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POLINSAR 2009 WORKSHOP POLINSAR 2009 WORKSHOP 26-29 January 2009 ESA-ESRIN, Frascati (ROME), Italy Evaluation and Bias Removal of Evaluation and Bias Removal of Multi- -Look Effect on Look Effect on Multi α /A (H/ α Entropy/Alpha /Anisotropy (H/ Entropy/Alpha /Anisotropy /A) ) Jong- Jong -Sen Lee*, Thomas Ainsworth Sen Lee*, Thomas Ainsworth Naval Research Laboratory Naval Research Laboratory Washington DC 20375, USA Washington DC 20375, USA * CSRSR, National Central University, Taiwan * CSRSR, National Central University, Taiwan J.S. Lee, et al., “Evaluation and bias removal of multi-look effect on Entropy/Alpha/Anisotropy in polarimetric SAR decomposition,” IEEE Transactions on Geoscience and Remote Sensing, October 2008

INTRODUCTION INTRODUCTION • Entropy/Anisotropy/Alpha (H/A/ α ): Widely applied and effective for PolSAR data analysis. • Geophysical parameter estimation: • Anisotropy —Surface roughness • Entropy and Alpha — Soil Moisture • Entropy — Biomass • Accurate H/A/ α estimation require averaging: • Underestimate Entropy • Overestimate Anisotropy • Alpha?

MOTIVATION MOTIVATION • Evaluate multi-look asymptotic behavior of H and A by a simple simulation technique: • The effect of number of looks on Averaged α . • The H/A/ α bias problem for L-band and X-band data • Devise a bias removal scheme: • Entropy • Anisotropy • Alpha C. Lopez-Martinez, E. Pottier and S.R. Cloude, “Statistical assessment of eigenvector based target decomposition Theorems in radar polarimetry,” IEEE Trans. Geoscuence and Remote Sensing, September 2005.

H / A / α α DECOMPOSITION DECOMPOSITION H / A / 1 [ ] = + − T k S S S S 2 S TARGET VECTOR XX YY XX YY XY 2 N N [ ] 1 ∑ 1 ∑ [ ] = ⋅ = * T LOCAL ESTIMATE OF T k k T i i i THE COHERENCY MATRIX N N = = i 1 i 1 = λ * T + λ * T + λ * T [ ] T u u u u u u 1 1 1 2 2 2 3 3 3 3 SCATTERING PROCESSES S.R. CLOUDE E. POTTIER α α α ⎡ ⎤ cos ( ) cos ( ) cos ( ) 1 2 3 ⎢ ⎥ [ ] δ δ δ j 1 j 2 j 3 U 3 = α β α β α β sin ( )cos( )e sin ( )cos( )e sin ( )cos( )e ⎢ ⎥ 1 1 2 2 3 3 γ γ γ j 1 j 2 j 3 ⎢ ⎥ α β α β α β ⎣ ⎦ sin( )sin ( )e sin( ) sin ( )e sin( )sin( )e 1 1 2 2 3 3

H / A / α α DECOMPOSITION DECOMPOSITION H / A / α PARAMETER ENTROPY ANISOTROPY λ − λ 3 ∑ = = − α = α + α + α 2 3 H P log ( P ) A P P P λ + λ i 3 i 1 1 2 2 3 3 = i 1 2 3 λ = i P i 3 ∑ λ k = k 1 3 ROLL INVARIANT PARAMETERS MULTI-LOOK (AVERAGING) EFFECT ON H/A/ α : • UNDERESTIMATE OF H • OVERESTIMATE OF A • α DEPENDS ON SCATTERING MECHANISM, BUT HAS LESS EFFECT. C. Lopez-Martinez recommends 9x9 for H and 11x11 for A

ENTROPY(H) VERSUS MULTI- -LOOKING LOOKING ENTROPY(H) VERSUS MULTI |HH-VV|, |HV|, |HH+VV| Freeman and Durden Decomposition H Original (4 looks) 5x5 9x9

and α α VERSUS MULTI Anisotropy and VERSUS MULTI- -LOOKING LOOKING Anisotropy A Aniso- tropy Original (4 looks) 5x5 9x9 α ALPHA

SIMULATION AREA SELECTION SIMULATION AREA SELECTION E-SAR L-BAND POLSAR DATA OF OBERPFAFFENHOFEN Urban (D. B.) Forest (Volume) Grass Freeman/Durden Decomposition (Surface)

SIMULATION PROCEDURE SIMULATION PROCEDURE For a given < T> , simulate single-look complex data: 1 / 2 T 1. Compute T = 1 / 2 1 / 2 * ( ) T T T ν 2. Simulate a complex random vector, , CN(0,I) 3. Form a single-look complex vector u = 1 / 2 ν T 4. Compute a n look covariance matrix, n 1 ∑ = * T T uu n n 1 Compute the n look H/A/ α 5. Verification: = 1 / 2 1 / 2 = T T * T E [ uu ] T E [ vv ]( T ) T

EIGENVALUE ESTIMATION EIGENVALUE ESTIMATION • Mean value of n-look estimation • Dominant Eigenvalue changes little • Forest (Volume) eigenvalues within 4 dB High Entropy, Low Anisotropy • Urban (D.B.): two dominant scatterings Medium Entropy, High Anisotropy • Grass (Surface): One dominant Low Entropy, Medium Anisotropy

ENTROPY ESTIMATION ENTROPY ESTIMATION • Entropy is underestimated (1000 samples) • Rate of increase changes at 5x5 looks. • 7x7 looks sufficient for Entropy • 5x5 may severely underestimate entropy. • Remove bias is possible: 3x3 looks and above. 5x5 looks is recommended. • Boxcar average includes mixed media.

