part 3 ‐ applications ofyazici/icassptutorial/icassp... · birsen yazıcı & venky krishnan...

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Part 3 Part 3 Applications of Applications of Part 3 Part 3 Applications of Applications of Microlocal Microlocal Techniques to Imaging Techniques to Imaging Birsen Yazıcı & Venky Krishnan Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engineering March 15 th , 2010 ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

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Page 1: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Part 3Part 3 ‐‐ Applications ofApplications ofPart 3 Part 3  Applications of Applications of MicrolocalMicrolocal Techniques to ImagingTechniques to Imagingq g gq g g

Birsen Yazıcı & Venky KrishnanBirsen Yazıcı & Venky KrishnanRensselaer Polytechnic Institute

Electrical, Computer and Systems Engineering, p y g g

March 15th,  2010

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

Page 2: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Outline

• Synthetic Aperture Imaging (SAI) modalities• SAI forward model• SAI image formation via microlocal techniquesg q

– Bistatic SAI– Monostatic SAI– Multistatic SAI– Synthetic Aperture Hitchhiker– Doppler Synthetic Aperture Hitchhiker

• Conclusions

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 2

Page 3: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Synthetic Aperture Imagingy p g g

Applicable to –

• Synthetic aperture radar• Synthetic aperture sonary p• Seismic imaging• Microwave imaging• Microwave imaging• Ground penetrating radar and sonar• Synthetic aperture imaging in dispersive• Synthetic aperture imaging in dispersive medium

• Diffu e o ti al i a i

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 3

• Diffuse optical imaging

Page 4: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Synthetic Aperture Imaging Modalitiesy p g g

• SAI systems form images from backscattered waves  measured along the source and detector trajectory(ies)measured along the source and detector trajectory(ies)– Mono‐static‐SAI– Bi‐static‐SAIMulti static SAI

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 4

– Multi‐static SAI – Passive SAI

Page 5: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Monostatic Synthetic Aperture Imaging

• Monostatic SAI – transmitter and receiver are colocated

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 5

Page 6: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Mono‐static SAI – Flat Topography

• Iso‐range surfaces = Spheres• Iso‐range contours = Intersection of spheres with topography

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 6

Iso range contours   Intersection of spheres with topography• Flat topography  Circles

Page 7: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Mono‐SAI – Plane Wave Approximationpp

• Approximate spherical wavefronts with planar wavefronts• Intersection of planes with flat surface = lines

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 7

f p f f• Spotlight Mode – Radon Transform

Page 8: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Bi‐static Synthetic Aperture Imaging

• Bi‐static SAI – Transmitter and receiver are sufficiently far apart

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 8

p

Page 9: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

BiSAI – Flat Topography

• Iso‐range surfaces = Ellipsoid• I t I t ti f lli id ith t h

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 9

• Iso‐range contours = Intersection of ellipsoids with topography• Flat topography  Ellipses

Page 10: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Multi‐static Synthetic Aperture Imaging

• Multi‐static SAI – Sufficiently apart multiple antennas that can either receive, transmit or both

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 10

Page 11: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Passive Synthetic Aperture Imagingy p g g

• Passive SAI –– Scene illuminated by transmitters of opportunity: TV, cell‐phone stations, communication satellites; ambient noise etc.Receive only antennas use backscattered measurements to

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 11

– Receive only antennas use backscattered measurements to make an image of the scene

Page 12: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Hitchhiker – Flat Topography

• Iso‐range surfaces = Hyperboloids• Iso range contours = Intersection of hyperpoloids with topography

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 12

• Iso‐range contours = Intersection of hyperpoloids with topography• Flat topography  Hyperbolas 

Page 13: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Outline

• Synthetic Aperture Imaging (SAI) modalities• SAI forward model• SAI image formation via microlocal techniquesg q

– Bistatic SAI– Monostatic SAI– Multistatic SAI– Synthetic Aperture Hitchhiker– Doppler Synthetic Aperture Hitchhiker

• Conclusions

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 13

Page 14: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Model for the  Received Signal

