An algorithm for exact super-resolution and phase retrieval

Yuxin Chen, Yonina C. Eldar, Andrea J. Goldsmith

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

We explore a fundamental problem of super-resolving a signal of interest from a few measurements of its low-pass magnitudes. We propose a 2-stage tractable algorithm that, in the absence of noise, admits perfect super-resolution of an r-sparse signal from 2r2 -2r + 2 low-pass magnitude measurements. The spike locations of the signal can assume any value over a continuous disk, without increasing the required sample size. The proposed algorithm first employs a conventional super-resolution algorithm (e.g. the matrix pencil approach) to recover unlabeled sets of signal correlation coefficients, and then applies a simple sorting algorithm to disentangle and retrieve the true parameters in a deterministic manner. Our approach can be adapted to multi-dimensional spike models and random Fourier sampling by replacing its first step with other harmonic retrieval algorithms.

Original languageEnglish (US)
Title of host publication2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages754-758
Number of pages5
ISBN (Print)9781479928927
DOIs
StatePublished - Jan 1 2014
Externally publishedYes
Event2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014 - Florence, Italy
Duration: May 4 2014May 9 2014

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
CountryItaly
CityFlorence
Period5/4/145/9/14

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Keywords

  • Hankel matrix
  • Low-pass Frequencies
  • Matrix Pencil
  • Phase Retrieval
  • Quadratic Measurements
  • Super-resolution
  • sorting

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  • Cite this

    Chen, Y., Eldar, Y. C., & Goldsmith, A. J. (2014). An algorithm for exact super-resolution and phase retrieval. In 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014 (pp. 754-758). [6853697] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2014.6853697