matteoli ieee gold_2010_clean

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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

South of Italy Chapter

Remote Sensing & Image Remote Sensing & Image Processing GroupProcessing Group

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Background - Hyperspectral Target Detection

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Outline

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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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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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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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Target detection

Global background vs local background

GΨ[ ]jiL ,Ψ

[ ] jiji GL ,,, ∀Ψ⊆Ψ

[ ] GL djid ≤,

[ ] GL ji εε >,


Global background subspace

Local background subspace

generally

[ ]ji,

GΨ

[ ]jiL ,Ψ

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Livorno, 30.04.2010


Target detection

Global background vs local background


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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Global background estimation : N-S

Target detection


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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Local background estimation : LBSS

Target detection


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!

LBSS main limitation

• target leakage (overestimation)• false alarms (underestimation)

( ) TLBSSLBSS

TLBSSLBSS BBBBIPB

1−⊥ −=

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Local background estimation : a new algorithm

Target detection


local neighborhood

LBSEAutomatic techniqueAdaptive estimation on a per-pixel basisEstimated local background subspace tailored to background spatial variability

[ ]ji,

Local Background Subspace Estimation

Statistical hypothesis

testing

SVD

LBSE

[ ] [ ]jidjid LLBSE ,ˆ,ˆ =local subspace dimension

[ ]jiLLBSE ,B̂B = LBSEdbx ˆbasis vectors

SNdbx −ˆ[ ]jiL ,Ψ̂

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LBSE procedure

whitening SVD

NΛ̂

( ) [ ]kk eeeM 21

ˆ =

{ } LBSEKllX 1=≡ x

Orthogonal Projection

2⋅ { }⋅= LBSEKl ,...,1

max

( ){ } LBSEK

lk

lR1=

( )kΘ[ ]

[ ] ( ) [ ]

=

=

jiji

kjid

Ld

L

,ˆ,ˆ

,ˆ

ˆMM

θpfa

′0H

′1H

1+= kk

θλ

LBSE block{ } LBSEKllZ 1=≡ z ( )beee 21

( ) ⊥kM̂

dewhitening [ ] [ ]jiji NLBSE ,ˆˆ,ˆ 21 MΛB ⋅=

whitening SVD

NΛ̂

( ) [ ]kk eeeM 21

ˆ =

{ } LBSEKllX 1=≡ x

Orthogonal Projection

2⋅ { }⋅= LBSEKl ,...,1

max

( ){ } LBSEK

lk

lR1=

( )kΘ[ ]

[ ] ( ) [ ]

=

=

jiji

kjid

Ld

L

,ˆ,ˆ

,ˆ

ˆMM

θpfa

′0H

′1H

1+= kk

θλ

LBSE block{ } LBSEKllZ 1=≡ z ( )beee 21

( ) ⊥kM̂

dewhitening [ ] [ ]jiji NLBSE ,ˆˆ,ˆ 21 MΛB ⋅=

( ) ( )

( ) 20

2

|

ˆ

kbk

l

lkk

l

HR

R

−′

⊥

∈

⋅=

χ

zM

( ) ( ){ } ( )k

H

H

kl

Kl

k RLBSE

θλ'0

'1

,...,1max

<

>

==Θ

yetreachednotLd kdL =ˆ

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Livorno, 30.04.2010


Target detection step


Target detection

( ) η0

1

ˆ1

ˆ

ˆ1

ˆ

ˆ

ˆ

H

H

TTT

TTT

<

>

⊥−⊥

⊥−⊥

⋅⋅⋅⋅

⋅⋅⋅⋅=

sPΛPs

xPΛPsx

BNB

BNB

( ) TT BBBBIPB

ˆˆˆˆ 1

ˆ ⋅⋅⋅−=−⊥

each considered background basis estimation algorithm (N-S, LBSS, and LBSE) should be embodied in a subspace-based target detector

Generalized Matched Filter (GMF)

defined in the orthogonal complement of the background subspace

[ ][ ]

=−

ji

ji

LBSE

LBSS

SN

,ˆ

,ˆ

ˆ

ˆ

B

B

B

B

N-S

LBSS

LBSE

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Results: 1) LBSE adaptability to spatially variable backgrounds

20 40 60 80 100 120

20

40

60

80

100

120

True-color image LBSE map LBSE map histogram

urban area: high complexity

vegetated rural area: low complexity

10 15 20 25 30 350

500

1000

1500

2000

2500

3000

occu

rren

ces

LBSEN-S

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Results: 2) Simulation methodology

[ ] ( ) [ ] [ ]jijiji T ,,1, NβBsX +⋅−+⋅= αα

( ) ˆˆ

21 γαφ TsPΛ

BN ⋅⋅⋅= ⊥−

N-S, LBSS, LBSE

( ) orTinTT ,, sss ⋅+= γγ

the scalar value allows to set a desired value of the target residual energy on the orthogonal complement of the N-S estimated subspace

2

,2

,02

1ˆ orTSN sΛN ⋅⋅= −− γφ

simulation performed over N=1000 imagesTarget detection results averaged over the 1000 images

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Data-set

Indian Pine (IN, USA)COLLECTION SITE

~ 4 KmSENSOR ELEVATION

1 mradIFOV

0.4 – 2.5 μm (VNIR-SWIR)SPECTRAL RANGE

AVIRISSENSOR

10 nm (average)SPECTRAL SAMPLING

145 x 145# PIXELS

224# BANDS

Indian Pine (IN, USA)COLLECTION SITE

~ 4 KmSENSOR ELEVATION

1 mradIFOV

0.4 – 2.5 μm (VNIR-SWIR)SPECTRAL RANGE

AVIRISSENSOR


145 x 145# PIXELS

224# BANDS

20 40 60 80 100 120 140

20

40

60

80

100

120

140

SIMULATION PARAMETERS dBSN |0 −φ {-10, -8, -6, -4, -2, 0, 2, 4, 6, 8,10}

α {0.1, 0,2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1}

SNd −ˆ 17

LBSSK {4, 9, 16, 25}

N 1000

Results: 2) Simulation results (1000 images)

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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


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


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


1024 x 1100# PIXELS

512# BANDS

• Best performance obtained with LBSE

• LBSS results exhibit diversity w.r.t. KLBSS

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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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Pisa, 30.11.2007

Livorno, 30.04.2010

Thanks for your attention!

South of Italy Chapter

matteoli ieee gold_2010_clean

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