Sparse representations and compressive sensing for imaging and vision

111 Pages·2013·2.328 MB·English

by  Vishal M. Patel, Rama Chellappa (auth.)

SpringerBriefs in Electrical
and Computer Engineering
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Vishal M. Patel • Rama Chellappa
Sparse Representations
and Compressive Sensing
for Imaging and Vision
123
VishalM.Patel RamaChellappa
CenterforAutomationResearch DepartmentofElectricalandComputer
UniversityofMaryland EngineeringandCenterfor
A.V.WilliamsBuilding AutomationResearch
CollegePark,MD A.V.WilliamsBuilding
UniversityofMaryland
CollegePark,MD
ISSN2191-8112 ISSN2191-8120(electronic)
ISBN978-1-4614-6380-1 ISBN978-1-4614-6381-8(eBook)
DOI10.1007/978-1-4614-6381-8
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2012956308
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To mysistersJulie,DhartiandGunjali
—Vishal M.Patel

Acknowledgements
Wethankformerandcurrentstudentsaswellascollaborators-RichardBaraniuk,
Volkan Cevher, Pavan Turaga, Ashok Veeraraghavan, Aswin Sankaranarayanan,
Dikpal Reddy, Amit Agrawal, Nalini Ratha, Jaishanker Pillai, Hien Van Nguyen,
SumitShekhar,GarrettWarnell,QiangQiu,AshishShrivastava-forlettingusdraw
upontheirwork,thusmakingthismonographpossible.
Researcheffortssummarizedinthismonographweresupportedbythefollowing
grantsandcontracts:AROMURI(W911NF-09-1-0383),ONRMURI(N00014-08-
1-0638),ONRgrant(N00014-12-1-0124),andaNISTgrant(70NANB11H023).
vii

Contents
1 Introduction ................................................................... 1
1.1 Outline.................................................................... 2
2 CompressiveSensing ......................................................... 3
2.1 Sparsity................................................................... 3
2.2 IncoherentSampling..................................................... 5
2.3 Recovery.................................................................. 6
2.3.1 RobustCS........................................................ 7
2.3.2 CSRecoveryAlgorithms........................................ 9
2.4 SensingMatrices......................................................... 11
2.5 PhaseTransitionDiagrams.............................................. 12
2.6 NumericalExamples..................................................... 15
3 CompressiveAcquisition..................................................... 17
3.1 SinglePixelCamera ..................................................... 17
3.2 CompressiveMagneticResonanceImaging............................ 18
3.2.1 ImageGradientEstimation...................................... 21
3.2.2 ImageReconstructionfromGradients.......................... 23
3.2.3 NumericalExamples............................................. 24
3.3 CompressiveSyntheticApertureRadarImaging....................... 25
3.3.1 Slow-timeUndersampling....................................... 27
3.3.2 ImageReconstruction ........................................... 28
3.3.3 NumericalExamples............................................. 29
3.4 CompressivePassiveMillimeterWaveImaging........................ 30
3.4.1 MillimeterWaveImagingSystem .............................. 31
3.4.2 AcceleratedImagingwithExtendedDepth-of-Field........... 34
3.4.3 ExperimentalResults............................................ 36
3.5 CompressiveLightTransportSensing .................................. 37
4 CompressiveSensingforVision ............................................. 41
4.1 CompressiveTargetTracking............................................ 41
4.1.1 CompressiveSensingforBackgroundSubtraction ............ 42
ix