POLARIMETRIC COHERENCE OPTIMIZATIONFOR MULTIBASELINE SAR DATA

Maxim Neumann1,2, Laurent Ferro–Famil1 and Andreas Reigber2

1 IETR Laboratory, UMR CNRS 6164, University of Rennes 1Campus de Beaulieu Batiment 11D 263 Avenue General Leclerc, CS 74205 35042 Rennes Cedex, France

2 Berlin University of Technology, Computer Vision and Remote Sensing Group,Franklinstrasse 28/29, Sekretariat FR3-1, D-10587 Berlin, Germany

Email: maxn@cs.tu-berlin.de

Abstract— This paper analyzes different approaches forpolarimetric optimization of multibaseline interferometriccoherences. Two general methods are developed which simul-taneously optimize coherences for more than two datasets.The first method is based on multiset canonical correlationanalysis, and it provides every dataset with a distinguisheddominant scattering mechanism. The second optimizationmethod is constrained to the use of an identical scatteringmechanism for every dataset. A framework for a multi-baseline orthogonal optimal scattering mechanisms decom-position is presented. The both methods are evaluated onreal data acquired by DLR’s ESAR sensor at L–band.As experimental results indicate, preferring simultaneousmultibaseline coherence optimization to single–baseline opti-mization improves the estimation of the dominant scatteringmechanisms and their interferometric phases.

I. INTRODUCTION

Polarimetric signal to clutter and contrast optimizationproblems led to the development of different optimizationmethods for polarimetric radar data. With the introductionof polarimetric SAR interferometry (POLINSAR) a co-herence optimization technique was presented by Cloudeand Papathanassiou [1]. This method was developed firstand is considered the most general one, since it allowsdifferent polarization states at the two baseline ends. Muchattempt has be been devoted to the optimization of thePOLINSAR coherence using equal polarization states atbaseline ends, e.g. by Sagues et al. [2], Flynn et al. [3],Gomez–Dans and Quegan [4], Qong [5], and Colin et al.[6]. However, no analytical solution to the given problemis possible with the current state of mathematics. Theapproach by Colin et al. [6] can be considered as the mostfundamental, since she identified the coherence maximum(using equal polarization states) as the numerical radiusof the modified POLINSAR coherency matrix, a wellknown concept from matrix analysis [7]. Another classof POLINSAR optimization techniques deals with theoptimization of interferometric phases, as in Tabb et al.[8], or with identifying the most dominant interferometricphase centers as in Yamada [9].

POLINSAR optimization provides each illuminated res-olution cell with the polarimetric scattering mechanism(SM) of the highest coherence value. In the case of non–volumetric scatterers, coherence optimization techniques

are used, for example, to maximize the signal–to–noiseratio. This maximization allows to estimate the topographymore accurately. Polarimetric coherence optimization isalso applied to vertically structured media for obtainingdominant scattering centers.

However, in the attempt to increase the accuracy of re-mote sensing, POLINSAR methods are going to be appliedto multiple baselines. To analyze effectively multibaseline(MB) data and to extract the most important out of theredundant information, new methods have to be developed.Thus, this paper aims to provide a framework for simulta-neous polarimetric optimization of MB coherence. Given aset of multibaseline datasets, coherences can be optimizedindependently for every baseline. This partly reproducesthe results and errors and leads to different dominantscattering centers in dependence of the chosen baseline.A better approach to find the most coherent and dominantscatterer is a simultaneous optimization of multibaselinecoherences. This approach will lead to lower coherencemagnitudes, but the corresponding scattering mechanismsand their interferometric phases will be estimated includ-ing all available information more accurately.

Most of the current air–borne and space–borne POLIN-SAR systems have spatial and temporal baseline sepa-rations. Considering baseline separation properties, twocoherence optimization criteria come to mind. With prox-imate baselines one would prefer to extract equal scat-tering mechanisms (ESM) with highest coherence. Withmore diverged baseline properties, another idea is morereasonable, that is to use slightly different polarizations(multiple scattering mechanisms, MSM) at different tracksto estimate the coherence of the dominant scatterers. E.g.,due to higher spatial baselines, geometric properties ofscatterers can be changed in regard to the radar coordinatesystem. A temporal change might also cause a change ofSM for the same scatterers, e.g. meteorological influencesor vegetation growth. These two approaches are analyzedfor simultaneous MB coherence optimization.

