POLINSAR 2009 WORKSHOP 26-29 January 2009 ESA-ESRIN, Frascati (ROME), Italy Evaluation and Bias Removal of Multi-Look Effect on Entropy/Alpha /Anisotropy (H/ (H/α/A) Jong-Sen Lee*, Thomas Ainsworth Naval Research Laboratory Washington DC 20375, USA * 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 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 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 DECOMPOSITION TARGET VECTOR LOCAL ESTIMATE OF THE COHERENCY MATRIX 1 k = S + S S S S 2 [ XX YY XX YY 2 XY ] 1 N 1 N N N i= 1 i= 1 * [ T] = ki k T i = [ Ti ] T * T 1 * T 2 [ T ] = λ u u + λ u u + λ u 1 1 2 2 3 3 u * T 3 3 SCATTERING PROCESSES S.R. CLOUDE E. POTTIER [ U 3 ] = cos( α 1) cos( α 2) cos( α 3) j sin( )cos( )e 1 j α sin( )cos( )e sin( )cos( )e 1 β1 α 2 β 2 2 α 3 β3 j sin( 1)sin ( 1 )e 1 j α β sin( α 2) sin ( β2)e 2 sin( α 3)sin( β3)e δ δ jδ3 γ γ jγ 3
H / A / α DECOMPOSITION H = P i ENTROPY = 3 i= 1 λ 3 k= 1 P log i λ i k 3 ( P i ) α PARAMETER α = P + + 1α 1 P2α 2 P3 α 3 ROLL INVARIANT PARAMETERS 3 ANISOTROPY A = λ2 λ3 λ + λ 2 3 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 HH-VV, HV, HH+VV Freeman and Durden Decomposition H Original (4 looks) 5x5 9x9
Anisotropy and α VERSUS MULTI-LOOKING LOOKING A Anisotropy Original (4 looks) 5x5 9x9 α ALPHA
SIMULATION AREA SELECTION E-SAR L-BAND POLSAR DATA OF OBERPFAFFENHOFEN Urban (D. B.) Forest (Volume) Freeman/Durden Decomposition Grass (Surface)
SIMULATION PROCEDURE For a given <T>, simulate single-look complex data: 1. Compute T T 1/ 2 1/ 2 ( T 1/ 2 ) *T = 2. Simulate a complex random vector,, CN(0,I) T ν 3. Form a single-look complex vector u = T 1/ 2 ν 4. Compute a n look covariance matrix, T 1 n n 1 * T 5. Compute the n look H/A/α n = uu Verification: E[ uu T ] = T 1/ 2 E[ vv T ]( T 1/ 2 ) * T = T
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 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 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 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 Peculiar asymptotic behavior for Volume High entropy 3 scattering mechanisms λ1 λ2 λ3 α 1 decreases asymptotically and α increase asymptotically α2 3 α 1
ENTROPY BIAS REMOVAL The Ratio H( n) R = H ( ) Scattering mechanism dependent?
ENTROPY BIAS REMOVAL Ratios are based on Complex Wishart statistical model (Surface) Linear relation (Urban) Identical linear relation for other L-Band PolSAR systems (Forest) Identical linear relation for other frequencies (X-band C-band and P-band). The Ratio R H( n) = H ( ) Entropy bias removal: Hˆ o ( n) = H o ( n) R( n)
ENTROPY BIAS REMOVAL AIRSAR L-band L-Band ALOS/ PALSAR from Tomakomai, Japan
ENTROPY BIAS REMOVAL L-band AIRSAR San Francisco
ENTROPY BIAS REMOVAL The Ratio L-band PISAR from Tsukuba, Japan
ENTROPY BIAS REMOVAL X-band PISAR from Tsukuba, Japan
ENTROPY BIAS REMOVAL H( n) R = H ( ) AIRSAR L-band
ENTROPY BIAS REMOVAL The Ratio H( n) R = H ( ) 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 3x3 Average H 0 (7.5) Bias removed ˆ 0(7.5) H Entropy bias removal: ˆ H ( ) ( ) 0 n H 0 n = R( n) The 3x3 averaged data have ENL=7.5
ENTROPY BIAS REMOVAL H 0 (18), 5x5 Average Bias removed Hˆ 0(18 ) H ˆ ( n) = H( n) R( n) The 5x5 averaged data have ENL=18
ANISOTROPY BIAS REMOVAL E-SAR L-Band The Ratio R A A( n) = A ( ) Surface and volume scattering requires bias removal. Bias removal requires 49 looks data.
Anisotropy Bias Removal 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, 7x7 average Bias compensated 13x13 average Surface and volume scattering requires bias removal.
ALPHA BIAS EVALUATION E-SAR L-Band The Ratio α = α( n) α( ) Bias is very small Only the surface category requires bias removal
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 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 Alpha α Bias is small Bias removal for entropy and alpha for surface is required for soil moister estimation
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 Alpha Angle of λ 1 For Forest (Volume): α for forest has the same peculiar effect Over sampling affects α 1
MIXED PIXEL EFFECT Boxcar averaging includes mixed pixels Mixed pixels affect surface scattering pixels: Increase Entropy Decrease Anisotropy Change Averaged Alpha