A New Approach to Estimate Forest Parameters Using Dual-Baseline POL-InSAR Data

Transcription

1 Jan 26-30, 2009 Frascati, Italy A New Approach to Estimate Forest Parameters Using Dual-Baseline POL-InSAR Data Lu Bai, Wen ong, Fang Cao, Yongsheng Zhou bailu8@gmail.com fcao@mail.ie.ac.cn National Key Laboratory of Microwave Imaging Technology Institute of Electronics, Chinese Academy of Sciences

2 Outlines Forest Model in DoA Techniques Decorrelation Effects Dual-baseline Solution Experiment Results Conclusions 2/28

3 Forest Model in DoA Techniques Forest Characteristics Volume scatterers Vertical structure Canopy, trunk, ground Complex scattering Single, double, multiple scattering Average results of all echoes Scattering Mechanisms volume scattering dihedral scattering direct ground scattering Mechanisms are separable Their contributions can be regarded as returns from equivalent point-like scattering centers. Ref. Cloude S.R., Papathanassiou K.P. Polarimetric SAR Interferometry Figure. Pottier E. Advanced Concepts in POLSAR POL-InSAR Image Analysis /28

4 Forest Model in DoA Techniques Forest Model 4/28 SAR observation s s s d = E = s σ + n POLSAR Observation E k = 2EV = Sσ + n E VV = 4π 4π d j R j R λ d λ σ σ e σ e n: Addictive white Gaussian noise d: number of the independent scattering centers σ i : scattering amplitude of i th scattering center R i : slant range of i th scattering center T E Ref. Guillaso S. Polarimetric Interferometric SAR Data Analysis Based on ESPRIT /MUSIC Methods R 2 R R Polarimetric information d s... s d S = 2 sv... 2sV d svv... s VV d 3, V, VV : 3 dimensions At most 3 independent scattering mechanisms

5 Forest Model in DoA Techniques Forest Model POL-InSAR Observation k = S σ + n 2 = S2σ 2 + n2 k = 4π 4π d j R j R λ d λ σ σ e σ e T k 2 k 3 R 2 Ref. Yamada. Polarimetric SAR Interferometry for Forest canopy analysis by using the super-resolution method R 2 3 R R 2 2 R R 5/28 DoA Equivalent scattering centers are stable S S 2 σ i i σ R i i i 2 2 R +ΔR k = Sσ + n k = SΦ σ + n 2 2 Interferometric information 4π j ΔR λ e 0 Φ= 4π d j ΔR λ 0 e

6 Forest Model in DoA Techniques DoA Techniques Observations kk kk 2 C C S C6 = = = σσ + σ S Φ S E E kk 2 kk 2 2 C C SΦ Estimate signal subspaces Calculate interferometric phases Inverse forest height 2 2 n n n /28

7 Forest Model in DoA Techniques DoA Techniques MUSIC / CAPON P Signals are orthogonal to noises (large SNR) Search for peak spectrum defined as ( φ ) = a s a s ( φ) a ( φ) ( φ) R a ( φ) CAPON ( R = C ) ; MUSIC( R = E E ) Interferometric phases s s 6 2 i i i i * i * i * jφ i * jφ i * jφ i * a s ( φ ) = s 2sV svv e s e 2sV e s VV 4π i i j ΔR jφ λ * e e, conjugate, conjugate and transpose = n n 4π 4π j R j R λ Δ jφ λ Δ e = e,..., e = e d d jφ Ref. Kasilingam D. A Technique for Removing Vegetation Bias from Polarimetric SAR Interferometry. 7/28

8 Forest Model in DoA Techniques DoA Techniques ESPRIT Algorithm (SB ESPRIT) Eigen decomposition C = [ e... e... e ] Λ [ e... e... e ] 6 d 6 6 d 6 Signal subspaces Eigen vectors E X = λe... λde ST d = EY SΦT λ >... > λ λ... λ d d+ 6 EX E E2 E E2 [ X Y] = ' E E Λ EY E2 E22 E2 E22 λ ' >... > λ ' > λ ' >... > λ ' d d+ 2d Results T ΦT= E E = E Λ E 2 22 d d d 4π 4π d j ΔR j R d jφ λ Δ λ λ jφ e = e =,..., e = e = λ λd λ d 8/28 Ref. Guillaso S. Evaluation of the ESPRIT approach in polarimetric interferometric SAR.

