=Paper=
{{Paper
|id=Vol-2076/paper-16
|storemode=property
|title=Feature Enhancement of InSAR Data Products Using Coherence Maps
|pdfUrl=https://ceur-ws.org/Vol-2076/paper-16.pdf
|volume=Vol-2076
|authors=Nina S. Vinogradova,Andrey V. Sosnovsky
}}
==Feature Enhancement of InSAR Data Products Using Coherence Maps==
https://ceur-ws.org/Vol-2076/paper-16.pdf
Feature Enhancement of InSAR Data Products
Using Coherence Maps
Nina S. Vinogradova and Andrey V. Sosnovsky
Ural Federal University, Yekaterinburg, Mira st., 19, Russia,
n.s.vinogradova@urfu.ru
Abstract. Analysis of the coherence map generation techniques for
SAR image pair processing is presented. The areas of map coherence
acceptable values for the averaging window are calculated. The map co-
herence enhancement method based on the results is submitted. The SAR
interferogram calculation using submitted method is performed. The re-
sult accuracy improvement in comparison with the classical technique is
shown.
Keywords: image analysis, coherence map, InSAR processing, com-
puter simulation
1 Introduction
Coherence map is an image of the SAR pair correlation coefficients field. It
gives information about deviation degree of the absolute phase from its true
value. Such deviation may be caused by the phase noise, a surface variability,
and the stability of the radio signal reflected from various parts of the Earth
surface [1]. Coherence map may be useful for a wide range of problems solved
by systems of radar sense remote data such as urban planning, emergencies
monitoring, and issues of environmental protection [2, 3]. It allows one to view the
characteristics of the satellite system, atmospheric and weather conditions, the
properties of the radar signal and the Earth surface, and, ultimately, the quality
of products created on the basis of SAR data, such as DEM (digital elevation
models) and terrain displacement maps [4–6]. According to the definition, the
brightness value of the coherence map elements may take values in the range [0, 1]
only. The value 0 corresponds to complete decorrelation, the value 1 corresponds
to absolute coherence of the corresponding elements of the Earth’s surface. It is
conventionally accepted to classify the elements of the coherence map into three
classes: zones with low coherence corresponding to dark areas, zones with high
coherence corresponding to light regions, and zones with intermediate coherence
values corresponding to gray areas [7, 8].
The coherence map development is performed at the stage of the SAR inter-
ferogram creating. According to the traditional technique, value of each element
is calculated as the correlation coefficient between the values of the first and
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second SAR images in the pair. The classical method of coherence map devel-
opment is based on multiplying the first (reference) image of the interferometric
pair by the second (auxiliary) one that is complex-conjugate to itself [1, 5, 9]
PM −1 PN −1 ∗
| x=0 y=0 Z1 (x, y) · Z2 (x, y)|
γ̂ = qP , (1)
M −1 PN −1 2·
PM −1 PN −1 2
x=0 y=0 |Z 1 (x, y)| x=0 y=0 |Z2 (x, y)|
where Z1 , Z2 are the radar images of the reference and auxiliary signals respec-
tively, M , N are the dimensions of the averaging region size, ∗ is the complex
conjugation operator.
Despite the fact that the correlation function has been thoroughly studied in
details [10, 11], the issue of its usage for two-dimensional digital signals obtained
by radar interferometric survey is still unclear.
2 Coherence magnitude estimation analysis
Firstly, it is necessary to obtain the minimum averaging region size N with is
used during the coherence map development. The plot of dependence of the
bias of estimate of coherence magnitude dγ̂ at zero correlation on the averaging
region size is constructed. The size N in terms of expression (1) is similar to the
sample size used in calculating the correlation coefficient. Due to the finiteness
of the sample, a bias of the correlation estimate may occur in the coherence map
development. The displacement value will increase with decreasing coherence and
reach the maximum values at zero. For calculations, the test image corresponding
to a flat terrain without any relief changes is used. Test images are combined
with the Gaussian noise by complex multiplication operation. The range of the
averaging window is from 3 to 65 elements. The results are shown in Fig.1.
Fig. 1. The dependence of bias estimate on coherence magnitude dγ̂ for the size of the
averaging region N
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As it follows from the figure, the minimum averaging region size is the size
of 11 elements for the classical method of coherence map development. Using
the smaller one, the bias in the coherence estimate exceeds 0.1. This effect may
deeply distort the interpretation of the output product. The dependence has the
form of a hyperbolic curve slowly converging to zero value, which corresponds to
the classical notions of the significance of estimating the bias from the window
size [10].
