=Paper=
{{Paper
|id=Vol-1452/paper20
|storemode=property
|title=Algorithm of Interferometric Coherence Estimation for Synthetic Aperture Radar Image Pair
|pdfUrl=https://ceur-ws.org/Vol-1452/paper20.pdf
|volume=Vol-1452
|dblpUrl=https://dblp.org/rec/conf/aist/SosnovskyK15
}}
==Algorithm of Interferometric Coherence Estimation for Synthetic Aperture Radar Image Pair==
https://ceur-ws.org/Vol-1452/paper20.pdf
Algorithm of Interferometric Coherence
Estimation for Synthetic Aperture Radar Image
Pair
Andrey Sosnovsky and Victor Kobernichenko
Ural Federal University, pr. Mira, 19, Yekaterinburg, 620002,
Russian Federation
sav83@e1.r
Abstract. Interferometric coherence is an important indicator of relia-
bility for interferograms obtained by interferometric synthetic aperture
radar (Interferometric SAR, InSAR). Areas with low coherence values are
unsuitable for interferometric data processing. Also, it may be used as
a classification parameter for various coverage types. Coherence magni-
tude can be calculated as an absolute value of the correlation coefficient
between two complex SAR images with averaging in a local window.
The problem in coherence estimation is in its dependence on phase slope
caused by relief topography (topographic phase). A method for suppres-
sion of the topographic phase influence is proposed, based on the spatial
phase derivation.
Keywords: Synthetic aperture radar images, InSAR systems, Coherence
estimation
1 Introduction
Interferometric data processing for extraction of information about the Earth
terrain and its changes becomes one of the general guidelines in the develop-
ment of contemporary space-based radar systems together with the implemen-
tation modes of ultra-high spatial resolution (1-3 meters) and full–polarimetric
processing. The method of space-based radar interferometry implies a joint pro-
cessing of the phase fields obtained by simultaneous scattering of the terrain
with two antennas or by non-simultaneous scattering with one antenna moved
by two different parallel orbits [1, 4]. This method combines high accuracy of the
phase measurements with high resolution of the synthetic aperture radars (SAR)
technology. Technology of the differential SAR interferometry (InSAR) makes
possible to get maps of the elevation changes between the radar passages. The
stages of the interferometric processing are implemented in specialized software
systems for the remote sensing data processing such as the SARscape, IMAGINE
Radar Mapping, Photomod Radar, RadarTools. So we can talk about Informa-
tion technology (IT) of the digital elevation models (DEM) generation by remote
sensing data.
However, for practical application of these technologies, one has to overcome
a number of significant problems. Two general problems of interferometry are
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the temporal and spatial decorrelation of the received data and the problem of
phase unwrapping, i.e. a recovery of the absolute phase information from the
relative phase, which is wrapped into [−π, π]-interval. Another important field of
investigation in radar interferometry is selection of the most efficient processing
algorithms and obtaining the experimental estimates of the generated DEM
accuracy. This work is devoted to the first of the mentioned problems, i.e. to the
data decorrelation (summary temporal and spatial) and its estimation.
2 Interferometric coherence
Interferometric coherence is an important indicator of suitability of the data
scene obtained by a radar remote sensing system for the further processing and
solving the final problem, i.e. generation of digital elevation model or terrain
changes map. The coherence factor is calculated as the absolute value of the
correlation coefficient between samples of two complex radar images (single-look
data complex, SLC) got in the local windows
Σ ż1 (m, n) · z̄2 (m, n)
γˆ0 = |ρˆ˙0 | = p , (1)
Σ|ż1 (m, n)|2 · |z̄2 (m, n)|2
where z1(2) (m, n) is the SLC samples (z̄1(2) (m, n) are complex-conjugate sam-
ples) [2–5], γˆ0 takes values in interval [0, 1], near-zero values correspond to areas
of high or full decorrelation, which are not suitable for interferometric data pro-
cessing. The values higher than 0.5 mean good data correlation.
However, this approach entails some problems because, in fact, a random
variable is estimated here, but not a random process. So, any phase gradients
caused by both natural topography variability and by point-of-view geometry
(remote sensing radar systems have a side-scattering configuration) lead to the
degradation of the estimate (1). Its value depends on the slope and tends towards
the value |ρ12 (N )|ρ=0 , i.e. a bias of the estimate for independent Gaussian values
of the correlation coefficient (N is the number of samples) [3], which in practice
takes the value about 0.1–0.3. Thus, coherence loses its properties as measure
of the quality of the interferogram, its value becomes dependent on relation
between topographic and fluctuation components of the phase.
3 Differential phase coherence estimate
To eliminate the effect described above, the following modification of the coher-
ence estimate can be offered taking into account influence of the topographic
component. Modified coherence evaluates not the samples z1 (m, n) and z2 (m, n)
of the SLC–image pair, but the following values:
ẇ1 (m, n) = ż1 (m, n) · z̄1 (m + 1, n), ẇ2 (m, n) = ż2 (m, n) · z̄2 (m + 1, n), (2)
where the new phase values of the w1 (m, n) and w1 (m, n) will characterize the
slope of the topographic phase in the direction of growth of the mth picture co-
ordinate. So, this operation performs the phase derivation along one coordinate.
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Similarly, one can use the gradients along the nth coordinate. Expression for the
coherence estimation using values (2) looks as follows:
s
Σ ẇ1 (m, n) · w̄2 (m, n)
γˆ1 = p . (3)
Σ|ẇ1 (m, n)|2 · |w̄2 (m, n)|2
Although this estimate is non-Gaussian, it is wealthy, and it can be shown that
it is insensitive to the linear phase trend.
4 Experimental results
Test now the work of the coherence estimation algorithms for RADARSAT–1
data (wavelength 56 mm). Figure 1 presents a fragment of the radar image of an
area with surfaces of different reflectance including surfaces with volume scatter-
ing and the water surface, which has generally low coherence. Signal differential
phase for the given fragment has a slope in the horizontal direction of the order
of 0.3 radians per sample (due scattering geometry). The coherence maps of the
fragment were constructed using conventional estimate γˆ0 and modified estimate
γˆ1 with the sampling size 11 × 11 are presented in Figs. 2a, 2b.
Fig. 1. A RADARSAT-1 radar image scene
One can see that the first map is degraded since different surfaces give the
same low coherence values regardless on the surface type. The map obtained
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a) Traditional estimate γˆ0 b) Modified estimate γˆ1
Fig. 2. Coherence map calculated
using modified estimate (Fig. 2b) has a good sensitivity to the surface type.
However, the estimate has a larger bias at low values than the γˆ0 , and, so, it
requires increasing the sample value towards to γˆ0 (Fig. 3a, 3b). A quantitative
accuracy assessment for the scene is not available because of poor reference DEM
for this territory.
a) Traditional estimate γˆ0 b) Modified estimate γˆ1
Fig. 3. Coherence estimates biases for different sample sizes (N =2, 5, 10, 25)
5 Conclusion
A modified method for estimation of spatial coherence of the interferometric
radar images pairs is developed. The method consists in calculation of the cor-
175
relation between pairs of complex multiplications of neighbour elements. The
research is implemented on radar images RADARSAT–1. The result shows that
the modification allows one to solve the problem of estimate degradation under
the differential phase trend, which always takes place in side-scattering radar
systems.
Acknowledgment The work was supported by the RFBR grants Nos. 13-07-
12168, 13-07-00785.
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