• Measurement Model Transmitterlocation

Receiverlocation

Reflectivity

Phase TermTransmitter and Receiver

Reflectivity fnc

• This model allows for:Amplitude Term

Receiverbeampatterns

– Arbitrary waveforms, trajectories; spatially distributed antennas– Array antennas in which different elements are activated with 

different waveforms– Applicable to both spotlight and strip‐map SAI mode

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 14

Page 15: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Construction of the Imaging Operator

• The imaging operator            has the same phase as(L2 adjoint)(L adjoint)– Compare with inverse Fourier transform and inverse Radon transform

• Forward map

e e

• Inverse mapPhase of L2 adjoint

scene

To be determinedimage

Backprojection Filter

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 15

To be determined

Page 16: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Outline

• Synthetic Aperture Imaging (SAI) modalities• SAI forward model• SAI image formation via microlocal techniquesg q

– Bistatic SAI– Monostatic SAI– Multistatic SAI– Synthetic Aperture Hitchhiker– Doppler Synthetic Aperture Hitchhiker

• Conclusions

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 16

Page 17: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Bi‐static Synthetic Aperture Imaging

receiverS th ti A t

transmitter

receiverSynthetic Aperture:

• Bi‐static SAI – Forward Model

antenna beam pattern, geometrical spreading factors etc

reflectivityfast‐timegeometrical spreading factors, etc.slow‐time: trajectory

C.E. Yarman, B. Yazıcı, and M. Cheney, “Bistatic synthetic aperture radar imaging with arbitrary trajectories,” IEEE Transaction on Image Processing, Vol. 17, No: 1, pp: 84‐93, 2008.ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

Page 18: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Isorange Contours of BiSAR

• Main contributions come from isorange curves40

20

30

isorange curves

Ellipsoids of revolution with foci               and0

10

isorange curvesintersection of ellipsoids with topography

Flat topography and fixed altitude−20 −10 0 10 20 30 40

−20

−10

at topog ap y a d i ed a titude

Backproject onto isorange curves …ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

Page 19: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

FBP Image Formation for BiSAI

Filtered backprojection onto isorange curves …I

filterInverse map

image

How do we determine the filter?image

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

Page 20: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

How to Determine the FBP Filter

• Study the Point Spread Function (PSF) of the imaging b h h d f i hoperator by the method of stationary phase

• PSF ‐Mapping from the scene/medium to the imageH fi d PSF? Pl i h d d l i h• How to find PSF? Plug in the data model into the inverse map and do the t integration

• Ideal PSF functionPoint Spread Function (z,x)

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

Page 21: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Forming an Ideal Point Spread Function

Phase of the point spread function‐

• Use stationary phase theorem to determine where the main contributions to a point in the image come from – Gradient with respect to omega and slow‐time variables 

Defines iso‐range and iso‐Doppler curves

• Determine conditions so that the main contributions• Determine conditions so that the main contributions are when

• Perform linearization in the phase of the PSF Taylor• Perform linearization in the phase of the PSF – Taylor series expansion around the main contributions

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

Page 22: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Stationary Phase of BiSAI PSF

Stationary Phase ‐IsoDoppler contours (Red)+ I oRa e o tou (Blue)

Bistatic Range 

+ IsoRange contours (Blue)

30

40

10

20

Bistatic Doppler−10

0

Bistatic Doppler

Flat topography and fixed altitude

−20 −10 0 10 20 30 40−20

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

Page 23: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Bistatic SAI Reconstruction

• Bistatic PSF  ‐ Perform linearization in the phase of PSF

• Perform change of variablesg

L di d t ib ti• Leading order contribution Jacobian from CV

Choose Filter

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

Page 24: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Bistatic SAI Resolution

• Leading order contribution to the PSF Indicator function

• Data collection manifold ‐ Set of Fourier vectors contributing to the reconstruction of the point z

• Band‐limited Fourier reconstruction ‐ The frequency content hence resolution determined by the data collection manifold

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 24

Page 25: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Data Collection Manifold for  Bistatic SAI

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 25

Page 26: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Data Collection Manifold & Visibility

Data Collection Manifold:

edge visible in

Example: Isotropic transmitters and receivers & Flat Topography

visible edge not a visible edgeg g

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 26

Page 27: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Numerical Simulations

