Compressive Sensing in Healthcare (Advances in ubiquitous sensing applications for healthcare)

304 Pages·2020·13.526 MB·English

by  Mahdi Khosravy (editor), Nilanjan Dey (editor), Carlos A. Duque (editor)

Compressive Sensing
in Healthcare

Advances in Ubiquitous Sensing Applications
for Healthcare
Compressive Sensing
in Healthcare
Volume Eleven
Volume Editors
Mahdi Khosravy
Osaka University, Osaka, Japan
Nilanjan Dey
Techno International New Town, Kolkata, India
Carlos A. Duque
Federal University of Juiz de Fora, Juiz de Fora, MI, Brazil
Series Editors
Nilanjan Dey
Amira S. Ashour
Simon James Fong
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Contents
Listofcontributors ............................................. xiii
CHAPTER 1 Compressive sensing theoretical foundations in a
nutshell........................................ 1
Mahdi Khosravy, Naoko Nitta, Kazuaki Nakamura,
Noboru Babaguchi
1.1 Introduction ...................................... 1
1.2 Digitalsignalacquisition ............................ 3
1.3 Vectorialrepresentationofsignal ...................... 4
l norm ................................... 5
1
l norm ................................... 5
2
l∞norm .................................. 5
Spheresmadebydifferentl normsasdistance
p
criterion................................... 6
Basis/dictionary ............................. 8
Orthonormalbasis/dictionary ................... 8
Frame/over-completedictionary ................ 9
Alternate/dualframe ......................... 9
1.4 Sparsity ......................................... 10
k-sparsesignal .............................. 10
Non-linearityofsparsity ...................... 10
Sparsityandcompressibility ................... 11
1.5 Compressivesensing ............................... 11
Compressivesensingmodel .................... 11
1.6 Essentialpropertiesofcompressivesensingmatrix ......... 12
1.6.1 Nullspaceproperty(NSP) ..................... 12
1.6.2 Restrictedisometryproperty ................... 17
1.6.3 CoherenceasimplewaytocheckNSP............ 18
1.7 Summary ........................................ 19
Appendix1.A ....................................... 20
Nullspacepropertyoforder2k ................. 20
References....................................... 21
CHAPTER 2 Recovery in compressive sensing: a review....... 25
Mahdi Khosravy, Neeraj Gupta, Nilesh Patel,
Carlos A. Duque
2.1 Introduction ...................................... 25
2.1.1 Compressivesensingformulation................ 26
2.2 Criteriarequiredforacompressivesensingmatrix ......... 26
v
vi Contents
2.2.1 Nullspaceproperty .......................... 27
2.2.2 Restrictedisometryproperty ................... 28
2.2.3 Coherenceproperty .......................... 29
2.3 Recovery ........................................ 30
2.3.1 Recoveryviaminimizationofl norm ............ 31
1
2.3.2 Greedyalgorithms ........................... 33
2.4 Summary ........................................ 38
References....................................... 39
CHAPTER 3 A descriptive review to sparsity measures ........ 43
MahdiKhosravy,NaokoNitta,NeerajGupta,NileshPatel,
Noboru Babaguchi
3.1 Introduction ...................................... 43
3.2 Compressivesensing ............................... 45
3.3 Sparsity ......................................... 47
k-sparsesignal .............................. 47
3.4 Reviewtosparsitymeasures ......................... 47
MeasureS ................................ 50
l0
MeasureS ............................... 51
l0,(cid:2)
MeasureS ............................. 51
tanha,b
MeasureS ............................... 51
log
MeasureS ................................ 52
l1
MeasureS ............................... 52
lp
MeasureS ............................... 52
l2
l1
Measureκ4 ................................ 53
MeasureS ............................... 54
uθ (cid:3) p
MeasuresHG,HS,HS,andl− .................. 55
Hoyermeasure ............................. 56
pq-meanmeasure............................ 56
MeasureS .............................. 56
Gini
3.5 Summary ........................................ 57
References....................................... 58
CHAPTER 4 Compressive sensing in practice and potential
advancements .................................. 65
Ayan Banerjee, Sandeep K.S. Gupta
4.1 Introduction ...................................... 65
4.2 Compressivesensingtheory .......................... 68
4.3 Examplecompressivesensingimplementations ........... 69
4.3.1 Compressivesensinginphysiologicalsignal
monitoring................................. 69
4.3.2 CompressivesensinginTHEMISimaging ......... 71
4.4 ReviewofCSliterature ............................. 72
4.4.1 Practicalmanifestationsoftheoreticalbounds ...... 74
Contents vii
4.5 Advancementsincompressivesensing .................. 75
4.5.1 Personalizedbasis ........................... 75
4.5.2 Non-linearmodel-basedcompressivesensing....... 78
4.5.3 ROIawarecompressivesensing ................. 82
4.6 Conclusion ...................................... 85
Acknowledgments ................................. 85
References....................................... 85
CHAPTER 5 A review of deterministic sensing matrices ....... 89
Daniel Ramalho, Katia Melo, Mahdi Khosravy,
Faramarz Asharif, Mir Sayed Shah Danish,
Carlos A. Duque
5.1 Introduction ...................................... 89
5.2 Compressivesensing ............................... 90
5.3 Chirpcodescompressivematrices ..................... 91
5.3.1 (cid:5)forsparsespectrumsignals .................. 93
5.4 SecondorderReed–Mullercompressivesensingmatrix ..... 93
5.4.1 Fastreconstructionalgorithm ................... 95
5.5 AminiapproachtoRIP-satisfyingmatrices .............. 96
5.6 Amini–Marvastibinarymatrix ........................ 97
