Recurrent neural networks for atmospheric noise removal from InSAR time series with missing values
Introduction
Interferometric Synthetic Aperture Radar (InSAR) has become a promising technology for land subsidence and infrastructural deformation monitoring in the last decade (Lin et al., 2017, Ma et al., 2019b, Shi et al., 2018, Zhang et al., 2019). The high-level noise in InSAR caused by atmospheric delay is the primary error source of deformation estimation in InSAR technologies. Atmospheric delay is typically split into ionospheric and tropospheric terms. The ionospheric delay is caused by variations in free electrons along the travel path, which is only significant in long wavelength signals such as P-band and L-band SAR (Gray et al., 2000). Since we use the C-band Sentinel-1 SAR data in our work, the ionospheric delay is not considered. The tropospheric delay is caused by the refraction of the radar signal passing through the troposphere. It can be divided into stratified delay (hydrostatic component) and turbulent mixing delay (wet component) (Hanssen, 2001). The stratified delay depends on pressure and temperature and is correlated with the topography. The turbulent mixing delay mainly depends on variations in water vapor. In general, pressure and temperature vary much less in time and space than does water vapor. Therefore, the impact on InSAR from the stratified delay may cancel out, and the impact of turbulent mixing delay on interferograms becomes more significant than the stratified delay (Murray et al., 2019). When practicing time series InSAR techniques, the tropospheric delay can be assumed as uncorrelated in time domain if the InSAR data consists of sufficient images without long temporal gaps and each image mainly reflects turbulent mixing delays (Li et al., 2019).
Since our study mainly focuses on urban areas without high relief (strong topography), we treat the turbulent mixing delay as the dominant component of the atmospheric delay and assume the atmospheric noise in the InSAR deformation time series as stochastic. Under the hypothesis that atmospheric delays are temporally uncorrelated and ground deformations are temporally correlated, low-pass temporal filtering, like Gaussian filtering and triangular filtering, is commonly used to estimate and mitigate the atmospheric noises involved in the deformation time series (Ma et al., 2019b, Ferretti et al., 2000). However, its performance heavily depends on parameter settings, like weighting strategies and filtering window length. Insufficient filtering may cause much noise left in the deformation, while excessive filtering may neglect small changes unexpectedly. Therefore, it is necessary to develop data-driven methods for better removing the atmospheric noises from the deformation time series of each InSAR measure point (MP) and deriving the accurate deformation estimation.
Deep learning has come into its own primarily in the past decade and shown excellent results in many areas such as computer vision (Krizhevsky et al., 2012), speech recognition (Amodei et al., 2016), and natural language processing (Vaswani et al., 2017). Recently, the remote-sensing community has also paid lots of attention to deep learning, especially convolutional neural networks (CNNs) (Zhu et al., 2017, Ma et al., 2019a). CNN shows great advantages in image analysis and has achieved significant success at many tasks including scene classification, object detection, land-use & land-cover classification, and image registration (Anantrasirichai et al., 2019, Kussul et al., 2017, Marmanis et al., 2018, Paoletti et al., 2018, Sharma et al., 2017, Vetrivel et al., 2018, Wang et al., 2018). On the other hand, recurrent neural networks (RNNs), such as Long Short-Term Memory (LSTM) (Hochreiter and Schmidhuber, 1997) and Gated Recurrent Unit (GRU) (Cho et al., 2014), specialize in discrete sequence analysis tasks like time series forecasting, classification, or change detection. Taking advantage of RNN, time series based analysis is another promising research direction in remote-sensing (Lyu et al., 2016, Mou et al., 2017, Ienco et al., 2017, Cai et al., 2018, Ho Tong Minh et al., 2018) but has been studied much less.