9 Forest Model in DoA Techniques DoA Techniques Phase Difference between Ground and Canopy Single Stable Scattering Center Δ φ = 0 Two Stable Scattering Center Errors Caused by Phase unwrapping 2 { } Δ φ = Max φ φ Three Stable Scattering Center Phase difference between ground and canopy is the largest Errors Caused by Phase Unwrapping m k { } Δ φ = max φ φ mk, =,..., d 9/28 Forest eight Estimation h V Δφ = κ z

10 Decorrelation in Forest Problems Model Applicability good for equivalent scattering center in canopy? assumption for stable scattering center in forest inaccurate interferometric information volume scattering is strong but its coherence is low Interferometric Phases hard to identify canopy and ground information errors caused by phase unwrapping 0/28

11 Outline Forest Model in DoA Techniques Decorrelation Effects Dual-baseline Solution Experiment Results Conclusions /28

12 Dual-baseline solution Our aim Improve forest height estimations solve phase wrapping Estimate the stable scattering centers Separate the stable SM and the unstable SM: coherence Only use the SM with high coherence suffer less from temporal and volume decorrelation provide interferometric information of high quality Dual-Baseline Data Long Time interval changes of forest scatterers temporal decorrelation Additional Baseline distribution of scatterers volume decorrelation More interferometric phases estimate phase error provide accurate phase difference k 2 k 3 R 2 2 R 2 3 R R 2 2 R R 2/28

13 Dual-baseline solution 3/28 Proposed Approach Stable scattering centers always keep high coherences γ pq ω ω pq ( C ω) = ωc ω ωc ω DB Coherence Optimization pp qq optimization criteria ( ωc ω pq γ ω) = pq p q p q ωc ω ωc ω pq pq iterative estimation for optimal vector (Maxim) N m m jφ pq ωopt = λ C eω opt = C pqe, C e = pp p q N C Estimate number p= φ m m ( ) pq =arg ω opt C pq ω opt ω of Scattering m ω k = 0 opt opt Centers Signal components are separated according to coherences C = γ σ σ ω ω + γ σ σ ω ω + γ σ σ ω ω pq pq p q opt opt pq p q opt opt pq p q opt opt γ ( ω ) γ ( ω ) ( ) m m m ( σ = ω C ω ) m m m If there is coherence,, or γ ω lower than 0.5, the m th 2 opt 3 opt 23 opt scattering center is not stable. The number of stable scattering centers is d. Ref. Maxim N., Lauren F. Andreas R. Polarimetric Coherence Optimization for Multibaseline SAR Data p opt pp opt

14 Dual-baseline solution 4/28 Dual-Baseline ESPRIT Algorithm (DB ESPRIT) Eigen decomposition Signal subspaces Eigen vectors C C2 C3 C9 = C2 C22 C23 C 3 C32 C33 = [ e... e... e ] Λ [ e... e... e ] d 9 9 d 9 EX ST E = λ e... λ e = SΦ T Y d d 2 E Z SΦ3T E X EY [ EX EY EZ] = EΛ3dE EZ E E2 E3 Obtain sub matrices satisfying E E E E = E E E X 2 Y 22 Z 32 X 3 Y 23 Z 33 Estimate interferometic phases m m φ2 = arg ( λ2 ) from ( )( ) m m φ3 = arg λ3 ( )( ) ( ) E E + E E + E E = 0 E E + E E + E E = 0 2 = = d2λd2 d2 T Φ T E E E E E E E E E E 3 = = d3λd3 d3 T Φ T E E E E E E E E E E

15 Proposed Approach Dual-baseline solution Interferometric Phases Suppress volume and temporal decorrelation { d d d γ, γ, γ }...{ γ, γ, γ } Obtain the interferometric Phases of igh Quality ( ) ( ) ( ) φ = arg γ, φ = arg γ, φ = arg γ ( ) ( ) ( ) φ = arg γ, φ = arg γ, φ = arg γ d d d d d d /28

16 Dual-baseline solution Phase Estimation Direct Phase Estimation problems: unwrapping three unknowns two equations Phase Unwrapping intergral number m2, m3 satisfying m m κ z2h = φ2 + 2m2π m m κ z3h = φ3 + 2m3π 6/28

17 Phase Estimation Dual-baseline solution Estimate Interferometric Phase Difference Phase difference would not exceed the range Select Phase Combination ( 2 π,2π 7/28 according to mk mk { φ, φ } m k m k { φ φ, φ φ } m k m k { 2 π φ φ, φ φ } m k m k { φ φ,2π φ φ } m k m k { 2 π φ φ,2π φ φ } Δ Δ = 2 3 and sin ce mk mk ( κz2 κz3 )( φ2 φ3 ) Δ Δ 0 Min Δφ κ Δφ κ mk mk 2 z3 3 z2 Δ h = Δ φ κ = Δφ κ mk mk mk 2 z2 3 z3 2