• 22 x 22 km2 scene• Rectangular  targets at the scene• Circular flight trajectory at 6.5 km height

Ult id b d f• Ultra‐wideband waveforms 

Transmitter 1

Receiver 1

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 27

Page 28: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Numerical Simulations

100

Bi‐SAIMobile Transmitter

Bi‐SAIFixed Transmitter

110160

Mono‐staticSAI

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Receiver trajectoryReceiver trajectoryTransmitter location/trajectoryTransmitter location/trajectoryICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

Page 29: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Outline

• Synthetic Aperture Imaging (SAI) modalities• SAI forward model• SAI image formation via microlocal techniquesg q

– Bistatic SAI– Monostatic SAI– Multistatic SAI– Synthetic Aperture Hitchhiker– Doppler Synthetic Aperture Hitchhiker

• Conclusions

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 29

Page 30: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Synthetic Aperture Imaging

receivertransmitter

Synthetic Aperture:Synthetic Aperture:

• SAI – Forward Model

antenna beam pattern,  reflectivityfast‐time pgeometrical spreading factors, etc.

f yslow‐time

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

B. Yazıcı, M. Cheney, C.E. Yarman “Synthetic aperture inversion in the presence of noise and clutter,” Inverse Problems, Vol. 22, pp: 1705‐1729, 2006

Page 31: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

SAI in the Presence of Clutter & Noise

Obj f iObject of interestClutter (Unwanted scatterers)

Data model:Object of interest Clutter noise

10

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Data model:

30

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50

60

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60 20 40 60 80 100 120

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50

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ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 31

10 20 30 40 50 6010 20 30 40 50 60

B. Yazıcı, M. Cheney, C.E. Yarman “Synthetic aperture inversion in the presence of noise and clutter,” Inverse Problems, Vol. 22, pp: 1705‐1729, 2006

Page 32: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

SAI in the Presence of Noise and Clutter

• FBP ReconstructionBackproject onto isorange curves– Backproject onto isorange curves

– Choose filter wrt to a figure of merit that takes into account noise, clutter and target statisticsSt d th bi d i f th lti ti t b th d– Study the bias and variance of the resulting estimate by method of stationary phase Mono‐static inversion map 

• Figure of merit – Minimum mean square error

D i th FBP filt h th t i i i i d!

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 32

Design the FBP filter such that is minimized!

Page 33: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Optimal Filter in the Presence of Noise and Clutter

• Explicit expression for the FBP filter 

Target spectrumBeylkin determinant

• Space varying filter because belongs to the MS dataClutter spectrum noise 

spectrum

• Space varying filter, because  belongs to the MS data collection manifold and varies for each pixel reconstructed

• In the absence of clutter and noise

Filter:

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 33

Filter:

Page 34: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Numerical Simulations

ProjectionsBeylkin Recon Wiener Recon

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ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan34

20 40 60 80 100 120

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Page 35: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Clutter Suppression

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 35

Page 36: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Outline

• Synthetic Aperture Imaging (SAI) modalities• SAI forward model• SAI image formation via microlocal techniquesg q

– Bistatic SAI– Monostatic SAI– Multistatic SAI– Synthetic Aperture Hitchhiker– Doppler Synthetic Aperture Hitchhiker

• Conclusions

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 36

Page 37: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Multi‐static Synthetic Aperture Imaging

• Multiple transmitters traversing arbitrary trajectories, and transmitting arbitrary waveforms simultaneouslytransmitting arbitrary waveforms simultaneously. 

• Interference causes artifacts in reconstructed images.

• Multistatic SAI – Sufficiently apart multiple antennas that can either receive transmit or both

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 37

that can either receive, transmit or bothV. Krishnan, J. Swoboda, C.E. Yarman, B. Yazıcı, ʺMulti‐static Synthetic Aperture Radar Image Formation,ʺ to appear in IEEE Transaction on Image Processing.

