Compressed Sensing and Parallel Acquisition

Parallel acquisition systems arise in various applications to moderate problems caused by insufficient measurements in single-sensor systems. These systems allow simultaneous data acquisition in multiple sensors, thus alleviating such problems by providing more overall measurements. In this paper, w...

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Published inIEEE transactions on information theory Vol. 63; no. 8; pp. 4860 - 4882
Main Authors Il Yong Chun, Adcock, Ben
Format Journal Article
LanguageEnglish
Published New York IEEE 01.08.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Coils
Compressed sensing
Detection
incoherence
Magnetic resonance imaging
Mathematical analysis
Mathematical models
Matrix methods
nonuniform recovery
parallel acquisition
Phase transitions
Recovery
Sampling
Sensor systems
Sensors
Sparse matrices
sparsity in levels
Online AccessGet full text
ISSN0018-9448
1557-9654
DOI10.1109/TIT.2017.2700440

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Abstract Parallel acquisition systems arise in various applications to moderate problems caused by insufficient measurements in single-sensor systems. These systems allow simultaneous data acquisition in multiple sensors, thus alleviating such problems by providing more overall measurements. In this paper, we consider the combination of compressed sensing with parallel acquisition. We establish the theoretical improvements of such systems by providing nonuniform recovery guarantees for which, subject to appropriate conditions, the number of measurements required per sensor decreases linearly with the total number of sensors. Throughout, we consider two different sampling scenarios-distinct (i.e., independent sampling in each sensor) and identical (i.e., dependent sampling between sensors)-and a general mathematical framework that allows for a wide range of sensing matrices. We also consider not just the standard sparse signal model, but also the so-called sparse in levels signal model. As our results show, optimal recovery guarantees for both distinct and identical sampling are possible under much broader conditions on the so-called sensor profile matrices (which characterize environmental conditions between a source and the sensors) for the sparse in levels model than for the sparse model. To verify our recovery guarantees, we provide numerical results showing phase transitions for different multi-sensor environments.
AbstractList Parallel acquisition systems arise in various applications to moderate problems caused by insufficient measurements in single-sensor systems. These systems allow simultaneous data acquisition in multiple sensors, thus alleviating such problems by providing more overall measurements. In this paper, we consider the combination of compressed sensing with parallel acquisition. We establish the theoretical improvements of such systems by providing nonuniform recovery guarantees for which, subject to appropriate conditions, the number of measurements required per sensor decreases linearly with the total number of sensors. Throughout, we consider two different sampling scenarios-distinct (i.e., independent sampling in each sensor) and identical (i.e., dependent sampling between sensors)-and a general mathematical framework that allows for a wide range of sensing matrices. We also consider not just the standard sparse signal model, but also the so-called sparse in levels signal model. As our results show, optimal recovery guarantees for both distinct and identical sampling are possible under much broader conditions on the so-called sensor profile matrices (which characterize environmental conditions between a source and the sensors) for the sparse in levels model than for the sparse model. To verify our recovery guarantees, we provide numerical results showing phase transitions for different multi-sensor environments.
Author Il Yong Chun
Adcock, Ben
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Snippet Parallel acquisition systems arise in various applications to moderate problems caused by insufficient measurements in single-sensor systems. These systems...
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SubjectTerms Coils
Compressed sensing
Detection
incoherence
Magnetic resonance imaging
Mathematical analysis
Mathematical models
Matrix methods
nonuniform recovery
parallel acquisition
Phase transitions
Recovery
Sampling
Sensor systems
Sensors
Sparse matrices
sparsity in levels
Title Compressed Sensing and Parallel Acquisition
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