This paper is organized as follows. Section II brieflyintroduces MB–POLINSAR data processing. Section IIIanalyzes concepts for multibaseline optimization and twoalgorithms are developed. Finally, the results of initialexperiments are presented and discussed in Section V.

Fig. 1. Schematic multibaseline configuration with three separatedtracks.

II. MULTIBASELINE POLARIMETRIC SARINTERFEROMETRY

A multibaseline n–track geometry contains n2 (n − 1)

direct baselines, as shown for instance for threedatasets in Fig. 1. The tracks (nodes) represent thepolarimetric information, while baselines (arrows)represent polarimetric and interferometric relationshipbetween any pair of tracks. Fully polarimetric, monostaticdata can be represented in the Pauli basis, assumingreciprocity, for every track i ∈ [1, n] by the scatteringvector ki:

ki = 1√2[SHH

i + SV Vi , SHH

i − SV Vi , 2SHV

i ]T (1)

The MB–POLINSAR coherency matrix T, representingestimated covariances between polarimetric and interfero-metric channels, is generated by multi–looking of the outerproduct of the aggregated scattering vector k:

T =⟨kk†

⟩=

[ T11 ... T1n

.... . .

...T†

1n ... Tnn

], with k =

[k1

...kn

](2)

where 〈〉 represents the multi–looking operator, and †

the Hermitian transformation. While Tii contain onlypolarimetric information (baseline is equal to zero), thematrices Tij (i6=j) contain polarimetric and interferometricinformation which is baseline dependent. To emphasizethis difference in information content, matrices Tij (whichare not Hermitian anymore, contrary to Tii) are also oftendenoted by Ωij .

Crucial to polarimetric interferometry is the conceptof scattering mechanism (SM), which can be understoodas a representation for polarization states in the transmitand receive channels, or as a parameterization related tophysical characteristics of scatterers (hence the name).For the monostatic case, the SM vector corresponds toa complex unitary vector ω ∈ C3 with four degrees offreedom. To extract the scattering coefficient for some spe-cific transmit/receive polarizations, the scattering vectoris projected along the scattering mechanism: Si = ω†

iki.SM vectors can be used to examine the covariance of thetwo interferometric datasets i, j along specific polariza-tion states ωi,ωj : σij =

⟨SiS

∗j

⟩= ω†

iΩijωj . In thecommon case, the covariances are examined along equalpolarizations, utilizing the same SMs: ωi = ωj . Generally,the corresponding interferometric coherence and phase

estimates are the following:

γij(ωi,ωj) = |γ|eiφ =σij√σiiσjj

=ω†

iΩijωj√ω†

iTiiωiω†jTjjωj

(3)

The interferometric coherence and phase for same polar-ization (ωi = ωj) can be modeled by means of dominantcontributions [10]:

|γij(ω)| = γtempγthermγgeomγerr

φij(ω) = φtopo + φerr + ∆φprop + ∆φscat(4)

The coherence is modeled as a product of terms related totemporal, thermal, and geometrical decorrelation, as wellas processing errors. The interferometric phase consistsof the topographic phase of scatterers, error phase term,the phase difference due to propagation effects, and phasechange due to changes related to the scatterers, includingdisplacement and scattering behavior change. In general, itcan be assumed that most of the terms depend on baselineand polarization. The indices have been omitted for thesake of readability. Polarization diversity at baseline endscan be introduced into these functions with two additionalterms ηpol and φpol, which represent the modification incoherence magnitude and phase due to the change ofpolarization at the second baseline end in respect to thefirst one:

|γij(ωi,ωj)| = |γij(ωi)|ηpol(ωi,ωj), ηpol ∈ R ≥ 0 (5)

φij(ωi,ωj) = φij(ωi) + φpol(ωi,ωj), φpol ∈ R (6)

These values can be obtained from measured coherencesat given polarizations:

ηpol(ωi,ωj) =|γij(ωi,ωj)||γij(ωi,ωi)|

φpol(ωi,ωj) = arg γij(ωi,ωj) − arg γij(ωi,ωi)

(7)

The coherence modification term ηpol is not anymorerestricted to be ≤ 1, although |γij(ωi,ωj)| still is. This isa simplified but sufficient model for the purpose of thispaper.

