New reweighted atomic norm minimization approach for line spectral estimation

• Published in: Signal processing 2023-05, Vol.206, p.108897, Article 108897
• Main Authors: Chu, Yonghui, Wei, Zhiqiang, Yang, Zai
• Format: Article
• Language: English
• Subjects: Atomic norm minimization (ANM); Continuous compressed sensing; Hankel–Toeplitz model; Line spectral estimation; Reweighted atomic norm minimization (RAM)
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2022.108897

•We propose a new reweighted atomic norm minimization approach for line spectral estimation based on the Hankel–Toeplitz model.•The proposed approach promotes sparsity, enhances resolution and converges faster than existing reweighted atomic norm method.•The first step is a new formulation of atomic norm minimization for which theoretical guarantees are provided.•Numerical simulations show the superior performance of our proposed approach. 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.