1 Livorno, 30.04.2010 . Stefania Matteoli Hyperspectral Target Detection via Local Background Suppression Pisa, 30.11.2007 Stefania Matteoli a Nicola Acito b Marco Diani a Giovanni Corsini a a Dipartimento di Ingegneria dell’Informazione, Università di Pisa, Pisa, Italy b Accademia Navale, Livorno, Italy Livorno, 30.04.2010 Hyperspectral Target Detection via Local Background Suppression South of Italy Chapter Remote Sensing & Image Remote Sensing & Image Processing Group Processing Group
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Livorno, 30.04.2010
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Pisa, 30.11.2007
Stefania Matteoli a
Nicola Acito b
Marco Diani a
Giovanni Corsini a
a Dipartimento di Ingegneria dell’Informazione, Università di Pisa, Pisa, Italyb Accademia Navale, Livorno, Italy
Livorno, 30.04.2010
Hyperspectral Target Detection via Local Background Suppression
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Background - Hyperspectral Target Detection
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Livorno, 30.04.2010
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Outline
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Livorno, 30.04.2010
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Linear Mixing Model (LMM)
[ ] [ ] [ ]jijiji T ,,, NsβBX +⋅+⋅= α
random vector associated to the test pixel
spectral signature of the target
scalar value accounting for sub-pixel targets
matrix spanning the background subspace
vector of background components
background subspace of dimension
zero-mean Gaussian random noise vector with covariance matrix
number of spectral bands
[ ]ji,X
Ts
1xb [ ]ji,x
0>α
ΨB dbx
1xb
( ) bd <Ψ= dim
[ ]ji,N
[ ]ji,β
b
Ψ
NΛ
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Livorno, 30.04.2010
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Subspace-based target detection scheme
original data space
[ ] [ ] [ ][ ] [ ] [ ]jijijiH
jijijiH
T ,,,:
,,,:
1
0
NsβBX
NβBX
+⋅+⋅=+⋅=
α
Background is suppressed via orthogonal projection
background suppression
[ ] [ ]jijiT
,, XBY ⋅= ⊥
⊥B ( )dbb −xprojection matrix onto ⊥Ψ
[ ] [ ][ ] [ ]jijiH
jijiH
,,:
,,:
1
0
1
1
NρY
NY
+⋅==
α
residual subspace ⊥Ψ
[ ]( ) η
0
1
,
H
H
jiT<
>Y
target detection
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Livorno, 30.04.2010
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Target detection scheme, detection performance
Background suppression
Target detection performance (PD and PFA) depends on
NΛ2
T
T
sB⊥=ε
noise covariance matrix
target residual energy
PD is expected to be an increasing function of .ε
Target detection
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Livorno, 30.04.2010
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Target detection
Global background vs local background
GΨ[ ]jiL ,Ψ
[ ] jiji GL ,,, ∀Ψ⊆Ψ
[ ] GL djid ≤,
[ ] GL ji εε >,
Background suppression
Global background subspace
Local background subspace
generally
[ ]ji,
GΨ
[ ]jiL ,Ψ
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Livorno, 30.04.2010
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Target detection
Global background vs local background
Background suppression
Global approach
Local approach
[ ]ji,
GΨ
[ ]jiL ,Ψ
The background subspace basis is unknown and has to be estimated from the data
• Global background lies in a high-dimensional subspace
• Low target residual energy after suppression (major risk of target leakage)
Provides lower-dimensional subspacesHigher residual energy after projection (which benefits to detection performance)
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Livorno, 30.04.2010
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Global background estimation : N-S
Target detection
Background suppression
NWHFC
SVD
all image pixels
N-SGSN dd ˆˆ =−
subspace dimension (Virtual Dimension, VD)
GSN BB ˆ=− SNdbx −ˆbasis vectors
GΨ̂
N-P based test on covariance and correlation matrix eigenvaluesbased on asymptotic properties
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Livorno, 30.04.2010
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Local background estimation : LBSS
Target detection
Background suppression
local neighborhood
LBSSA set of neighboring pixels is let span the background subspace[ ]ji,
Local Background Subspace Selection
LBSSLBSS Kd =ˆ
[ ]jiLLBSS ,B̂B =SNdbx −
ˆ[ ]jiL ,Ψ̂The local subspace dimension is imposed by the number of neighboring pixelsLBSS cannot account for background spatial variability within the scene!
