A Spectral Method for Stable Bispectrum Inversion with Application to Multireference Alignment

Hua Chen, Mona Zehni, Zhizhen Zhao

Research output: Contribution to journalArticle

Abstract

We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we estimate the mean, power spectrum, and bispectrum of the signal from the observations. Since the bispectrum contains the phase information of the signal, reliable algorithms for bispectrum inversion are useful in many applications. We propose a new algorithm using spectral decomposition of the bispectrum phase matrix for this task. For clean signals, we show that the eigenvectors of the bispectrum phase matrix correspond to the true phases of the signal and its shifted copies. In addition, the spectral method is robust to noise. It can be used as a stable and efficient initialization technique for local nonconvex optimization for bispectrum inversion.

Original languageEnglish (US)
Pages (from-to)911-915
Number of pages5
JournalIEEE Signal Processing Letters
Volume25
Issue number7
DOIs
StatePublished - Jul 2018

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A Spectral Method for Stable Bispectrum Inversion with Application to Multireference Alignment'. Together they form a unique fingerprint.

  • Cite this