The DOI matches its Crossref record; 37 of the 37 references it cites were found in a registry or an index.
Enhancing Sparsity and Resolution via Reweighted Atomic Norm Minimization
Open accessAbstract
The mathematical theory of super-resolution developed recently by Candès and Fernandes-Granda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set of uniform time-space samples. This theory was then extended to the cases of partial/compressive samples and/or multiple measurement vectors via atomic norm minimization (ANM), known as off-grid/continuous compressed sensing (CCS). However, a major problem of existing atomic norm methods is that the frequencies can be recovered only if they are sufficiently separated, prohibiting commonly known high resolution. In this paper, a novel (nonconvex) sparse metric is proposed that promotes sparsity to a greater extent than the atomic norm. Using this metric an optimization problem is formulated and a locally convergent iterative algorithm is implemented. The algorithm iteratively carries out ANM with a sound reweighting strategy which enhances sparsity and resolution, and is termed as reweighted atomic-norm minimization (RAM). Extensive numerical simulations are carried out to demonstrate the advantageous performance of RAM with application to direction of arrival (DOA) estimation.
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Cites
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Enhancing Sparsity by Reweighted ℓ 1 Minimization
Candès, E. J., Wakin, M. B., & Boyd, S. P. (2008) · Journal of Fourier Analysis and Applications · doi:10.1007/s00041-008-9045-x · Cited by 4,863
Two decades of array signal processing research: the parametric approach
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A sparse signal reconstruction perspective for source localization with sensor arrays
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SDPT3 — A Matlab software package for semidefinite programming, Version 1.3
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Iteratively reweighted algorithms for compressive sensing
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Towards a Mathematical Theory of Super‐resolution
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Cited by
Yang, Z., Xie, L., & Stoica, P. (2016) · IEEE Transactions on Information Theory · doi:10.1109/tit.2016.2553041 · Cited by 292
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Metadata
- Authors
- Yang, Z., & Xie, L.
- Venue
- IEEE Transactions on Signal Processing
- Published
- 2016-02
- Volume
- 64
- Issue
- 4
- Pages
- 995-1006
- ISSN
- 1053-587X (ISSN-L)
- 1941-0476
- OpenAlex
- W2963326253
- Cited by
- 304
- References
- 37
- FWCI
- 19.20
- Type
- journal article
- Language
- en
- Open access
- green
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