Page 38: Part 3 ‐ Applications ofyazici/ICASSPTutorial/ICASSP... · Birsen Yazıcı & Venky Krishnan Rensselaer Polytechnic Institute Electrical, Computer and Systems Engggineering March

Multi‐static Synthetic Aperture Imaging

• Artifacts (additional singularities) due to interference if bi static reconstruction is usedbi‐static reconstruction is used

• Three transmitters on linear trajectories & one receiver on a circular trajectoryj y

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 38Original phantom Image reconstructed 

using a bi‐static method

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Bi‐static Received Signal Model

• M transmitters and N receiverFast‐time

S bSlow‐time Scene to be reconstructed

Received data at the qth A b

• Bi static distance

Received data at the qth receiver due to pth 

transmitterAntenna beampatterns

• Bi‐static distance

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 39

qth receiver trajectory

pth transmitter trajectory

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Multi‐static Synthetic Aperture Imaging

• Multi‐static data model – Measurement at the qth receiver due toBi t ti SAI qth receiver due to pth transmitter

Bistatic SAI forward model

Scene to be 

Measurements at the qth receiver

Bistatic delay• Plus additive noise – reconstructedBistatic delay 

for the p‐q pair

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 40

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Multi‐static Image Formationg

• Idea – Backproject with respect to a particular transmitter suppress the data due to other transmitterstransmitter, suppress the data due to other transmitters by a suitably designed filter

• Filter Suppress the Fourier components due to all• Filter – Suppress the Fourier components pq due to all the transmitters, but the one data is backprojected to.

• This converts the multi‐static data to bi‐static data• This converts the multi‐static data to bi‐static data

• Do this for each transmitter and coherently sum up the images to form the final imageimages to form the final image

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 41Fourier vector pq

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Multi‐static Image Formation 

• Backprojection operator

B k j ti t Filter

Image 

Backprojection wrt to the pth transmitter to be determined

greconstructed with the qth received signal

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 42Artifacts to be suppressed

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Design of FBP Filters

• Best possible image we can form

• The Fourier space data collection manifold• The Fourier space data collection manifold

• Choose the FPB filters so that

Projection ontothe tangent plane at z

Bi‐static bisector

• Choose the FPB filters so that 

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 43minimized

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Design of FBP Filters

• Reconstructed image due to (p,q)th pair

Bi static recon due

• Mean Square Error

Bi‐static recon due to (p,q)th pair Artifact images Image due to noise

Images to be suppressed

I1

I2

I3

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 44

I4

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FBP Filter

• Filter for the p‐q pair

Scene power spectral 

density

Noise power spectral 

density

JacobianDue to change of 

variables densityvariables

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 45

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Multi‐static Image Formation

• When backprojecting wrt 1st (2nd) transmitter suppress the Fourier component ξ (ξ )the Fourier component ξ2   (ξ1).

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 46

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Numerical Simulations

• Two transmitters and a one receiver• 22 x 22 km2 scene• Rectangular  targets at the scene• Circular flight trajectory at 6 5 km height• Circular flight trajectory at 6.5 km height• Ultra‐wideband waveforms • π/6 degrees apart

Transmitter 1

Transmitter 2Receiver 1

B. Yazıcı & V. KrishnanICASSP 2010, Dallas, TX47

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Numerical Simulations

Multi‐static ReconBi‐SAI Recon• Two transmitters and a one receiver on circular flight trajectory

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 48

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Numerical Simulation

• Three transmitters on linear trajectories & on receiver on a circular trajectorya circular trajectory

Multi‐static ReconBi‐SAR Recon

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 49

Multi static ReconBi SAR Recon

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Outline

• Synthetic Aperture Imaging (SAI) modalities• SAI forward model• SAI image formation via microlocal techniquesg q

– Bistatic SAI– Monostatic SAI– Multistatic SAI– Synthetic Aperture Hitchhiker– Doppler Synthetic Aperture Hitchhiker

• Conclusions

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 50

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Passive Synthetic Aperture Radary p

• Synthetic Aperture Hitchhiker– Scene illuminated by wideband transmitters of opportunity: cell‐phone stations; ambient noise etc.

C.E. Yarman, B. Yazıcı, ʺSynthetic aperture hitchhiker imaging,ʺ IEEE Transaction on Image Processing, Vol. 17, No. 11, pp: 2156‐2173, 2008.

• Doppler Synthetic Aperture Hitchhiker– Scene illuminated by ultra‐narrowband transmitters of 

dopportunity: TV, radio stations etc.

