Quantization for spectral super-resolution

@article{Gntrk2022QuantizationFS,
  title={Quantization for spectral super-resolution},
  author={C. Sinan G{\"u}nt{\"u}rk and Weilin Li},
  journal={ArXiv},
  year={2022},
  volume={abs/2103.00079}
}
We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, we define the oversampling ratio λ as the largest integer such that ⌊M/λ⌋ − 1 ≥ 4/∆, where M denotes the number of Fourier measurements and ∆ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number K… 

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References

SHOWING 1-10 OF 35 REFERENCES
Super-Resolution Limit of the ESPRIT Algorithm
TLDR
This paper provides an explicit error bound on the support matching distance of ESPRIT in terms of the minimum singular value of Vandermonde matrices and establishes the near-optimality of ESP RIT.
Conditioning of restricted Fourier matrices and super-resolution of MUSIC
  • Weilin Li, Wenjing Liao
  • Computer Science
    2019 13th International conference on Sampling Theory and Applications (SampTA)
  • 2019
TLDR
A separated clumps model is proposed where point sources are clustered in far apart sets, and an accurate lower bound of the Fourier matrix with nodes restricted to the source locations is proved.
Fast Binary Embeddings and Quantized Compressed Sensing with Structured Matrices
TLDR
This paper proposes fast methods to replace points from a subset of Χ, associated with the euclidean metric, with points in the cube {±1}m, and it is the first such binary embedding result that applies to fast Johnson‐Lindenstrauss maps while preserving ℓ2 norms.
High-performance quantization for spectral super-resolution
  • C. S. Güntürk, Weilin Li
  • Mathematics
    2019 13th International conference on Sampling Theory and Applications (SampTA)
  • 2019
We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the
Distributed Noise-Shaping Quantization: II. Classical Frames
TLDR
This chapter constitutes the second part in a series of papers on distributed noise-shaping quantization and it is shown in several classical examples of deterministic frames that entropic rate-distortion performance is achievable.
Distributed noise-shaping quantization: II
  • Classical frames. In Excursions in Harmonic Analysis,
  • 2017
Compressive Spectral Estimation with Single-Snapshot ESPRIT: Stability and Resolution
TLDR
Stability and resolution analysis with performance guarantee for Single-Snapshot ESPRIT (SS-ESPRIT) is the main focus and compares favorably with those of the leading approaches to compressed sensing in the continuum.
Deterministic performance analysis of subspace methods for cisoid parameter estimation
TLDR
A deterministic, finite sample size, and finite-SNR performance analysis of the ESPRIT algorithm and the matrix pencil method is presented, based, inter alia, on a new upper bound on the condition number of Vandermonde matrices with nodes inside the unit disk.
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