To analyze the behavior of the estimation using the classical method, the
dependence STD of estimate of coherence magnitude on the varied coherence
σγ̂ = σγ̂ (γ) is performed. The STD estimate changes in the coherence interval
from 0 to 1 with step of 0.005. The calculations are made for the averaging
region size 11 × 11, 19 × 19, 27 × 27, 35 × 35, 43 × 43, 51 × 51, 67 × 67. Averaging
at 600 points is performed. The obtained dependences are presented in Fig. 2.
The abscissa axis shows a range from 0 to 0.3 for clarity.
Fig. 2. The dependence STD of estimate of coherence magnitude on the varied coher-
ence; the positions of the dropping peaks are shown by a vertical dotted line
As it follows from the figure, behavior of the dependence σγ̂ = σγ̂ (γ) is
similar to the lower Rao-Kramer boundary [10, 12–14]. The discrepancy with the
theoretical dependency is due to the fact that the Rao-Cramer formula shows
reliable values for sufficiently large sampling values. Also, the dropping peaks
are distinctly distinguished at the calculated values, after which the value o
thef STD estimate drops sharply to the minimum values. The reason for this
is that there is a bias in the STD estimate (Fig. 1). Position of the dropping
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peak depends on the window size: the smaller the window size, the farther from
the zero is the peak. This fact is caused by a decrease in the STD estimate
of coherence magnitude with increasing sample size. It follows that the range
of brightness values on the output coherence map corresponding to the set of
coherence values (which are located between the zero and the dropping peak) is
incorrect and have to be removed from the output coherence map. A summary
of the obtained results is presented in Table 1.
Table 1: The dependence of the dropping peak position γdp and bias of
estimate of coherence magnitude dγ on the averaging region size N
N dγ γdp N dγ γdp N dγ γdp
11 0.081 0.160 31 0.030 0.070 51 0.019 0.055
13 0.069 0.145 33 0.028 0.070 53 0.018 0.055
15 0.060 0.130 35 0.027 0.070 55 0.018 0.055
17 0.053 0.115 37 0.025 0.065 57 0.017 0.050
19 0.048 0.100 39 0.024 0.065 59 0.017 0.050
21 0.043 0.095 41 0.023 0.065 61 0.016 0.050
23 0.040 0.090 43 0.022 0.065 63 0.014 0.050
25 0.037 0.085 45 0.021 0.060 65 0.014 0.045
27 0.034 0.080 47 0.020 0.060 67 0.013 0.045
29 0.032 0.075 49 0.020 0.055 69 0.013 0.045
To illustrate the data of Table 1, the coherence map for two images of SAR pair
was modeled using the classical expression (1) (the data are taken from [15]).
The calculation was carried out with the averaging window sizes 11 × 11, 21 ×
21, 45 × 45. The regions with coherence values below γdp are sown by color.
As it follows from the Fig. 4, during increasing averaging region size, the
effective area of the coherence map increases too. It becomes possible to build a
mask of pixels, which are incorrect. At the same time, it should be noted that
during increasing averaging region size, the final product details decrease. The
present result will be used to improve the interferogram accuracy for the SAR
image pair in the tasks of DEM creation.
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Fig. 3. Simulation of the coherence maps of the PCA-pair fragment for different sizes
of the averaging window: a) coherence maps; b) regions with a coherence value below
γdp for a fixed averaging window size
3 Experimental results
For interferogram accuracy of obtained products, the STD of absolute phase de-
viation from a reference DEM was calculated as a quality indicator for the inter-
145
ferometric coherence estimate. The better estimates should give a less-fluctuation
decreasing dependence for at least for low- and medium-valued coherences with
a possible wider range of both coherence and STD values. The method based
on coherence map masking has shown the more accurate result: the range of
deviation is wider by 11 percent in comparison with traditional techniques.
The reference DEM covered a territory of 8 × 5 km, which contained average
hills and river valleys. The averaging window size was 15 × 15, the value of
responding dropping peak γdp was 0.13. Two coherence maps were used for
interferogram creation: one was obtained with the traditional method, and ano-
ther was generated according to the proposed method. The results are shown in
Fig. 4.
