A METHOD OF TIME-SERIES CHANGE DETECTION USING FULL POLSAR IMAGES FROM DIFFERENT SENSORS

Most of the existing change detection methods using full polarimetric synthetic aperture radar (PolSAR) are limited to detecting change between two points in time. In this paper, a novel method was proposed to detect the change based on time-series data from different sensors. Firstly, the overall difference image of a time-series PolSAR was calculated by ominous statistic test. Secondly, difference images between any two images in different times ware acquired by Rj statistic test. Generalized Gaussian mixture model (GGMM) was used to obtain time-series change detection maps in the last step for the proposed method. To verify the effectiveness of the proposed method, we carried out the experiment of change detection by using the time-series PolSAR images acquired by Radarsat-2 and Gaofen-3 over the city of Wuhan, in China. Results show that the proposed method can detect the time-series change from different sensors. * Correspondence: yangj@whu.edu.cn


INTRODUCTION
Due to the all-time and all-weather mapping capability of synthetic aperture radar (SAR), which is independent of, for instance, cloud cover, night-time, and severe weather, change detection of SAR has played an important role in the understanding of the relationships and interactions between people and natural phenomena in recent years (Bruzzone, 2013;Hachicha, 2014;Singh, 1989).Change detection with SAR images has been used in applications such as disaster monitoring ( Conradsen, 2003;Giustarini, 2013), ecological monitoring (Zhao, 2014;Zhao, 2016), regulatory policy development (Sun, 2016;Zhao, 2013), and environmental impact assessment (Zhao, 2014).The Chinese Gaofen-3 (GF-3) satellite was launched on 10 August, 2016.It is the first multipolarization SAR imaging satellite to be developed in China and it has promoted research into change detection based on SAR images (Sun, 2017).Meanwhile, full polarimetric synthetic aperture radar (PolSAR) data contain both phase and amplitude information from radar returns transmitted in two different polarizations, signifying that more scattering information can be used for change detection (Zhao, 2017).Therefore, many researchers have focused on change detection using bi-temporal PolSAR images (Liu, 2014;Moser, 2006;Sumaiya, 2016).
Although the traditional pixel-based unsupervised change detection method using bi-temporal PolSAR images can detect the change between two different times with same sensor (Akbari, 2016), they could not detect the total changes of the entire time series from different sensors (Conradsen, 2016).To solve these problems, some researchers simply compared the pair-wise images in the time-series images and detected the time-series change, which suffers from some deficiencies, such as it is time-consuming and couldn't detect some small continuous changes (Conradsen, 2016).When analyze the difference images, traditional methods such as two-dimensional entropic segmentation (TDES) algorithm (Jansing, 1999), Otsu's algorithm (Otsu, 1975), improved K&I algorithm (Zhao, 2017) and Kapur entropy algorithm (Yetgin, 2012) and so on, assume the probability density function (PDF) of the difference image complies with the Gaussian distribution.While the difference images calculated by ominous statistic test and Rj statistic test algorithm are not complies with the Gaussian distribution (Conradsen, 2016).In consequence, traditional algorithm is not suitable for the analysis of difference image which obtained by ominous or Rj statistic test algorithm.Fortunately, Gaussian mixture models (GMM) can fit any distribution of data (Rasmussen, 2000).In our previous work (Liu, 2017), by improving the GMM algorithm, it can better adapt to the analysis of difference image.
Focusing on above problems, a method (named OS_GMM) of time series change detection using full PolSAR images from different sensors is proposed in this paper.OS_GMM integrates the respective advantages of the omnibus test (Conradsen, 2016) and generalized GMM (Liu, 2018) techniques.The proposed method should not be regarded as a combination of many methods but as a fully unified algorithm with different steps.In this method, the use of the omnibus statistic is an effective strategy for obtaining the difference images from PolSAR timeseries images, and we use the generalized GMM algorithm to help us to choose the threshold of change detection map.

Omnibus Test
The omnibus statistic test algorithm effectively utilizes polarimetric and temporal information from time-series PolSAR images.The PolSAR image includes the backscattering coefficients of the four polarimetric channels of the object (Conradsen, 2003).For orthogonal polarizations basis, the scattering information of ground objects can be represented by the following covariance matrix C: ) and probability density functions (PDF) of C can be described as follows. 1 Where, () tr  is the trace of covariance matrix C, n is the number of look of PolSAR image, and p represents the dimension of matrix C. For fully PolSAR image, p is equals to 3 (Conradsen, 2016).
Assuming that the multi-parameters PolSAR images are independent, and they obey the complex Wishart distribution: where p represents the dimension of According to omnibus statistic test theory, 0 H hypothesis can be described as , where  is the set of parameters of the probability function that has generated the data.0 , and the likelihood ratio of the omnibus statistic test is shown as follows: where, , this leads to the desired likelihood-ratio omnibus statistic test: X n C    and Equation ( 6) in logarithm form as follows: In general, the overall similarity of time-series PolSAR images is measured by lnQ  . The larger the value, the greater the probability that change will generally occur in time-series PolSAR images.

