Compressed Sensing with Linear Correlation Between Signal and Measurement Noise

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Abstract

Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and introduce a simple technique for improving compressed sensing reconstruction from such measurements. The technique is based on a linear model of the correlation of additive noise with the signal. The modification of the reconstruction algorithm based on this model is very simple and has negligible additional computational cost compared to standard reconstruction algorithms, but is not known in existing literature. The proposed technique reduces reconstruction error considerably in the case of linearly correlated measurements and noise. Numerical experiments confirm the efficacy of the technique. The technique is demonstrated with application to low-rate quantization of compressed measurements, which is known to introduce correlated noise, and improvements in reconstruction error compared to ordinary Basis Pursuit De-Noising of up to approximately 7 dB are observed for 1 bit/sample quantization. Furthermore, the proposed method is compared to Binary Iterative Hard Thresholding which it is demonstrated to outperform in terms of reconstruction error for sparse signals with a number of non-zero coefficients greater than approximately 1⁄10th of the number of compressed measurements.
Original languageEnglish
JournalSignal Processing
Volume98
Pages (from-to)275-283
ISSN0165-1684
DOIs
Publication statusPublished - May 2014

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Compressed sensing
Additive noise
Costs
Experiments

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@article{2be59da1b1f94620a4f3d5362de16db9,
title = "Compressed Sensing with Linear Correlation Between Signal and Measurement Noise",
abstract = "Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and introduce a simple technique for improving compressed sensing reconstruction from such measurements. The technique is based on a linear model of the correlation of additive noise with the signal. The modification of the reconstruction algorithm based on this model is very simple and has negligible additional computational cost compared to standard reconstruction algorithms, but is not known in existing literature. The proposed technique reduces reconstruction error considerably in the case of linearly correlated measurements and noise. Numerical experiments confirm the efficacy of the technique. The technique is demonstrated with application to low-rate quantization of compressed measurements, which is known to introduce correlated noise, and improvements in reconstruction error compared to ordinary Basis Pursuit De-Noising of up to approximately 7 dB are observed for 1 bit/sample quantization. Furthermore, the proposed method is compared to Binary Iterative Hard Thresholding which it is demonstrated to outperform in terms of reconstruction error for sparse signals with a number of non-zero coefficients greater than approximately 1⁄10th of the number of compressed measurements.",
author = "Thomas Arildsen and Torben Larsen",
year = "2014",
month = "5",
doi = "10.1016/j.sigpro.2013.10.021",
language = "English",
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pages = "275--283",
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issn = "0165-1684",
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}

Compressed Sensing with Linear Correlation Between Signal and Measurement Noise. / Arildsen, Thomas; Larsen, Torben.

In: Signal Processing, Vol. 98, 05.2014, p. 275-283.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Compressed Sensing with Linear Correlation Between Signal and Measurement Noise

AU - Arildsen, Thomas

AU - Larsen, Torben

PY - 2014/5

Y1 - 2014/5

N2 - Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and introduce a simple technique for improving compressed sensing reconstruction from such measurements. The technique is based on a linear model of the correlation of additive noise with the signal. The modification of the reconstruction algorithm based on this model is very simple and has negligible additional computational cost compared to standard reconstruction algorithms, but is not known in existing literature. The proposed technique reduces reconstruction error considerably in the case of linearly correlated measurements and noise. Numerical experiments confirm the efficacy of the technique. The technique is demonstrated with application to low-rate quantization of compressed measurements, which is known to introduce correlated noise, and improvements in reconstruction error compared to ordinary Basis Pursuit De-Noising of up to approximately 7 dB are observed for 1 bit/sample quantization. Furthermore, the proposed method is compared to Binary Iterative Hard Thresholding which it is demonstrated to outperform in terms of reconstruction error for sparse signals with a number of non-zero coefficients greater than approximately 1⁄10th of the number of compressed measurements.

AB - Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and introduce a simple technique for improving compressed sensing reconstruction from such measurements. The technique is based on a linear model of the correlation of additive noise with the signal. The modification of the reconstruction algorithm based on this model is very simple and has negligible additional computational cost compared to standard reconstruction algorithms, but is not known in existing literature. The proposed technique reduces reconstruction error considerably in the case of linearly correlated measurements and noise. Numerical experiments confirm the efficacy of the technique. The technique is demonstrated with application to low-rate quantization of compressed measurements, which is known to introduce correlated noise, and improvements in reconstruction error compared to ordinary Basis Pursuit De-Noising of up to approximately 7 dB are observed for 1 bit/sample quantization. Furthermore, the proposed method is compared to Binary Iterative Hard Thresholding which it is demonstrated to outperform in terms of reconstruction error for sparse signals with a number of non-zero coefficients greater than approximately 1⁄10th of the number of compressed measurements.

U2 - 10.1016/j.sigpro.2013.10.021

DO - 10.1016/j.sigpro.2013.10.021

M3 - Journal article

VL - 98

SP - 275

EP - 283

JO - Signal Processing

JF - Signal Processing

SN - 0165-1684

ER -