Fig. 4. The dependence of phase STD on the coherence magnitude estimation. 1) The
one was obtained with traditional method; 2) The one was obtained with coherence
map masking
4 Conclusion
The traditional method of the coherence map generation was investigated. Some
statistics results related to a classical expression were obtained. The new method
of interferogram creation based on dropping peak position was proposed. The
method has shown the more accurate result: the range of deviation is wider by
3.8 percent in comparison with traditional techniques.
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5 Acknowledgment
This work was supported by the Ural Federal University’s Center of Excellence
in “Geoinformation technologies and geophysical data complex interpretation
methods” (according to the Act 211 Government of the Russian Federation,
contract 02.A03.21.0006)
References
1. Monti Guarnieri, A., Guccione, P., Pasquali, P., Desnos, Y. L.: Multi-mode EN-
VISAT ASAR interferometry: techniques and preliminary results. IEE Proc.-Radar
Sonar Navig., Vol. 150, No. 3, 193–200 (2003)
2. Arciniegas, G. A., Bijker, W., Kerle, N., Tolpekin, V. A.: Coherence- and
Amplitude-Based Analysis of Seismogenic Damage in Bam, Iran, Using ENVISAT
ASAR Data. IEEE Transactions on Geoscience and Remote Sensing, Vol. 45, Iss. 6,
1571-1581 (2007)
3. Takeuchi, S., Suga, Y.: Detection of Urban Disaster Using InSAR - A Case Study
for the 1999 Great Taiwan Earthquake. Geoscience and Remote Sensing Sym-
posium, 2000. Proceedings. IGARSS 2000. IEEE 2000 International, 1201–1224
(2000)
4. Askne, J., Hagberg, J. O.: Potential of interferometric SAR for classification; of
land surfaces. Proc. Int. Geoscience and Remote Sensing Symp. (IGARSS’93),
Tokyo, Japan. 985-987 (1993)
5. Gens, R., van Genderen, J. L.: SAR interferometryIssues, techniques. Int. J. Re-
mote Sens., Vol. 17, 18031835 (1996)
6. Lee, H.: Analysis of Topographic Decorrelation in SAR Interferometry Using Ra-
tio Coherence Imagery. IEEE Transactions On Geoscience And Remote Sensing,
Vol. 39, No. 2, 223-232 (2001)
7. Abdelfattah, R., Nicolas, J. M.: Coherence Estimation from Complex Coherence
Map using Second Kind Statistics. Intern. Conf. on Image Processing, ICIP’05, II
229-232 (2005)
8. Cattabeni, M., Monti-Guarnieri, A., Rocca, F.: Estimation and Improvement of
Coherence in SAR Interferograms. Geoscience and Remote Sensing Symposium,
IGARSS ’94. Surface and Atmospheric Remote Sensing: Technologies, Data Anal-
ysis and Interpretation. Vol. 4, 720–722 (1994)
9. Wang, T., Liao, M., Perissin, D.: InSAR Coherence decomposition analisys. IEEE
Geoscience and Remote Sensing Letters 7, Vol. 1, 156–160 (2010)
10. Goriainov, V. B., Pavlov, I. V., Tsvetkova, G. M. et al.: Matematika v tekhnich-
eskom universitete. Iss. XVI. Matematicheskaia statistika. Bauman Moscow State
Technical University (2001)
11. Levin, B. R. Teoreticheskie osnovy‘ statisticheskoi‘ radiotekhniki. Kniga 2. Sovet-
skoe radio, Moscow (1968)
12. Touzi, R., Lopes, A., Vachon, P. W.: Coherence Estimation for SAR Imagery //
IEEE Transactions On Geoscience And Remote Sensing, Vol. 37, No. 1, 135–149
(1999)
13. Valeev, V. G. Pomehoustoi‘chivost‘ radiotekhnicheskikh izmeritel‘ny‘kh sistem.
Kirov Ural Polytechnic Institute, Sverdlovsk (1987)
14. Van Trees, H. L.: Detection, estimation and modulation theory. P. 1. Detection,
estimation and linear modulation theory. Krieger Publishing Co., Inc. Melbourne,
FL, USA, (1992)
147
15. Sentinel Online https://sentinel.esa.int
16. Sosnovsky, A. V., Kobernichenko, V. G., Vinogradova, N. S. Tsogtbaatar, O.: In-
SAR data coherence estimation using 2D fast fourier transform. 1st International
Workshop on Radio Electronics and Information Technologies, REIT 2017, CEUR
Workshop Proceedings, Vol. 1814, 98–105 (2017)