On Gridless Sparse Methods for Line Spectral Estimation From Complete and Incomplete Data

By Zai Yang, Lihua Xie. IEEE Transactions on Signal Processing, 2014

346 citations recorded by the source corpus.

This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based approaches, e.g., ℓ1 optimization and SPICE, with an infinitely dense grid. We generalize AST (atomic-norm soft thresholding) to the case of nonconsecutively sampled data (incomplete data) inspired by recent atomic norm based techniques. We present a gridless version of SPICE (gridless SPICE, or GLS), which is applicable to both complete and incomplete data without the knowledge of noise level. We further prove the equivalence between GLS and atomic norm-based techniques under different assumptions of noise. Moreover, we extend GLS to a systematic framework consisting of model order selection and robust frequency estimation, and present feasible algorithms for AST and GLS. Numerical simulations are provided to validate our theoretical analysis and demonstrate performance of our methods compared to existing ones.

Subfields: Civil and Structural Engineering, Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/decc3c005d2bf41a5f08b0924cb29dcfde14a5fa

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Jian Li
2. P. Stoica
3. Lihua Xie
4. Zai Yang
5. Sergiy A. Vorobyov

In Computational Mechanics

1. P. Stoica
2. Jian Li
3. Lihua Xie
4. Zai Yang
5. Sergiy A. Vorobyov

In Signal Processing

1. Jian Li
2. P. Stoica
3. Lihua Xie
4. Zai Yang
5. Yuanhao Cui
6. Weijie Yuan
7. Sergiy A. Vorobyov
8. Christos Masouros

Citations in the corpus

• Integrated Sensing and Communications: Recent Advances and Ten Open Challenges (2023, background): “Another family is constituted by the sparse signal reconstruction frameworks, including on-grid [103], off-grid [104], and gridless [105] algorithms.”
• Sparse Methods for Direction-of-Arrival Estimation (2016, methodology): “In this subsection, we show that GLS is equivalent to ANM as if there were no noise and with a slightly different frequency retrieval process [130].”