Compressed sensing with side information: Geometrical interpretation and performance bounds

João F. C. Mota, Nikos Deligiannis, Miguel Raul Dias Rodrigues

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

35 Citations (Scopus)


We address the problem of Compressed Sensing (CS) with side information. Namely, when reconstructing a target CS signal, we assume access to a similar signal. This additional knowledge, the side information, is integrated into CS via ℓ1-ℓ1 and ℓ1-ℓ2 minimization. We then provide lower bounds on the number of measurements that these problems require for successful reconstruction of the target signal. If the side information has good quality, the number of measurements is significantly reduced via ℓ1-ℓ1 minimization, but not so much via ℓ1-ℓ2 minimization. We provide geometrical interpretations and experimental results illustrating our findings.

Original languageEnglish
Title of host publication2014 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2014
Number of pages5
ISBN (Electronic)9781479970889
Publication statusPublished - Feb 2014
Event2014 IEEE Global Conference on Signal and Information Processing - GA, Atlanta, United States
Duration: 3 Dec 20145 Dec 2014


Conference2014 IEEE Global Conference on Signal and Information Processing
Abbreviated titleGlobalSIP 2014
CountryUnited States


  • Basis pursuit
  • Compressed sensing
  • Gaussian width
  • ℓ-ℓ minimization

ASJC Scopus subject areas

  • Signal Processing
  • Information Systems

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