18 Dual-baseline solution height difference estimation using least square method ( 2 2 ) κ 2 φ 2 κ 3 φ 3 mk mk mk mk mk Δ h est = Min z Δh Δ + z Δh Δ h = Max Δh V ( mk ) eight difference between ground and canopy is the largest. est Suppress phase errors Ref. Cloude SR. and Papathanassiou KP Three-stage inversion process for polarimetric SAR Interferometry /28

19 Outline Forest Model in DoA Techniques Decorrelation Effects Dual-baseline Solution Experiment Results Conclusions 9/28

20 Experimental Data 20/28 L band ESAR Data Truanstein, Germany (2003) pixel Master Data Slave- Data (B2) 20 minutes interval Slave-2 Data (B3) Bh BV Bh = m = 0.067m B V = = 0.30m minutes interval Test Site Eight Forest Areas Known Forest eights V VV Google Earth Map

21 2/28 Experiment Design SB ESPRIT (B3) vs DB ESPRIT(B2-B3 ) DB ESPRIT Centers number estimated from Coherence optimization separate signal subspaces estimate forest height analyze the improvement brought by additional baseline DB ESPRIT vs Proposed Approach DB ESPRIT Centers number estimated from Coherence optimization separate signal subspaces interferometric phase for dual-baseline calculate height differences and forest height Proposed Approach Centers number estimated from Coherence optimization interferometric phase for dual-baseline calculate height differences and forest height discuss the influence of decorrelations SB ESPRIT discuss errors caused by phase unwrapping

22 EXPERIMENTAL RESULTS Forest eight SB ESPRIT overestimation DB ESPRIT Under estimation Proposed Approach Closest estimation Reference height SB ESPRIT DB ESPRIT Proposed Approach 22/28

23 EXPERIMENTAL RESULTS Average Forest eight SB ESPRIT Large overestimation DB ESPRIT Closer estimation Proposed Approach Closest Estimation Effective to handle phase unwrapping and phase error Test Areas SB ESPRIT DB ESPRIT Proposed Approach Indicator Reference eight Average eight Average eight Average eight T T T T T T T T /28

24 EXPERIMENTAL RESULTS Deviation from Reference eight DB ESPRIT Large deviation Proposed Approach Smaller deviation Test Areas SB ESPRIT DB ESPRIT Proposed Approach Indicator Reference eight Deviation (m) Deviation (m) Deviation (m) T T T T T T T /28 T

25 Forest Model in DoA Techniques DoA Techniques Phase Difference between Ground and Canopy Single Stable Scattering Center Δ φ = 0 Two Stable Scattering Center Errors Caused by Phase unwrapping 2 2 {,2 } Δ φ = Max φ φ π φ φ Three Stable Scattering Center Phase difference between ground and canopy is the largest Errors Caused by Phase Unwrapping m k m k { } Δ φ = max φ φ,2 π φ φ mk, =,..., d 25/28 Forest eight Estimation h V Δφ = κ z

26 EXPERIMENTAL RESULTS SB ESPRIT Considering Phase Unwrapping () mk, =,..., d Neglect Phase Unwrapping (2) m k Δ φ = Max φ φ mk, =,..., d m k m k {,2 } Δ φ = Max φ φ π φ φ { } Reference height SB ESPRIT SB ESPRIT2 Test Areas SB ESPRIT SB ESPRIT 2 Indicator Reference eight Average eight eight Deviation Average eight eight Deviation T T T T T T T /28 T

27 Outline Forest Model in DoA Techniques Decorrelation Effects Dual-baseline Solution Experiment Results Conclusions 27/28

28 Conclusions- Dual-baseline data Additional observation detect the change of scattering center the interferometric phase differences between different baselines provide additional information for stable scattering center Use the phase differences to improve height estimate (SB ESPRIT vs DB ESPRIT) Estimate scattering centers number keep high coherence all the time Proposed Approach Coherence Optimization Suppress volume and temporal decorrelation Improve the quality of interferometric phases eight difference Estimation andle the phase unwrapping Provide accurate phase estimations 28/28

29 Jan 26-30, 2009 Frascati, Italy Please contact via National Key Laboratory of Microwave Imaging Technology Beijing, 0090, P. R. China Institute of Electronics, Chinese Academy of Sciences Beijing, 0090, P. R. China