C.E. Yarman, L. Wang, B. Yazıcı, ʺDoppler Synthetic Aperture Hitchhiker Imaging ʺ accepted to Inverse Problems October 2009

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 51

Hitchhiker Imaging,  accepted to Inverse Problems, October 2009.

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Why Passive Imaging?

• Rapid growth in the number of broadcasting stations, mobile phone base stations, terrestrial and space based communication and navigation satellites  Passive SAI offers a viable approach to imagingoffers a viable approach to imaging 

• Can provide wide area coverage in urban environments

C l t ti t t i f• Can complement active systems to increase frequency and angular diversity

• O ly i lude e ei e i e e i e obile e atile• Only includes receivers  inexpensive, mobile, versatile, and suitable for rapid deployment

• Less vulnerable

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 52

• Less vulnerable 

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Outline of the Approachpp

• Novel synthetic aperture imaging modalities based on correlation of received signal and microlocal analysiscorrelation of received signal and microlocal analysis.

• Two types of correlation ‐– Hitchhiker – Delay based correlation– Doppler Hitchhiker – Scaling and delayed based correlation

• Correlation‐based processing removes transmitter related terms from the phase of the resulting signalterms from the phase of the resulting signal.

• Resulting forward models involve FIOs where the scene radiance is projected onto certain curved manifolds.p j– SAH – projection onto hitchhiker iso‐range curves– DSAH – projection onto hitchhiker iso‐Doppler curves

• Image Formation: Invert SAH and DSAH FIOs using

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 53

• Image Formation: Invert SAH and DSAH FIOs using microlocal techniques.

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Synthetic Aperture Hitchhiker

• Hitchhiker –T i b i i b h– Transmitters can be stationary or moving or both

– Transmitters can be cooperative or non‐cooperative– Receive‐transmit pair data association may not be possible

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 54

Receive transmit pair data association may not be possibleC.E. Yarman, B. Yazıcı, ʺSynthetic aperture hitchhiker imaging,ʺ IEEE Transaction on Image Processing, Vol. 17, No. 11, pp: 2156‐2173, 2008.

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Bi‐static Received Signal Model

slow‐timefast‐time reflectivity

Bistatic range:

Trans. location Receiver trajectory

Receiver Antenna :

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 55

Transmitter Antenna :

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Hitchhiker Received Signal Model

Integrate over all transmitters:

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 56

ith receiver

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SAH ‐ Spatio‐temporal Correlation of Received DataReceived Data

• Perform spatio‐temporal correlation of the received data

fast‐timeslow‐time

ith receive antenna data

jth receive antenna data

• Eliminates the transmitter related information from the phase of the forward map Passive detection & imagingphase of the forward map  Passive detection & imaging

• Takes into account multiple scattering from the transmitter to target

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 57

to target

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Hitchhiker FIO Model

• SAH FIO ‐Scene radiance –Image to be formed

Phase Term –Antenna beampatterns + geometric spreading factorsPhase Term 

Hitchhiker Range – Main contributions to SAH FIO 

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 58

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Iso‐Range Contours of Hitchhiker for Flat TopographyFlat Topography

• Iso‐range contours = Intersection of hyperboloids with topography

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 59

Backproject onto isorange curves …

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Inversion of Hitchhiker FIO

• Filtered‐backproject onto hitchhiker iso‐range curves

Filter to be determined 

• Irrespective of the choice of filter, backprojection puts the singularities of the scene at the correct location and correct orientation

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 60

correct orientation

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How to Determine the FBP Filter

• Point Spread Function (PSF) ‐Mapping from the scene h ito the image

hh k S h

Point Spread Function (z,x)

• Hitchhiker PSF phase

• Ideal PSF functionHitchhiker range

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 61

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Iso‐Range and Iso‐Doppler Contours of HitchhikerHitchhiker

40Hitchhiker Range 

IsoDoppler contours (Red)+ IsoRange contours (Blue)

30

40

Intersection of hyperboloids and the ground topography

10

20

−10

0Hitchhiker Doppler

The difference between the radial 

−20 −10 0 10 20 30 40−20

ffvelocities at two different points in the trajectories. 

