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 141 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 142 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 143 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. 144 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. 146 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. 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