Measurement Bounds for Compressed Sensing with Missing Data

Geethu Joseph, Pramod K. Varshney

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

Abstract

In this paper, we study the feasibility of the exact recovery of a sparse vector from its linear measurements when there are missing data. For this setting, the random sampling approach employed in compressed sensing is known to provide excellent reconstruction accuracy. However, when there is missing data, the theoretical guarantees associated with the sparse vector recovery have not been well studied. Therefore, in this paper, we derive an upper bound on the minimum number of measurements required to ensure faithful recovery of a sparse signal when the generation of missing data is modeled using an erasure channel. We show that the number of measurements required scales as-[log(1-p + Cp)]-1 to overcome the missing data with arbitrarily high probability, where p is the probability of observing (not missing) a measurement and 0 < C < 1 is a constant that depends on the properties of the measurement matrix and the recovery algorithm. Our analysis is based on the restricted isometric property of the measurement matrix whose entries as well as the dimension are random.

Original languageEnglish (US)
Title of host publication2020 IEEE 21st International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728154787
DOIs
StatePublished - May 2020
Event21st IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2020 - Atlanta, United States
Duration: May 26 2020May 29 2020

Publication series

NameIEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC
Volume2020-May

Conference

Conference21st IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2020
CountryUnited States
CityAtlanta
Period5/26/205/29/20

Keywords

  • Compressed sensing
  • missing data
  • restricted isometric property

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Science Applications
  • Information Systems

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  • Cite this

    Joseph, G., & Varshney, P. K. (2020). Measurement Bounds for Compressed Sensing with Missing Data. In 2020 IEEE 21st International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2020 [9154229] (IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC; Vol. 2020-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SPAWC48557.2020.9154229