Any individual scattering vector and any coherency ma-trix can be transformed from the acquisition polarizationbasis to an arbitrary one via special unitary transformationmatrices:

k′i = Uiki T′ij = UiTijUj

† i, j ∈ [1, n] (8)

Every transformation matrix Ui can be considered to beconstructed by three unitary orthogonal vectors ω

a,b,ci

(associated with the scattering mechanisms): Ui =[ωa

i ,ωbi ,ω

ci ]†. Generalizing to the MB coherency matrix,

the block diagonal matrix U =⊕n

i=1 Ui is utilized:

T′ = UTU†, with U =

[U1 ... 0

.... . .

...0 ... Un

](9)

φopt23

γopt23

γopt13

φopt13

φopt12

γopt12

ωopt1 ω

opt2 ω

opt3

k3k1 k2

ωopt1 ω

opt2 ω

opt3

ωopt1ω

opt3ω

opt2

maximizeω1,..,ωn

∑|γij(ωi,ωj)

|

Fig. 2. Symbolic representation of the MB–MSM coherence op-timization. For the three given datasets, the coherence is optimizedsimultaneously delivering the most coherent dominant scattering mech-anism allowing different polarization signatures at different datasets.This provides the possibility to track changes in polarization along thedatasets.

III. MULTIBASELINE COHERENCE OPTIMIZATION

Contrary to the independent single–baseline coherenceoptimization methods, the multibaseline methods opti-mize coherences simultaneously. Thus they are expectedto deliver better estimates for optimized interferometricphases and dominant scattering mechanisms. The generalmultibaseline optimization problem can thus be stated as:

maximizeω1,...,ωn

n∑i=1

n∑j>i

|γij(ωi,ωj)| (10)

The general multibaseline multiple scattering mechanisms(MB–MSM) method can provide every track with a dis-tinctive scattering mechanism as symbolically shown inFig. 2. This approach allows to optimize the coherencefor SMs that might have different polarimetric signa-tures in different datasets. The multibaseline equal scat-tering mechanisms (MB–ESM) method supposes equalpolarimetric signatures of scatterers along all baselines(ωi=ωj ∀ i, j), see Fig. 3. The the application of thismethod is restricted to the use of only one SM for thedominant scatterer.

As it can be shown, there are no exact analytical meth-ods applicable for these optimization problems. However,two algorithms will be presented that help to achievesuch optimizations with a high degree of accuracy andstraightforwardness, as firstly presented in [11].

A. Multiple Scattering Mechanisms(MSM) Optimization

The single–baseline coherence optimization (SB–MSM)[1], a canonical correlation analysis (CCA) problem [12],optimizes the modulus of the covariance ω†

iΩijωj for twodatasets i, j, while keeping the variances ω†

iTiiωi andω†

jTjjωj constant. In [1], the modulus of the complexLagrangian L is maximized by introducing the real valued

ωopt

φopt23

γopt23

γopt13

φopt13

ωoptωopt

φopt12

γopt12

ωopt ωopt ωopt

k3k1

maximizeω

∑|γij(ω)|

k2

Fig. 3. Symbolic representation of the MB–ESM coherence optimiza-tion. For the three given datasets, the coherence is optimized simultane-ously delivering the most coherent dominant scattering mechanism forall datasets.

multipliers λi, λj :

L = ω†iΩijωj − λi(ω

†iTiiωi − 1)− λj(ω

†jTjjωj − 1)

(11)As has been shown, the solution can be obtained bysetting the partial derivatives of L with respect to variablesλi, λj ,ωi,ωj to zero:

∂L∂λi

= ω†iTiiωi − 1 = 0 (12)

∂L∂λj

= ω†jTjjωj − 1 = 0 (13)

∂L

∂ω†i

= Ωijωj − λiTiiωi = 0 (14)

∂L†

∂ω†j

= Ω†ijωi − λjTjjωj = 0 (15)

Optimal SMs and corresponding coherences are obtainedfrom the resulting eigenvalue problems:

T−1jj Ω†

ijT−1ii Ωijωj = λiλjωj (16)

T−1ii ΩijT−1

jj Ω†ijωi = λiλjωi (17)

Since Tii,Tjj are hermitian and positive definite, theinverses, as well as square roots, of these matrices exist.One can show that λi = λj = λ by left multiplying (14)and (15) with ω†

i and ω†j , and using (12), (13) and the fact

that ω†iΩijωj = (ω†

jΩjiωi)†. Furthermore, the complexLagrange function (11) can be transformed into a realvalued function. These two modifications allow to expressthe optimization problem in the following notation:

L =n∑

i=1

n∑j=1 6=i

ω†iΩijωj − λ

n∑i=1

(ω†iTiiωi − 1) (18)

This function is real valued due to the fact that the firstterm of L stands for the sum of Re(ω†

iΩijωj) for all i 6=j, because ω†

iΩijωj = (ω†jΩjiωi)†. This modification

uses the phase ambiguity between ωi and ωj (arg(ω†iωj))

to cause a shift of coherence phases towards the zero

phase. The second term in (18) is always real valuedbecause it contains quadratic forms of hermitian matrices.For n = 2, the optimization problem formulated in (18) isequivalent to (11), i.e. to a single–baseline case.

