Compressed Line Spectral Estimation Using Covariance: A Sparse Reconstruction Perspective

Efficient line spectral estimation methods applicable to sub-Nyquist sampling are drawing considerable attention in both academia and industry. In this letter, we propose an enhanced compressed sensing (CS) framework for line spectral estimation, termed sparsity-based compressed covariance sensing (SCCS). In terms of sampling, SCCS is implemented by periodic non-uniform sampling; In terms of recovery, SCCS focuses on compressed line spectral recovery using covariance information. Due to the dual priors on sparsity and structure, SCCS theoretically performs better than CS in compressed line spectral estimation. We explain this superiority from the mutual incoherence perspective: the sensing matrix in SCCS has a lower mutual coherence than that in classic CS. Extensive experimental results show a high consistency with the theoretical inference. All in all, SCCS opens many avenues for line spectral estimation.