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Results: 2) Simulation (1000 images), FAR@PD=1
0 0.2 0.4 0.6 0.8 110-4
10-3
10-2
10-1
100
α
FA
R
φ0,N-S = 6 (dB)
N-SLBSELBSS,K
LBSS=4
LBSS,KLBSS
=9
LBSS,KLBSS
=16
LBSS,KLBSS
=25
LBSS: KLBSS is a user-specified parameter. No criteria exist to set it and several configurations have to be tested in order to assure good performance.
-10 -5 0 5 1010
-3
10-2
10-1
100
φ0,N-S (dB)
FA
Rα = 0.5
N-SLBSELBSS,K
LBSS=4
LBSS,KLBSS
=9
LBSS,KLBSS
=16
LBSS,KLBSS
=25
-10 -5 0 5 1010
-3
10-2
10-1
100
φ0,N-S (dB)
FA
R
α = 0.7
N-SLBSELBSS,K
LBSS=4
LBSS,KLBSS
=9
LBSS,KLBSS
=16
LBSS,KLBSS
=25
0 0.2 0.4 0.6 0.8 110
-4
10-3
10-2
10-1
100
α
FA
R
φ0,N-S = 10 (dB)
N-SLBSELBSS,K
LBSS=4
LBSS,KLBSS
=9
LBSS,KLBSS
=16
LBSS,KLBSS
=25
dBSN 10 ,0 =−φ
dBSN 6 ,0 =−φ5.0 =α
7.0 =α
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Livorno, 30.04.2010
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Results: 3) Testing on real data
Obj. 1
Obj. 2
Obj. 3
Obj. 4
Obj. 1
Obj. 2
Obj. 3
Obj. 4
0 5 10 15 20 25 300
0.5
1
1.5
2
2.5
3x 10
4
dLBSE
Occ
urr
en
ce
LBSEN-SLBSS: K
LBSS=4
LBSS: KLBSS
=9
LBSS: KLBSS
=16
LBSS: KLBSS
=25
LBSEd̂
0 5 10 15 20 25 300
0.5
1
1.5
2
2.5
3x 10
4
dLBSE
Occ
urr
en
ce
LBSEN-SLBSS: K
LBSS=4
LBSS: KLBSS
=9
LBSS: KLBSS
=16
LBSS: KLBSS
=25
LBSEd̂
10-6
10-4
10-2
100
0.5
0.6
0.7
0.8
0.9
1
FAR
FoD
T
LBSE
N-S
LBSS: KLBSS
=4
LBSS: KLBSS
=9
LBSS: KLBSS
=16
LBSS: KLBSS
=25
real target detection scenario with ground-truthed targets
LBSE histogram
ROC curves
Rome countryside (Italy)COLLECTION SITE
~850 mSENSOR ELEVATION
0.7 mradIFOV
0.4 – 1.0 μm (VNIR)SPECTRAL RANGE
SIM-GASENSOR
1 nm (average)SPECTRAL SAMPLING
1024 x 1100# PIXELS
512# BANDS
Rome countryside (Italy)COLLECTION SITE
~850 mSENSOR ELEVATION
0.7 mradIFOV
0.4 – 1.0 μm (VNIR)SPECTRAL RANGE
SIM-GASENSOR
1 nm (average)SPECTRAL SAMPLING
1024 x 1100# PIXELS
512# BANDS
• Best performance obtained with LBSE
• LBSS results exhibit diversity w.r.t. KLBSS
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. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression
Conclusion
LBSE • novel and fully automatic algorithm for local background subspace estimation and suppression
• experimental evidence of three main advantages w.r.t exiting methodologies
being local, it is able at properly detecting targets with low residual energy w.r.t the global background subspace
provides unambiguous results through the automatic computation of a local background dimension for each pixel
it is capable of adapting to spatial variations of background complexity within the scene
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Livorno, 30.04.2010
. Stefania MatteoliHyperspectral Target Detection via Local Background Suppression