Consideration of more than two datasets is referred tothe multiset canonical correlation analysis (MCCA) [13].Setting the partial derivatives of (18) to zero will lead tothe following generalized eigenvalue problem that opti-mizes a linear combination of coherences (i ∈ [1, . . . , n]):

n∑j=1 6=i

Ωijωj = λTiiωi ⇐⇒ Aω = λBω ⇐⇒ 0 Ω12 ... Ω1n

Ω21 0 ... Ω2n

......

. . ....

Ωn1 Ωn2 ... 0

ω1ω2

...ωn

= λ

T11 0 ... 00 T22 ... 0

......

. . ....

0 0 ... Tnn

ω1ω2

...ωn

(19)

The optimized coherence modulus for the SB case is equalto the largest eigenvalue in Eq. (19) and the square root ofthe largest eigenvalues in Eqs. (16) and (17). For more thantwo datasets, the largest eigenvalue does not correspondto the optimized coherence moduli any longer. However,the eigenvectors include the optimal SMs, though un–normalized and containing phase ambiguities. Both theseissues, if not removed, might distort the interpretation ofoptimal SMs and interferometric phases.

MB–MSM coherence optimization can be summarizedby the following algorithm:

1) Obtain eigenvectors from the generalized eigenvalueproblem (19): Aω = λBω, where

A = T − B, B =n⊕

i=1

Tii,⊕

is the direct sum

operator.2) Normalize the SM vectors from ω = [ω1, . . . ,ωn]T

so that for all i ∈ [1, n] : ω†iωi = 1.

3) Remove the phase shift from these vectors in refer-ence to one arbitrary track m ∈ [1, n], so that for alli ∈ [1, n] : arg(ω†

mωi) = 0.4) Compute, when desirable, optimized coherences

according to (3) using normalized and phase–ambiguity removed scattering mechanism vectorsωi.

B. Equal Scattering Mechanisms(ESM) Optimization

Often, polarimetric coherency matrices Tii are verysimilar, assuming relative small temporal and spatial sep-aration of datasets. The utilization of different SMs atbaseline ends becomes less important. In [6] an opti-mization method is presented for single–baselines, whichconstrains the optimized SMs to be equal at all baselineends (SB–ESM). It is based on the numerical range [7],[14] properties of the modified polarimetric interferometriccoherency matrix Πij .

Πij = T−1/2e ΩijT−1/2

e , where Te = 1n

n∑i=1

Tii (20)

For the single–baseline case, as in [6], i = 1, j = 2, n = 2.The numerical range of matrix Πij , W(Πij), can be seenas the set of all coherences γ of Πij .

γij(w) = w†Πijw, w =√

Teωω†

√Teω

(21)

W(Πij) = x†Πijx : x ∈ C3,x†x = 1 (22)

The maximal coherence modulus of Πij corresponds tothe numerical radius r(Πij).

r(Πij) = max|x†Πijx| : x ∈ C3,x†x = 1 (23)

In [6] an iterative method [15] is used to compute r(Πij)for the single–baseline case.

At this point, an extension of the SB algorithm to themultibaseline case (MB–ESM) is presented. The coher-ence sum function

∑|γij(w)| is taken as the optimization

criterion, where the SMs are all equal: wi = wj = wfor all i, j ∈ [1, n]. In an attempt to cancel the modulusoperation, the phase shift variables θij∈[−π, π], θij=−θji,are introduced to validate the inequality:

maxw

n∑i=1

n∑j=1 6=i

γij(w)e−iθij ≤ max

w

n∑i=1

n∑j=1 6=i

|γij(w)|

(24)The left term is real valued, since γij(w)e

−iθij =(γji(w)e

−iθji)†, similar to the condition for Eq. (18). Themaximum on the left side depends on the given set ofphase shift variables θij, while the maximum on theright side is constant. Equality is achieved when phaseshifts are equal to the phases of optimal coherences, sothat the real parts of the phase shifted optimal coher-ences are equal to the coherence moduli. Therefore, theoptimization process consists in the simultaneous searchfor the optimized coherence phases and the correspondingoptimal scattering mechanism. Like in the single–baselineapproach, the MB–ESM coherence optimization is notanalytically solvable. However, an efficient iterative op-timization method is presented which converges asymp-totically towards a maximum in a few (i.e. 2–5) iterations.

