An Analysis of Coherence Optimization Methods in Compact Polarimetric SAR Interferometry

An Analysis of Coherence Optimization Methods in Compact Polarimetric SAR Interferometry

Meng Liu,Hong Zhang,Chao Wang, Bo Zhang

Vancouver, Canada July 29, 2011

IGRASS2011

Outline

Introduction1

2

3

Coherence Optimization of C-PolInSAR

4 Conclusions

Experiments and Results

Introduction

PolInSARPolInSAR uses the interferometric degree of coherence

estimated at different polarizations to extend the observation space of targets

Promising applications, especially in the field of forest remote sensing

Coherence optimization

Technique to enhance the interferometric coherence

It is achieved by the choice of a polarization basis within the

polarimetric observation space.

Introduction Coherence optimization in fully PolInSAR system

Unconstrained Lagrange multipliers method: the potential scattering mechanisms is different in both images

Constrained Lagrange multipliers method: assuming the same scattering mechanism in both images

Numerical radius method: gives a higher coherence than the constrained Lagrange multipliers method

IntroductionCompact Polarimetry (CP) system

A CP system transmits a wave on π/4 oriented linear or circular polarization, while receives the backward wave on two orthogonal linear or circular polarizations

A CP system has advantage over a fully polarimetric (FP) system in terms of reductions of pulse repetition frequency, data volume, and system power needs

Introduction

Three modes of CP

C-PolInSAR

C-PolInSARInSA

RCP

π/4 mode:

Dual Circular Polarimetric mode:

right circular transmit, linear (horizontal and vertical) receive

(CTLR) mode:

Introduction

The workflow of C-PolInSAR

ActualF-PolInSAR

C-PolInSARPseudo

F-PolInSARApplication

Simulation Reconstruction

reconstruction for coherence optimizationOnly two independent channels

The assumption: reflection symmetryinsignificance

IntroductionObjective Solve the coherence optimization problem in C-PolInSAR without the reconstruction of the pseudo F-PolInSAR covariance matrix

validation Compare coherence optimization of CP modes with the corresponding FP modes, as well as the conventional coherence optimization methods.

Coherence Optimization

The complex correlation coefficient of CP

The optimal coherent coefficient

the highest correlation of the two images can be selected by tuning the w i polarization in each resolution element

Coherence Optimization

Unconstrained Lagrange multipliers

Solving this equation leads to two 2×2 eigenvalue problems

[A][B] is similar to [B][A], they have the same real nonnegative eigenvalues.

Coherence Optimization

Constrained Lagrange multipliersIt assumes the same scattering mechanism in both images

The optimization of the magnitude of the complex correlation leads to one 2×2 eigenvalue problems

This approach take the same polarization basis transformation, which leads to a suboptimum result.

Coherence Optimization

Numerical radius

Define

It provides a new thought to solve the constrained Lagrange multipliers function.Assumption: [T11] is similar to [T22]

The maximum coherence corresponds to the numerical radius of the matrix [A]

Experiments and ResultsExperimental scene

Test area: Sanya region in China Acquired: East China Research Institute of Electronic Engineering

Band: X-band

The Pauli decomposition result

1 2

345

Areas Color

Forest-1 1

Forest-2 2

Crop 3

Road 4

Bare Land 5

Experiments and Results

(a) FP

case

(c) DC

P

mode

(b) π/4 m

ode

(d) CT

LR

m

ode

1. The histogram of FP case is right shifted compare to the position of any mode of CP cases

2. The trend of the coherence histograms for CP case is closed to the corresponding FP case, no matter which method or CP mode was selected

3. In most cases the ULM gives the highest coherence, followed by the NR and the CLM, this result is similar to the FP case.

ROIConventional Coherence FP Coherence

HH HV VV HH+VV HH-VV ULM NR CLM

forest 1 0.770 0.734 0.780 0.793 0.721 0.913 0.876 0.861

forest 2 0.809 0.774 0.796 0.817 0.750 0.924 0.892 0.870

crop 0.813 0.748 0.797 0.819 0.724 0.931 0.900 0.893

road 0.632 0.382 0.616 0.673 0.509 0.818 0.766 0.751

bare land 0.846 0.707 0.845 0.898 0.635 0.931 0.901 0.890

ROILin45 DCP CTLR

ULM NR CLM ULM NR CLM ULM NR CLM

forest 1 0.851 0.830 0.816 0.865 0.843 0.831 0.862 0.839 0.824

forest 2 0.874 0.855 0.836 0.880 0.863 0.845 0.881 0.861 0.846

crop 0.883 0.861 0.852 0.887 0.868 0.860 0.887 0.866 0.857

road 0.729 0.702 0.681 0.732 0.701 0.683 0.719 0.681 0.656

bare land 0.895 0.881 0.872 0.893 0.878 0.868 0.900 0.881 0.870

Conventional Coherence VS FP Coherence

Mean Coherence Values for Compact Polarimetric Modes

1. the degree of coherence for any CP case is lower than the corresponding FP case, but it is higher than the conventional cases.

2. The HH-VV conventional coherence seems to be the worst case in all case except for the road areas, where the HV conventional coherence is lowest.

3. Among the three compact modes, the situation becomes complicated. The DCP mode gives the highest coherence over forest 1 and crop areas. For the low forest (forest 2) areas, the CTLR mode is slightly better than other modes.

4. For the road and bare land areas, the π/4 mode seems to be the best compact mode.

Conclusions

1

Compared with the FP case, one can observe that there is a significant loss in coherence of 5-10% when CP modes are available.

2

The trend of the coherence histograms for CP case is closed to the corresponding FP case, no matter which method or CP mode was selected.

3

It is shown that the degree of coherence from CP case carries enough information for some polarimetric SAR interferometry applications.