D frequency components. Accordingly, the decoupled ANM (D-ANM) framework can be applied for super-resolution 2D frequency estimation. Moreover, the resulting RR-enabled D-ANM technique, termed RR-D-ANM, further allows an efficient relaxation under certain conditions, which leads to low computational complexity of the same order as the 1D case. Simulation results verify the advantages of our solutions over benchmark methods, in terms of higher computational efficiency and detectability for 2D harmonic retrieval.

Automated summary

This paper proposes an efficient solution for super-resolution 2D harmonic retrieval from multiple measurement vectors (MMV). By performing a redundancy reduction (RR) transformation, the problem size is effectively reduced without losing useful frequency information. The transformed 2D covariance matrices in the RR domain allow for a sparse representation using decoupled 1D frequency components, enabling super-resolution 2D frequency estimation. The resulting RR-enabled D-ANM technique, RR-D-ANM, achieves low computational complexity comparable to the 1D case. Simulation results confirm the superiority of our solutions in terms of computational efficiency and detectability for 2D harmonic retrieval.