An estimate for the optimal SM can be obtained fromthe eigenvector associated with the largest eigenvalue ofthe combined Hermitian matrix H in

Hw = λw, where H =n

4(n− 1)

n∑i=1

n∑j=1 6=i

Πije−iθij

(25)Estimates for optimal phase shifts are in turn obtainedfrom

θij = arg(w†Πijw) (26)

The phase shifts can then be reintroduced in (25) to obtainan improved estimate of the optimal SM w. By iterativelyadjusting the phase shifts θij one obtains further improvedestimates for w.

To note is that this method might lead to a sub–optimallocal maximum. To circumvent this, one can performseveral optimizations with different initial phase shifts orone can complicate the algorithm. Another approach is

Fig. 4. Scene in Pauli matrix basis.

an efficient way of initialization. According to the factthat ESM coherence sets describe simple convex filledregions in the unitary complex coherence plane [6], phaseshift angles θij can be initialized with the trace phasesof Πij . Such an initialization significantly improves theoptimization performance with respect to the number ofiterations and robustness of locating the global maximum.In cases of highly different POLSAR matrices, the ESMcoherence optimization might fail to maximize coherencestowards a global maximum. In such cases, the MSMcoherence optimization method should be preferred.

Finally, the structure of the whole MB–ESM coherenceoptimization algorithm is given by:

1) Initialization: θij = arg(traceΠij); λ = 02) Computation of H and w from (25) with current

estimates of optimal phase shifts θij . w is theeigenvector corresponding to the highest eigenvalueλmax.

3) Improved estimation of θij via (26) using computedw.

4) Termination criterion: λmax − λ ≤ ε, where ε is anarbitrary small constant. If the criterion is not met,then λ = λmax and go to step 2).

5) The optimal SM vector ω and corresponding op-timal coherences are calculated from w via ω =T−1/2

e w/(w†T−1/2e w) and (21).

IV. ORTHOGONAL SCATTERING MECHANISMDECOMPOSITION

SB–MSM optimization provides the property, that SMscorresponding to the highest three eigenvalues are or-thonormal, and build an orthogonal optimal scatteringmechanism decomposition (ω1

i⊥ω2i⊥ω3

i ). This is in gen-eral not the case for MB–MSM and MB–ESM. In thefollowing, a framework is presented, which generates thisorthogonal decomposition for multibaseline optimizationmethods.

After the first optimization, the most coherent SMvectors ω1

i and corresponding optimal coherences γ1i are

obtained. A second optimization is applied in a polariza-tion subspace U⊥

i , which builds the orthogonal comple-ment to the optimal SM: U⊥

i ω1i = 0. This condition

is fulfilled with U⊥i = [0,ωb

i ,ωci ]†, where ωb

i and ωci

build an orthonormal basis together with ω1i and are

SB–MSM

SB–ESM

MB–MSM

MB–ESM

0 0.5 1

Fig. 5. Optimal coherence moduli distribution in the Oberpfafenhoffenscene: forested region with 5 baselines. The lines correspond, from topto bottom, to SB–MSM, SB–ESM, MB–MSM and MB–ESM.

computed e.g. via Gram–Schmidt orthogonalization. Tis transformed with U⊥ =

⊕ni=1 U⊥

i as shown in (9),and the optimization is applied. Obtained optimal SMs inthe subspace ω⊥1

i have to be transformed back: ω2i =

U⊥†ω⊥1i . The obtained coherence values are the highest

simultaneously maximized coherences in the polarizationsubspace orthogonal to the first optimal coherence. Thethird optimal SM vector is received as the orthogonalcomplement to the first two: ω3

i = ω1i × ω2

i . With thisprocedure one obtains three optimal orthogonal SMs forevery dataset and the corresponding optimal coherences.

