Compressed sensing with side information: Geometrical interpretation and performance bounds

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

doi:10.1109/GlobalSIP.2014.7032170

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 proceeding › Conference contribution

36 Citations (Scopus)

Abstract

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 language	English
Title of host publication	2014 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2014
Publisher	IEEE
Pages	512-516
Number of pages	5
ISBN (Electronic)	9781479970889
DOIs	https://doi.org/10.1109/GlobalSIP.2014.7032170
Publication status	Published - Feb 2014
Event	2014 IEEE Global Conference on Signal and Information Processing - GA, Atlanta, United States Duration: 3 Dec 2014 → 5 Dec 2014

Conference

Conference	2014 IEEE Global Conference on Signal and Information Processing
Abbreviated title	GlobalSIP 2014
Country/Territory	United States
City	Atlanta
Period	3/12/14 → 5/12/14

Keywords

Basis pursuit
Compressed sensing
Gaussian width
ℓ-ℓ minimization

ASJC Scopus subject areas

Signal Processing
Information Systems

Access to Document

10.1109/GlobalSIP.2014.7032170

Cite this

@inproceedings{bf845f773e9b47fcad013a052f33ac3b,

title = "Compressed sensing with side information: Geometrical interpretation and performance bounds",

abstract = "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.",

keywords = "Basis pursuit, Compressed sensing, Gaussian width, ℓ-ℓ minimization",

author = "Mota, {Jo{\~a}o F. C.} and Nikos Deligiannis and Rodrigues, {Miguel Raul Dias}",

year = "2014",

month = feb,

doi = "10.1109/GlobalSIP.2014.7032170",

language = "English",

pages = "512--516",

booktitle = "2014 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2014",

publisher = "IEEE",

address = "United States",

note = "2014 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2014 ; Conference date: 03-12-2014 Through 05-12-2014",

}

Mota, JFC, Deligiannis, N & Rodrigues, MRD 2014, Compressed sensing with side information: Geometrical interpretation and performance bounds. in 2014 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2014., 7032170, IEEE, pp. 512-516, 2014 IEEE Global Conference on Signal and Information Processing, Atlanta, United States, 3/12/14. https://doi.org/10.1109/GlobalSIP.2014.7032170

TY - GEN

T1 - Compressed sensing with side information

T2 - 2014 IEEE Global Conference on Signal and Information Processing

AU - Mota, João F. C.

AU - Deligiannis, Nikos

AU - Rodrigues, Miguel Raul Dias

PY - 2014/2

Y1 - 2014/2

N2 - 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.

AB - 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.

KW - Basis pursuit

KW - Compressed sensing

KW - Gaussian width

KW - ℓ-ℓ minimization

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U2 - 10.1109/GlobalSIP.2014.7032170

DO - 10.1109/GlobalSIP.2014.7032170

M3 - Conference contribution

AN - SCOPUS:84978250660

SP - 512

EP - 516

BT - 2014 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2014

PB - IEEE

Y2 - 3 December 2014 through 5 December 2014

ER -

Compressed sensing with side information: Geometrical interpretation and performance bounds

Abstract

Conference

Keywords

ASJC Scopus subject areas

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