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IAPRS & SIS, Vol.34, Part 7, "Resource and Environmental Monitoring", Hyderabad, India,2002
EVALUATION OF PHASE UNWRAPPING ALGORITHMS USING
A SIMULATED REPEAT-PASS SAR INTERFEROMETRY SYSTEM
K.K. Mohanty
Earth Sciences and Hydrology Division, Marine and Water Resources Group,
Space Applications Centre (ISRO), Ahmedabad — 380 015, INDIA
mohantykk @yahoo.com
KEYWORDS: SAR, interferometry, phase unwrapping, DEM/DTM, Simulation
ABSTRACT:
Pairs of SAR phase images with varying degree of phase noise are simulated using Digital Elevation Model (DEM) and baseline
geometry satisfying critical baseline condition. The SAR phase image pairs are used to generate interferograms which are
subsequently evaluated using a number of unwrapping techniques such as Goldstein, quality-guided path following algorithm,
preconditioned conjugate gradient (PCG), weighted multi-grid efc. The unwrapped phase images are compared with a simulated
noise-free absolute phase image (a hypothetical phase image that preserves integral phase cycles), to evaluate relative advantages of
the unwrapping techniques. Weighted multigrid and quality-guided unwrapping algorithm are found to perform better in case of high
signal-to-noise ratio condition, even though most of the algorithms are equally effective under low noise conditions.
1. INTRODUCTION
Repeat-pass SAR interferometry using Satellite SAR images
has emerged as a potential technique for DEM generation,
surface deformation mapping and land subsidence studies
(Gens and Genderen, 1996). A large number of case studies
demonstrating these applications have been demonstrated in the
literature (Massonnet, 1997). Repeat-pass SAR interferometry
is limited by a number of critical issues, namely uncertainties
in baseline measurements, phase error related to thermal noise,
speckle, phase decorrelation, aliasing due to inadequate spatial
sampling, radar layover, foreshortening, cycle slip etc. Baseline
improvements are possible using post-computed precise orbits
or deployment of corner reflectors. In absence of ERS tandem
like missions, phase decorrelation is going to be one major
source of error in SAR interferometry (Zebker and Villasenor,
1992). Solving phase ambiguity in noisy SAR interferogram
has been a challenge. A number of approaches for phase
unwrapping have been developed over the time and new ones
are being proposed (Ghiglia and Pritt, 1998; Akerson et al.,
2000). The current study attempts to evaluate the performance
of a number of phase unwrapping techniques using simulated
SAR interferograms with varying signal to noise ratio (SNR).
2. PHASE UNWRAPPING
A phase image generated using SAR interferometry is only 27
modulo of absolute phase values. Phase unwrapping solves for
2m ambiguities in SAR interferometry. This is an essential step
for DEM generation and differential SAR interferometry.
Unwrapping of noise-free and adequately sampled SAR
interferograms is a trivial process. However, unwrapping a
noisy and spatially aliased interferogram is non-unique and
difficult.
Unwrapping techniques evaluated in the current study can be
broadly categorized under three groups, namely i) cut-line
algorithms, ii) region growing algorithm and iii) minimum
norm / least square techniques. Certain algorithms yield a better
solution when provided with a quality map for guiding the
unwrapping process. The cut-line algorithms identify local
phase inconsistencies, called residues. The positive and
negative residues are connected in pairs by cut-lines ie. a
positive residue is connected with a negative residue. Phase
unwrapping proceeds by adding or subtracting 2m at fringe
boundaries while ensuring that unwrapping algorithm doesn’t
cross a cut-line. The cut-line algorithms evaluated in the
current study are the classic Goldstein’s algorithm and mask
cut algorithm (Goldstein e£ al., 1988). The region growing
algorithms such as quality-guided path following algorithm and
Flynn's minimum discontinuity algorithm don't explicitly
generate the branch cut lines; rather follow an unwrapping path
guided by certain quality measure. They invariably result in
lines of discontinuities analogous to cut lines. Minimum norm
techniques such as Preconditioned Conjugate Gradient (PCG)
algorithm, weighted least square and minimum L? norm
algorithm, implement phase unwrapping as global constrained
optimization problem. The current study uses the unwrapping
software provided by Ghiglia and Pritt, 1998.
3. INTERFEROGRAM SIMULATION
Simulation of SAR phase images for interferogram generation
has both deterministic and stochastic components. The
stochastic components are due to random distribution of
scatterers within a resolution cell, reorientation of scatterers
within a resolution cell related to decorrelation for repeat-pass
SAR interferometry and random thermal noise. The stochastic
phase noise can be both additive and multiplicative in nature.
The thermal phase noise is additive in nature, while speckle is
multiplicative in nature. The deterministic components of
simulation are controlled by pure geometry of terrain and
sensor.
The modelling of repeat pass SAR interferometry geometry
uses DEM (Digital Elevation Model), an earth ellipsoid model,
orbital parameters, viewing geometry and noise models as
inputs for simulation of phase images. DEM, satellite altitude
and look-angle in the scene centre or at any specified point in
the DEM is used to compute the master satellite position. The