V. EXPERIMENTAL RESULTS AND DISCUSSION

The performance of optimization methods greatlydepends on acquisition system configuration (baselinelengths, acquisition times, frequency) and scattering me-dia. It is impossible to evaluate objectively the applica-tion of the proposed methods in different configurationscenarios. However, the initial evaluation experiments onreal data are presented to emphasize the difference and thesensitivity of the proposed MB– versus the SB– coherenceoptimization methods.

The test scene in the Oberpfaffenhofen area, Fig. 4, con-tains diverse scattering media, including forests, surface,and urban areas. Utilized are 5 tracks with baselines be-tween 5 and 37 meters and temporal separations between15 minutes and one hour. All datasets have been treatedwith equal pre–processing procedures, including flat–earthremoval, range spectral filtering, and multi–looking with16 looks. To underline is that multi–looking was doneby spatial summing–up, and not smoothing. This ensuresa high degree of statistical independence of neighboringpixels.

Figs. 6 and 8 present coherence moduli and coherencephases after optimization with SB–MSM, SB–ESM, MB–MSM, and MB–ESM methods respectively. The corre-sponding baseline has a 5 meters spatial and 15 minutestemporal separation. Fig. 7 presents the moduli of or-thogonally decomposed optimized coherences. The mod-uli images provide visual evidence that single–baselineoptimized coherences achieve higher values than theirmultibaseline counterparts. The decrease of coherencemoduli for multibaseline coherence optimization can alsobe observed on coherence moduli histograms for the given

(a) SB–MSM (b) SB–ESM

(c) MB–MSM (d) MB–ESM

Fig. 6. |γopt| over the first baseline: 5m, 15min.

scenes in Fig. 5. This all is related to the number ofconstraints and the dimension of the available searchspace. Conspicuous, especially over forested areas, isthe contrast improvement of MB optimization techniques.This tendency might be interpreted as the reduction ofoptimal coherence bias, which can also be caused by voidoptimization over the noise subspace. Here lies the advan-tage of utilizing numerous baselines for the optimization:By interferometric baseline–dependent multi–looking, i.e.by deliberately chosen baselines, the optimal coherencebias might be reduced. However, further experiments haveto be carried out to evaluate bias reduction possibilities ofMB optimization techniques.

To remember is the major difference between the SBand the MB methods. Since the single–baseline methodsoptimize coherences independently, they acquire highercoherence values, but corresponding phases and scatter-ing mechanisms will be different, relating to differentdominant scattering centers. Such effect can be exam-ined in relation to interferometric phases of optimizedcoherences and their spatial variances. The differences ofoptimized coherence phases in Figs. 8 are hardly visible.However, examination of the local phase correlation overhomogeneous areas reveals the improvement of the phasestability with a higher number of baselines. The correlationof optimized phases ρφ is computed from the alreadyoptimized coherence phases over a local window of N

(a) SB–MSM (b) SB–ESM

(c) MB–ESM (d) MB–MSM

Fig. 7. Orthogonal optimal coherence decomposition for baseline5m, 15min after SB and MB (5 tracks) optimization. Color com-position: Red: |γopt2

12 |, Green: |γopt112 |, Blue |γopt3

12 |.

pixels:

ρφ = |⟨eiφ

⟩| = | 1

N

N∑j=1

eiφj |, where φj = arg γoptj

(27)Examined are a few fields in the lower right edge ofthe Oberpfaffenhofen test site. This area is assumed tobe homogeneous and devoid of topographic variations.Fig. 9 shows the local phase correlation ρφ for differentmethods using a 7 by 7 averaging window. Presented is theaveraged correlation for all baselines. The diagram in Fig.10 presents the results of calculating the mean correlationcoefficient exclusively for homogeneous fields and fordifferent averaging windows. These results demonstratethe improvement of phase stability by utilization of simul-taneous multibaseline coherence optimization methods forboth MSM and ESM.

VI. CONCLUSION

Multibaseline coherence optimization concepts havebeen analyzed and two optimization algorithms have beendeveloped for the most general cases: one with multiplescattering mechanism (MSM) at baseline ends, and onewith equal scattering mechanisms (ESM). Initial exper-iments regarding MB coherence optimization propertieshave been conducted and discussed.

By using the optimal scattering mechanism along allbaselines by the same track–dependent scattering mecha-nisms, it is still possible to achieve very high coherences,coming close to single–baseline optimized coherences. It

(a) SB–MSM (b) SB–ESM

(c) MB–MSM (d) MB–ESM

Fig. 8. arg γopt over the first baseline: 5m, 15min.

has been shown that the utilization of multiple baselinesfor the coherence optimization has certain advantages overthe single–baseline optimization, in regard to optimal co-herence bias reduction, more accurate dominant scatteringmechanisms extraction and their optimal interferometricphases estimation.

