New reweighted atomic norm minimization approach for line spectral estimation

This paper is concerned with the problem of line spectral estimation. Reweighted atomic norm minimization based on Toeplitz model (RAM-T) is a promising approach that promotes sparsity and enhances resolution as compared to atomic norm minimization (ANM) by generalizing the atomic norm with a new sparsity metric. To address the slow convergence issue of RAM-T, in this paper, we propose a reweighted atomic norm minimization approach by exploiting the recently proposed Hankel–Toeplitz model, which achieves a better performance and converges faster than RAM-T. Furthermore, we reveal the connection between reweighted atomic norm minimization based on Hankel–Toeplitz model (RAM-HT) and RAM-T and give sufficient conditions for successful signal recovery of the first iteration of RAM-HT. Numerical experiments demonstrate the superior performance of our proposed approach.