Flat topographyd fi d

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 62

and fixed altitude

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Hitchhiker Resolution Analysis ‐ Fourier Domain Data Collection ManifoldDomain Data Collection Manifold 

Fourier vector

Fourier components contributing to the reconstruction of the point z – A vector in the direction of the difference of the unit vectors in the look directions of the two receivers with its length proportional to the

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 63

the look directions of the two receivers with its length proportional to the bandwidth of the transmitted waveform.

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Numerical Simulations

• 22 x 22 km2 scene• Multiple point targets• Circular flight trajectory at 6.5 km height• Infinite bandwidth waveform

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 64

Infinite bandwidth waveform • 128 x 128 pixel image

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Data Collection Manifolds for the Linear and Parabolic Trajectoriesfor the Linear and Parabolic Trajectories

Auto‐correlation of Linear ‐ 1

Auto‐correlation of Parabolic ‐ 2

Cross‐correlation of Linear & Parabolic ‐ 3

1+2+3

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 65

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Numerical Simulations –BiSAR and SAH Recon ComparisonBiSAR and SAH Recon Comparison

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 66ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

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Outline

• Synthetic Aperture Imaging (SAI) modalities• SAI forward model• SAI image formation via microlocal techniquesg q

– Bistatic SAI– Monostatic SAI– Multistatic SAI– Synthetic Aperture Hitchhiker– Doppler Synthetic Aperture Hitchhiker

• Conclusions

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 67

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Doppler Synthetic Aperture Hitchhiker

• Most sources of opportunity are single frequencySAH d ll i if ld i ll f l• SAH data collection manifold is small for ultra‐narrow band sources of opportunity

• New approach  Doppler SAH

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 68

pp ppC.E. Yarman, L. Wang, B. Yazıcı, ʺDoppler Synthetic Aperture Hitchhiker Imaging,ʺ accepted to Inverse Problems, October 2009.

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Doppler Synthetic Aperture Hitchhiker

• Spread of the hyperbolas determined by the range ambiguity 

Range ambiguity function of the transmitted waveform

Hyperbola formed by correlating received signals

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 69

p f yp y g g yfunction of the transmitted waveforms

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Doppler Synthetic Aperture Hitchhiker

• Window measurements, then scale& correlate…

Scaling parameterShift 

parameters

window:  ith received data:  filter to be determined

• Results in a new FIO• Larger data collection manifold…

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 70

g

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Doppler Hitchhiker FIO Model

• DSAH FIO ‐S diScene radiance –Image to be formed

Phase Term –hase erm

Hitchhiker‐Doppler Scale Factor –

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 71

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DSAH FIO Main Contributions –Hitchhiker Iso‐Doppler ContoursHitchhiker Iso‐Doppler Contours

• Iso‐Doppler surface ‐ Intersection of two constant Doppler cones  

Constant Doppler Cone 1 :Constant Doppler Cone 1 :

Constant Doppler Cone 2 :

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 72

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DSAH Iso‐Doppler Contours

• Iso‐Doppler contours for two receivers and flat topographytopography

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 73

Backproject onto iso‐Doppler curves …

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Inversion of DSAH FIO

• Weighted‐backprojection onto iso‐Doppler curves

Weight to be determined 

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 74

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Inversion of DSAH FIO

• Weighted‐backprojection onto iso‐Doppler curves

Weight to be determined 

Filter –

Weight – Jacobian that comes from a certain change of variables 

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 75

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DSAH Iso‐Doppler and Iso‐Doppler‐Rate ContoursContours

Iso‐Doppler curves Iso‐Doppler‐rate curves

~ radial acceleration in

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 76

Iso‐Doppler‐rate surface –~ radial acceleration in the look direction of the radar

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DSAH and SAH Contours

40

30

40

10

20

−10

0

DSAH contoursSAH contours−20 −10 0 10 20 30 40

−20

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 77

DSAH contoursSAH contours

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Resolution Analysis ‐ Fourier Domain Data Collection Manifold for DSAH 

Projections of the platform velocity onto the planes perpendicular to the radar line of sightperpendicular to the radar line of sight