The extension of polarimetric optimization to multi-baseline case will have possibilities for practical use.The possible applications are automated vegetation growanalysis and change detection, e.g. for extracting optimalSMs, and the observation of the coherence properties overa period of time. By utilization of many tracks with thehighest coherent SMs, a more accurate topography andDEM maps can be generated. The optimal coherences withcorresponding scattering mechanisms can also be utilizedfor classification purposes and vegetation parameter inver-sion.

REFERENCES

[1] S. Cloude and K. Papthanassiou, “Polarimetric optimization in radarinterferometry,” Electronic Letters, vol. 33, no. 13, pp. 1176–1178,June 1997.

[2] L. Sagues, J. Lopez-Sanchez, J. Fortuny, X. Fabregas, A. Broquetas,and A. Sieber, “Indoor experiments on polarimetric SAR interfer-ometry,” IEEE Trans. Geosci. Remote Sensing, vol. 38, pp. 671 –684, March 2000.

[3] T. Flynn, M. Tabb, and R. Carande, “Coherence region shapeextraction for vegetation parameter estimation in polarimetric SARinterferometry,” in Proceedings of IEEE–IGARSS, vol. 5, Toronto,June 2002, pp. 2596–2598.

[4] J. L. Gomez-Dans and S. Quegan, “Constraint coherence op-timisation in polarimetric interferometry of layered targets,” inProceedings of POLINSAR, Frascati, Jan. 2005.

[5] M. Qong, “Coherence optimization using the polarization stateconformation in PolInSAR,” IEEE Geosci. Remote Sensing Lett.,vol. 2, no. 3, pp. 301–305, July 2005.

(a) SB–MSM (b) SB–ESM

(c) MB–MSM (d) MB–ESM

Fig. 9. Local correlation ρφ of optimized interferometric phases withN = 7 × 7 = 49 over all baselines.

SB–MSM

SB–ESM

MB–MSM

MB–ESM0.98

1

0.96

0.94806040201

ρφ(N)

N

Fig. 10. Mean of ρφ as a function of spatial neighborhood averagingN . The lines correspond, from top to bottom, to MB–ESM, SB–ESM,MB–MSM and SB–MSM.

[6] E. Colin, C. Titin-Schnaider, and W. Tabbara, “An InterferometricCoherence Optimization Method in Radar Polarimetry for High-Resolution Imagery,” IEEE Trans. Geosci. Remote Sensing, vol. 44,no. 1, pp. 167– 175, Jan. 2006.

[7] R. A. Horn and C. R. Johnson, Topics in Matrix Analysis. Cam-bridge University Press, 1991.

[8] M. Tabb, J. Orrey, T. Flynn, and R. Carande, “Phase diversity: a de-composition for vegetation parameter estimation using polarimetricSAR interferometry,” in EUSAR, Cologne, June 2002, pp. 721–724.

[9] H. Yamada, Y. Yamaguchi, Y. Kim, E. Rodriguez, and W. Boerner,“Polarimetric SAR Interferometry for Forest analysis based on theESPRIT algorithm,” IEICE Trans. Electron., vol. E84-C, no. 12,pp. 1917–1924, Dec. 2001.

[10] R. Bamler and P. Hartl, “Synthetic aperture radar interferometry,”Inverse Problems, vol. 14, pp. R1–R54, 1998.

[11] M. Neumann, L. Ferro-Famil, and A. Reigber, “MultibaselinePolarimetric SAR Interferometry Coherence Optimization,” IEEEGeosci. Remote Sensing Lett., Nov. 2006, submitted.

[12] H. Hotelling, “Relations between two sets of variates,” Biometrika,vol. 28, no. 3, pp. 321–377, 1936.

[13] J. R. Kettenring, “Canonical analysis of several sets of variables,”Biometrika, vol. 58, no. 3, pp. 433–451, 1971.

[14] M. Neumann, A. Reigber, and L. Ferro-Famil, “POLInSAR Co-herence Set Theory and Application,” in EUSAR, Dresden, May2006.

[15] G. A. Watson, “Computing the numerical radius,” Linear Algebraand its Applications, vol. 234, pp. 163–172, Feb. 1996.