ANISOTROPY ESTIMATION ANISOTROPY ESTIMATION • Anisotropy is overestimated. • Rate of increase changes at 5x5 looks. • For forest (volume) area, impossible to obtain accurate estimate – very small. • 9x9 looks sufficient for Anisotropy • Remove bias is more difficult: 5x5 and above. 7x7 is recommended.

AVERAGED ALPHA ESTIMATION AVERAGED ALPHA ESTIMATION α is affected less by multi-looking, except for Surface • Underestimate or overestimate. • Peculiar asymptotic behavior for Volume • Sufficient using 5x5 independent looks • Bias compensation is required for Surface

AVERAGED ALPHA ESTIMATION AVERAGED ALPHA ESTIMATION Peculiar asymptotic behavior for Volume • High entropy – 3 scattering mechanisms λ ≈ λ ≈ λ 1 2 3 α • decreases asymptotically 1 α α • and increase asymptotically 2 3 α 1

ENTROPY BIAS REMOVAL ENTROPY BIAS REMOVAL The Ratio ( ) H n = H R ∞ ( ) Scattering mechanism dependent?

ENTROPY BIAS REMOVAL ENTROPY BIAS REMOVAL • Ratios are based on Complex Wishart statistical model • Linear relation (Surface) • Identical linear relation for other (Urban) L-Band PolSAR systems • Identical linear relation for other (Forest) frequencies (X-band C-band and P-band). ( ) H n Entropy bias removal: = H The Ratio R ∞ ( ) H ( n ) ˆ = o H ( n ) o R ( n )

ENTROPY BIAS REMOVAL ENTROPY BIAS REMOVAL AIRSAR L-band L-Band ALOS/ PALSAR from Tomakomai, Japan

ENTROPY BIAS REMOVAL ENTROPY BIAS REMOVAL L-band AIRSAR San Francisco

ENTROPY BIAS REMOVAL ENTROPY BIAS REMOVAL L-band PISAR from Tsukuba, Japan The Ratio

ENTROPY BIAS REMOVAL ENTROPY BIAS REMOVAL X-band PISAR from Tsukuba, Japan

ENTROPY BIAS REMOVAL ENTROPY BIAS REMOVAL H ( n ) = H R ∞ ( ) AIRSAR L-band

ENTROPY BIAS REMOVAL ENTROPY BIAS REMOVAL ( ) H n = H The Ratio R ∞ ( ) • X-band and L-band have the same ratio Frequency independent. • The ratio depends on the number of looks and H ( n )

ENTROPY BIAS REMOVAL ENTROPY BIAS REMOVAL ˆ ( 7 . 5 ) H 3x3 Average Bias removed H ( 7 . 5 ) 0 0 Entropy bias removal: H ( n ) ˆ = 0 H ( n ) 0 R ( n ) The 3x3 averaged data have ENL=7.5

ENTROPY BIAS REMOVAL ENTROPY BIAS REMOVAL ˆ ( 18 ) H , 5x5 Average Bias removed H ( 18 ) 0 0 H ( n ) ˆ = H ( n ) R ( n ) The 5x5 averaged data have ENL=18

ANISOTROPY BIAS REMOVAL ANISOTROPY BIAS REMOVAL E-SAR L-Band The Ratio A ( n ) = A R A ∞ ( ) Surface and volume scattering requires bias removal. Bias removal requires 49 looks data.

Anisotropy Bias Bias Removal Removal Anisotropy Ratio for Volume is very high cause the problem for bias removal. To compensate for bias for Volume class, create a ratio curve for Volume class alone. Do the same for Surface.

ANISOTROPY BIAS REMOVAL ANISOTROPY BIAS REMOVAL Anisotropy , 7x7 average Bias compensated 13x13 average Surface and volume scattering requires bias removal.

ALPHA BIAS EVALUATION ALPHA BIAS EVALUATION E-SAR L-Band The Ratio α ( ) n α = α ∞ ( ) Bias is very small Only the surface category requires bias removal

ALPHA BIAS EVALUATION ALPHA BIAS EVALUATION 7x7 Average 5x5 Average E-SAR L-Band 13x13 Average Only the surface scattering category may require bias removal for surface geophysical parameter estimation

SUMMARY SUMMARY • Evaluated the asymptotic behaviors of H and A as a function of the number of looks. • Bias removal: • Entropy – Robust linear characteristics • Linear relation is independent radar frequency and radar systems • 25 independent looks with bias removal • 49 without bias removal • Anisotropy • Bias removal is required for surface and volume • 49 independent looks with bias removal α • Alpha • Bias is small • Bias removal for entropy and alpha for surface is required for soil moister estimation

PIXEL CORRELATION EFFECT PIXEL CORRELATION EFFECT Assess the effect of over-sampling at 25%, 50% and 100% in both range and azimuth • Pixel correlations: 0.234 (25%), 0.415 (50%), 0.636 (100%) • At 50%, 5x5 looks has the same underestimate in Entropy of 3x5 (0%). • At 100%, very high number of looks is required to reduce bias.

PIXEL CORRELATION EFFECT PIXEL CORRELATION EFFECT Alpha Angle of λ 1 For Forest (Volume): α for forest has the same peculiar effect α Over sampling affects 1

MIXED PIXEL EFFECT MIXED PIXEL EFFECT Boxcar averaging includes mixed pixels • Mixed pixels affect surface scattering pixels: • Increase Entropy • Decrease Anisotropy • Change Averaged Alpha