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 78Fourier vector

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Rasolution of DSAH

• Larger the Fourier vector  higher the resolution

Fourier vector

• t : Support of the windowing function  

Fourier vector

pp g– Longer the support of the windowing function  Higher the 

resolution

• 2/ : Frequency• 2/ : Frequency – Larger the transmit frequency   Higher the resolution

• ’ : ~ Number of segments correlated

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 79

g– Higher sampling of ’  Higher the resolution

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Numerical Simulations

A single stationary transmitter, two moving receivers

• 22 x 22 km2 scene• A point target at [16, 11, 0] km• Circular flight trajectory at 6 5 km height• Circular flight trajectory at 6.5 km height• A fixed‐frequency waveform • 128 x 128 pixel image

Transmitter

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 80Image X‐profile Y‐profile

f0 = 0.4 MHz,    L =  3.657 s.

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Numerical Simulations f0 = 0.4 MHz,    L =  3.657 s.Shorteer w

indow s

Image X‐profile Y‐profile

support

f0 = 0.4 MHz,    L = 14.629 s. Longer window

 su

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 81X‐profile Y‐profileImage

Longer window support improves resolution

upport

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Numerical Simulation f0 = 0.4 MHz,    L =  3.657 s.

Smmaller frequ

Image X‐profile Y‐profile

ency

f0 = 4 MHz,    L = 3.657 s. Largerr  frequency

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 82X‐profile Y‐profileImage

Higher transmit frequency improves resolution

y

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Numerical Simulation 

16   τ′ values uniformly spaced in [0, 248.258]s

f0 = 4 MHz,    L = 3.657 s. 

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 83’ : ~ Larger the number of segments correlated, better the resolution

Partial data collection manifold      τ′= 165.5054s

Partial data collection manifold τ′=33.1011s

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Conclusions

• Microlocal analysis provides a unified mathematical f k f id f bl i i dframework for a wide‐range of problems in sensing and imaging problems

P id f l t i i i ht i t i i• Provides a powerful geometric insight into imaging

• Leads to novel modalities

h l d• Techniques result in adaptive processing

• Many open problems…l l A l I k h I• Microlocal Analysis in Imaging Workshop at RPI in 

August 2010.• Microlocal Analysis in Imaging tutorial for IEEE Trans

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan 84

Microlocal Analysis in Imaging tutorial for IEEE Trans. on Image Processing www.ecse.rpi.edu/~yazici

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ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan

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• [Nolan‐Cheney1] C. Nolan and  M. Cheney, ``Synthetic aperture inversion‘’, Inverse Problems 18 (2002) no 1 221 235Problems 18 (2002), no. 1, 221‐‐235. 

• [Nolan‐Cheney2], C. Nolan and M. Cheney,``Synthetic aperture inversion for arbitrary flight paths and nonflat topography’’, IEEE Trans. Image Process. 12 (2003), no. 9, 1035‐‐1043. 

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• [Treves] F. Treves, ``Introduction to pseudodifferential and Fourier integral operators’’. Vol. 1 & II. The University Series in Mathematics. Plenum Press, New York‐London, 1980. 

• [Yazici‐Cheney‐Yarman], B. Yazıcı, M. Cheney, C.E. Yarman “Synthetic aperture inversion in [ y ], , y, y pthe presence of noise and clutter,” Inverse Problems, Vol. 22, pp: 1705‐1729, 2006.

• [Yarman‐Yazici‐Cheney] C.E. Yarman, B. Yazıcı, and M. Cheney, “Bistatic synthetic aperture radar imaging with arbitrary trajectories,” IEEE Transaction on Image Processing, Vol. 17, No: 1, pp: 84‐93, 2008.

• [Yarman‐Yazici] C.E. Yarman, B. Yazıcı, ʺSynthetic aperture hitchhiker imaging,ʺ IEEE T ti I P i V l 17 N 11 2156 2173 2008Transaction on Image Processing, Vol. 17, No. 11, pp: 2156‐2173, 2008.

• [Yarman‐Wang‐Yazici] C.E. Yarman, L. Wang, B. Yazıcı, ʺDoppler Synthetic Aperture Hitchhiker Imaging,ʺ accepted to Inverse Problems, October 2009. 

ICASSP 2010, Dallas, TX B. Yazıcı & V. Krishnan