5.6.1 BCH-code ................................. 98
5.6.2 ExtremalSetTheory ......................... 101
5.6.3 Unbalancedexpandergraphs ................... 103
5.7 Sensingmatriceswithstatisticalrestrictedisometryproperty . 104
5.8 Deterministiccompressivematrixbyalgebraiccurvesover
finitefields....................................... 105
5.9 Summary ........................................ 106
References....................................... 106
CHAPTER 6 Deterministic compressive sensing by chirp codes:
a descriptive tutorial............................ 111
Mahdi Khosravy, Neeraj Gupta, Nilesh Patel,
Carlos A. Duque, Naoko Nitta, Noboru Babaguchi
6.1 Introduction ...................................... 111
6.2 Thestandardformulationcompressivesensing ............ 112
6.3 Compressivesensingbychirpcodes ................... 114
6.3.1 Buildingthecompressivesensingmatrixbychirp
codes ..................................... 115
6.3.2 Restrictedisometrypropertyforthechirpcode
compressivesensing ......................... 116
6.4 Recoveryofchirpcodecompressivelysensedsignal ....... 116
6.4.1 Stepbystepinoneiterationofrecovery ........... 119
6.5 Summary ........................................ 121
viii Contents
Appendix6.A ....................................... 121
6.A.1 Chirpsinusoid .............................. 121
References....................................... 122
CHAPTER 7 Deterministic compressive sensing by chirp codes:
a MATLAB® tutorial ............................. 125
Mahdi Khosravy, Naoko Nitta, Faramarz Asharif,
Katia Melo, Carlos A. Duque
7.1 Introduction ...................................... 125
7.2 Compressivesensing ............................... 125
7.3 Chirpcodescompressivesensing:MATLABtutorial ....... 126
7.3.1 Chirpcodes ................................ 127
7.3.2 Theapproachforextractionofparameters ......... 130
7.3.3 Bijectionbetweenthesets{r }and{2r TmodK} .... 134
i i
7.3.4 Dechirpingy .............................. 137
l
7.3.5 Sensingandrecovery ......................... 138
7.4 Summary ........................................ 140
References....................................... 142
CHAPTER 8 Cyber physical systems for healthcare applications
using compressive sensing ...................... 145
K. Keerthana, S. Aasha Nandhini, S. Radha
8.1 Introduction ...................................... 145
8.2 Relatedworks .................................... 146
8.3 Proposedwork.................................... 148
8.3.1 Imageacquisition ........................... 149
8.3.2 Pre-processingtechniques ..................... 149
8.3.3 Blockdivision .............................. 150
8.3.4 Compressivesensing ......................... 150
8.3.5 Uploadingdatatocloud ....................... 151
8.3.6 GUI(graphicaluserinterface) .................. 152
8.4 Performanceevaluation ............................. 152
8.4.1 Simulationresults ........................... 152
8.4.2 Experimentalresults ......................... 157
8.5 Conclusionandscopeforfuturework .................. 163
References....................................... 163
CHAPTER 9 Compressive sensing of electrocardiogram ....... 165
Felipe Meneguitti Dias, Mahdi Khosravy, Thales
Wulfert Cabral, Henrique Luis Moreira Monteiro, Luciano
Manhaes de Andrade Filho, Leonardo de Mello Honório,
Rayen Naji, Carlos A. Duque
9.1 Introduction ...................................... 165
9.2 Electrocardiogram ................................. 166
Contents ix
9.2.1 Historicalbackground ........................ 166
9.2.2 Heartanatomy .............................. 167
9.2.3 Conductionsystem .......................... 167
9.2.4 Electrophysiology ........................... 168
9.2.5 Electrocardiogramacquisition .................. 168
9.3 Compressivesensing ............................... 170
9.3.1 Compressivesensingsignalacquisition ........... 170
9.3.2 Compressivesensedsignalreconstruction ......... 170
9.3.3 CSimportanceintele-medicine ................. 172
9.4 CompressivesensingapproachtoECG ................. 172
9.4.1 ECGsignalquality .......................... 174
9.4.2 Bodysensornetworksandmonitoringsystems...... 174
9.4.3 Dictionarylearning .......................... 175
9.4.4 ECGsignalstructure ......................... 175
9.4.5 Waveletsandcompressivesensing ............... 176
9.4.6 Signalcompression .......................... 176
9.4.7 Reconstructionalgorithms ..................... 177
9.4.8 Discretewavelettransform(DWT)vscompressive
sensing(CS) ............................... 178
9.4.9 Hardwareimplementation ..................... 178
9.5 Conclusion ...................................... 179
References....................................... 179
CHAPTER 10 Multichannel ECG reconstruction based on joint
compressed sensing for healthcare applications .. 185
Sushant Kumar, Bhabesh Deka, Sumit Datta
10.1 Introduction ...................................... 185
10.2 Backgroundandrelatedwork......................... 187
10.2.1 Compressedsensing-basedMECGcompression .... 187
10.2.2 CompressedsensingbasedMECGreconstruction ... 188
10.3 Proposedmethod .................................. 189
10.4 Resultsanddiscussion .............................. 191
10.4.1 Experimentalsetup .......................... 191
10.4.2 Performancemetrics ......................... 192
10.4.3 Performanceevaluation ....................... 193
10.4.4 Healthcareapplicationperspective ............... 195
10.4.5 Powersaving ............................... 198
10.5 Conclusion ...................................... 198
References....................................... 198
CHAPTER 11 Neural signal compressive sensing .............. 201
Denise Fonseca Resende, Mahdi Khosravy, Henrique
L.M. Monteiro, Neeraj Gupta, Nilesh Patel,
Carlos A. Duque