Quantization for Spectral Super-Resolution

Research output: Contribution to journalArticlepeer-review

Abstract

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 over-sampling ratio λ as the largest integer such that ⌊ M/ λ⌋ - 1 ≥ 4 / Δ , where M denotes the number of Fourier measurements and Δ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number K≥ 2 of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order O(M1 / 4λ5 / 4K-λ/2) and O(M3 / 2λ1 / 2K-λ) , respectively, where the implicit constants are independent of M, K and λ. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order O(M- 1K- 1) only, regardless of the reconstruction algorithm.

Original languageEnglish (US)
JournalConstructive Approximation
DOIs
StateAccepted/In press - 2022

Keywords

  • ESPRIT
  • Quantization
  • Spectral estimation
  • Super-resolution
  • Total variation

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Computational Mathematics

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