TimeReversal and MultiModal Subspace Signal Processing for Subsurface Imaging and Remediation

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Time-Reversal and Multi-Modal Subspace Signal
Processing for Subsurface Imaging and Remediation

• Edwin A. Marengo and Anthony J. Devaney
• Center for Subsurface Sensing and Imaging Systems
  
• Department of Electrical and Computer Engineering
• Northeastern University, Boston MA 02115

September 20, 2004
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Landmine Detection/Location
Outline

• Time-reversal-based
• imaging of targets plus clutter including
  multiple scattering.
• Multi-modal signal subspace methods for target
  location.

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Data Versus Object Spaces
finite dimensional data space (a data vector)
infinite dimensional object space
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Data Versus Object Spaces
finite dimensional data space (a data vector)
Limited view problem
infinite dimensional object space
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Data Versus Object Spaces
finite dimensional data space (a data vector)
ill-posedness (noise forces finite
dimensionality and even further space reduction)
(an effective data vector)
infinite dimensional object space
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Gather Multi-Modal Data
field a
field b
field K
Spans larger portions of the entire object space
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A Priori Information and Object Models
Use a priori information
Parametric approach Use models that represent
reasonably well with a finite number of
parameters the main properties of the
object/medium.
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Do Both Multi-Modal Parametric Signal Subspace
Methods
field a
field b
field K
Use models that represent reasonably well with a
finite number of parameters the main properties
of the object/medium.
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Detecting/Locating Targets in Clutter
active sensor array of N transceivers
background medium
target
clutter
clutter
Clutter is part of the unknown medium.
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Detecting/Locating Targets in Clutter
active sensor array of N transceivers
scattering strength
location
Scalar single frequency point targets.
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Detecting/Locating Targets in Clutter
active sensor array of N transceivers
Data multistatic data matrix (scattering
matrix) K
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Detecting/Locating Targets in Clutter
active sensor array of N transceivers
scattering strength
location
Problem statement
Estimate target and clutter locations Xm and
scattering strengths ?m from the multistatic
data matrix K.
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Consider Multiple Scattering Effects
Central contribution
We solve for the exact inverse scattering of
multiply scattering targets plus clutter
Newmann series and Foldy-Lax equations approaches.
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Time-Reversal (TR) Electromagnetics
Ad hoc focusing or imaging of waves in complex,
heterogeneous environments.

• Seismic profiling
• Medical imaging and therapy (brain imaging and
• lithotripsy)
• Non-destructive testing of man-made structures
• Submarine communications
• Land mine detection and safe remediation

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Focusing
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TR focusing/remediation Lithotripsy
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Multiple Scattering in TR focusing
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First order scattering case
Well-resolved case
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Second order scattering Well-resolved
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Second order scattering Non-well-resolved
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Focusing
Conventional imaging
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TR Imaging
received field vector K transmit vector
K
Multistatic response matrix
Create eigenimage Use eigenvectors of the TR
matrix KK as input to the array and compute
field.
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Multiple Scattering in Conventional TR Imaging
(based on measured K)
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First order scattering case Conventional
eigenimages
Assuming a given background Green function
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Second order scattering case Conventional
eigenimages
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Second order scattering case Conventional
eigenimages
Non-well-resolved case Wave interference. Cannot
focus.
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Focusing
Conventional imaging
Subspace Methods (target location)
Uses K to determine target locations in known
background
Incorporate multiple scattering
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The basic configuration
incident field due to excitation of the jth
element
N point sources
excitation
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Exact scattering
(incident field)
(scattered field)
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Main result 1
introduce
TR matrix
Projects onto space spanned by complex conjugates
of Green function vectors.
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Subspace methods
signal subspace
SVD of K
K ?i ?i vi
null space (noise subspace)
K vi ?i ?i
T ?i K K ?i ?2i ?i
0
space of array signals
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Main result 2
signal subspace