Rj Statistic Test
The omnibus statistic test algorithm can be used to detect the overall change of the time-series PolSAR images, but it is limited to detecting the change between two any different times.To compensate for the shortcoming of omnibus statistic test, Conradsen et al. (Conradsen, 2016) formulated the j R statistic test algorithm, which is used to generate the different images between any two images in different times (Conradsen, 2016).According to j R statistic test, the likelihood ratio of the statistic can be shown as follows: ( 1) 1 1 ( 1) ...
Equation ( 8) in logarithm form is as follows: Similarly, the similarity of PolSAR images from two any different times is measured by j lnR  . The larger the value, the greater the probability that change will occur between the two images.

The Generalized Gaussian Mixture Model (GGMM) and Expectation Maximization (EM)
The GMM (Rasmussen, 2000) is an unsupervised statistical learning approach that is widely used in statistical pattern recognition.The GMM can represent an arbitrarily complex PDF and is suitable to fit an unknown data distribution of the difference images.The finite GMM with k components can be calculated as: In order to estimate  , it is usual to introduce the loglikelihood function defined as shown in Equation ( 13): The EM algorithm is an iterative method used to find the maximum likelihood or the maximum a posteriori estimates of the components in the GMM (Dempster, 1977).The EM iteration alternates between performing an (E) step and a maximization (M) step.The E-step creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters: where The M-step computes the parameters maximizing the expected log-likelihood found in the E-step.
( ( , (t))) 0 We update the parameter estimation according to Equation ( 16): The EM algorithm of the criterion of convergence is defined as: For a certain class of traditional GMM algorithm, there is an important parameter commonly referred to as K that specifies the number of components to detect (Liu, 2017).However, the correct choice of K is often ambiguous.Fortunately, it can avoid the use of empirical methods for the selection of the number of components for the GMM and find the optimal number of components K in our previous work (Liu, 2017).

The Proposed Method of Time-Series Change Detection Using Images from Different Sensors
The procedure of time-series unsupervised change detection based on different sensors is shown as Figure 1.where, '0' represents non-changeable class and '255' represents changeable classes.

Study Area and Background
Wuhan (as shown in Figure 2) lies East Longitude 113°41′-115°05′, North Latitude 29°58′-31°22′, and it is the only megalopolises in the China West.Wuhan is known as 'River City' because the third largest river (Yangtze River) in the world and the largest tributary of the Yangtze River (Han River) across this city and many lakes were formed, such as East Lake, LiangZi Lake and so on.Dramatic changes have taken place in the city of Wuhan during the 'Twelfth Five-Year Plan' period (from 2011 to 2015).In order to detect the dramatic changes of city, time-series PolSAR images were acquired by Radarsat-2 and GF-3 sensors.In this study, our aim was to detect the dramatic changes of city and monitor the changes associated with the tunnel construction on East Lake.The proposed approach is based on automatic generation of the different images using an omnibus statistic and a statistical clustering approach.The omnibus statistic is a good strategy for obtaining the difference images from time series PolSAR images from different sensors.Using the proposed method, we were able to accurately detect the changes associated with the construction of a tunnel on East Lake from 2011 to 2017, dramatic changes in the city of Wuhan during 'Twelfth Five-Year Plan period'.The experimental results indicates that the proposed method can detect changes in a series of images from Radarsat-2 and GF-3 sensors.However, some further improvements are still necessary in future.For example, the results of change detection are easy affected by the speckle noise when use PolSAR images, and the method may be timeconsuming to arrive at the convergence criterion in this paper.
According to j R statistic test, if the matrixes of any two different PolSAR images in time are equal ( ), the change happens between the two images.
Gaussian with specified mean and variance.In general, the distribution of difference image ( ()d px) can be modeled as a weighted sum of two distributions.One represents the 'changed' class and another represents 'unchanged' class data distributions(Celik, 2011), i.e. modeled using the k-component GMM(Zivkovic, 2004), i.e.where () pk is the prior probability of the data point having been generated from component n of the mixture, and d (x ) p k is the nth component density modeled with a Gaussian density function.The data distribution modeled with Equation (11) can be separated into two distributions representing the data distributions of the 'changed' and 'unchanged' classes.

Figure 1 .
Figure 1.The process flow of the proposed method.

Figure 2 .
Figure 2. Location of the study area.