noise subspace
(the propagators)
(?i?? 0)
(?i? 0)
SVD of K
K ?i ?i vi
K vi ?i ?i
T ?i K K ?i ?2i ?i
0
MUSIC pseudo-spectrum
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Computer Simulations
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Second order scattering Well-resolved
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Second order scattering Non-well-resolved
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Antenas dispersas
Sparse array (2?)
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Menos antenas
A few antennas (5)
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Super-resolution
Original object
Reconstructed object
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Backpropagated images
Two targets
Born
Quadratic
coupling lobe
coupling lobe
Scattering model-dependent
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Scattering amplitude estimation
Remember Parametric method
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Reduced noise subspace
Original object
Reconstructed object
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Illustration
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SNR10dB
A realization of K
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SNR10dB
A realization of K
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SNR20dB
A realization of K
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Foldy-Lax equations model to run full exact
scattering in the simulation data
targets plus clutter
transceiver array of 7 elements
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exact
Born
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Actual target (plus clutter) locations
Pseudospectrum from the Raw Data
Additive noise of 2.5 of signal energy
Pseudospectrum from the Interpolated Data
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New Coherent MUSIC For Target Location
Located 3 targets using only 3 antennas
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New Coherent MUSIC For Target Location
Located 4 targets using only 3 antennas
Can locate up to N(N1)/2-1 targets (E.A.
Marengo, IEEE Trans. Antennas Propagat. (2004)).
Ideal for multi-modal subspace signal processing.
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Multi-Modal Landmine Location
Sensor technology Maturity Cost and complexity
Passive/active infrared Near Medium Passive
mm-wave Far High mm-Wave radar Far High Ground
penetrating radar Near Medium Ultrawideband
radar Far High Active acoustic Mid Medium Activ
e seismic Mid Medium Neutron activation Near Hi
gh Charge particle detection Far High Nuclear
quadrupole Far High Chemical sensing Mid High B
iosensors Far High
Claudio Bruschini and Bertrand Gros, J. Hum.
Demining
Source
http//www.hdic.jmu.edu/JOURNAL/2.1/bruschini.htm
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Passive Infrared Images
Day
Night
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Target Location Problem
sensors a
(a1,a2,,aL)
field
source
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Target Location Problem
sensors a
(a1,a2,,aL)
field
source
M lt L sources
Standard direction-of-arrival version of MUSIC
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Target Location Problem
Entire data space
CL
sensors a
(a1,a2,,aL)
S
Signal subspace
Data vector A (a1,a2,,aL) ?m sm gm
SSpan(gm)
propagators that depend on target location
1 propagator vector gm per target location (per
target)
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Target Location Problem
Entire data space
N
S
Signal subspace

• Data known compute orthogonal complement of S
  N

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Target Location Problem
Entire data space
N
S
S0

• Data known compute orthogonal complement of S
  N
• Data are not arbitrary, i.e., S Span (gm)
• Assume given gms and consequently a given S0

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Target Location Problem
Entire data space
N
S
SS0

• Data known compute orthogonal complement of S
  N
• Data are not arbitrary, i.e., S Span (gm)
• Assume given gms and consequently a given S0
• Compute the projection of hypothesized S0 into N
• If projection yields zero then S S0 and found
  target
• locations.

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Multi-Modal Signal Processing
sensors a
active sensors K
(a1,a2,,aL)
passive sensors b
(K11,K12,K13,,KNN,)
(b1, b2,,bM)
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Multi-Modal Signal Processing
sensors a
active sensors K
(a1,a2,,aL)
passive sensors b
(K11,K12,K13,,KNN,)
(b1, b2,,bM)
gb(xm)
ga(xm)
gK(xm)
propagators K
propagators b
target location Xm
propagators a
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Multi-Modal Signal Processing
sensors a
active sensors K
(a1,a2,,aL)
passive sensors b
(K11,K12,K13,,KNN,)
(b1, b2,,bM)
Data vector A (a1,,aL, b1,, bM ,
K11,,KNN,) ?ia,b,K ?m sm(i) gm(i)
1 propagator subspace per target!
Total number of samples Nt M lt Nt targets
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Example
Nt 2N
N

N
field a
field b
?
gm(a)
gm(b)
Effective signal subspace remains of
dimensionality M.
Number of reconstructible features has then grown
by N, i.e., instead of locating up to N-1
targets now we locate up to 2N-1 targets.
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Conclusions

• TR is an interesting concept that is worth
  understanding
• for object reconstruction applications in
  complex
• environments.
• Useful for both remediation and imaging.
• TR imaging with MUSIC was generalized to the
  multiple
• scattering case.
• A new coherent form of the algorithm is ideally
  suited for
• multi-modal subspace signal processing.
• Need real data to test subspace signal
  processing
• algorithms, with particular interest in the
  multi-modal
• signal processing case.