This paper investigates applying the deep learning model, especially the RNN model, to remove the atmospheric noise from the InSAR time series. There are mainly three challenges in our application. First of all, deep learning models are data demanding; supervised learning models require sufficient labeled training data. As for the InSAR time series denoising task, it is practically impossible to obtain ground truth. The ground leveling data is always inconsecutive, and manually labeling the true deformations is also infeasible. On the other hand, we may expect to acquire SAR data regularly in each repeat cycle of a specific satellite. However, some data is missing in practice due to operational reasons. The missing values in InSAR data may significantly increase the difficulty of modeling the time series. Thirdly, the InSAR time series can constantly capture seasonal variations, which is hard to deal with effectively by deep learning models (Smyl, 2020). The interference of seasonal variations makes the denoising task much more difficult.
Synthetic data is increasingly being used for training deep learning models (Nikolenko, 2019). Synthetic interferograms have been used to tackle the unbalanced training data problem for volcano detection (Anantrasirichai et al., 2019). Synthetic satellite imageries also contribute to improving the performance of aircraft and vehicle detection (Howe et al., 2019, Liu et al., 2020). In this paper, we develop a physical-based simulation method to generate synthetic InSAR time series with diverse deformation patterns for training and evaluating our proposed denoising model.
Various data imputation methods have been proposed to handle the missing values of time series. Conventional imputation methods include forward fill, moving average, linear interpolation, etc. RNN models for imputation have also been studied in recent years (Bengio and Gingras, 1995, Tresp and Briegel, 1997, Parveen and Green, 2002, Lipton et al., 2016). These methods often result in a two-step process where imputation and the model for target application are separated. GRU-D (Che et al., 2018) was proposed to utilize the missing patterns and can be trained end-to-end aiming at the final classification or prediction tasks. BRITS (Cao et al., 2018) employs bidirectional RNN to derive time series from both forward and backward directions. BRITS also introduced estimation errors for using future observations to validate the previous imputation results with an eye on the final target applications. However, since the raw InSAR time series contain high-level noises in itself, simple imputation or taking the observed value as supervision may both introduce undesired bias. In this paper, we incorporate a GRU-D layer into our proposed GRU model for handling missing values in the InSAR time series. We extend the original GRU-D layer into a bidirectional form to take advantage of both preceding and succeeding observations. Our proposed GRU model is jointly trained to optimize all the components for generating denoised time series.
Seasonal variations in the InSAR time series are commonly associated with processes such as thermal contraction and expansion, seasonal precipitation, groundwater extraction, and freeze–thaw cycles. We denote such underlying processes as seasonal factors (SF). In (Yan et al., 2009), a theoretical model is proposed to estimate the thermal expansions of GPS monuments and nearby bedrock for 86 globally distributed GPS stations based on surface air temperatures. The cumulative precipitations were adopted as the rainfall factors to predict the periodic displacement of a landslide in (Zhou et al., 2016). With the aid of seasonal factors, we can better analyze the seasonal variations presented in ground deformation. Based on such consideration, we introduce seasonal factors (SF) signals, like temperature or precipitation, as an auxiliary input to the GRU model for better estimating the seasonal variations presented in the InSAR time series.
The rest of our paper is organized as follows. Section 2 introduces the simulation method for generating the synthetic InSAR time series. Section 3 gives the formulation of our problem and introduces the architecture of our proposed GRU model. Section 4 conducts experiments on both synthetic data and Hong Kong International Airport (HKIA) real-world data from Sentinel-1 to verify the feasibility and validity of our proposed GRU method. Section 5 gives discussions on the robustness of our proposed model on various noise levels, the effectiveness of introducing GRU-D for handling the missing values, and the superiority of incorporating SF signal for dealing with seasonal variations. We also demonstrate the estimated atmospheric phase screen (APS) over HKIA and the limitations of our study in this section. Section 6 gives the conclusions and future work directions.
Section snippets
Generation of synthetic InSAR time series
To fulfill the data demanding nature of deep learning models, we first propose the InSAR time series simulation methods based on the physical mechanisms of typical deformations. An overview of the synthesis process is illustrated in Fig. 1.
Problem formulation
Atmospheric noise removal from the InSAR time series can be seen as a sequence-to-sequence regression problem. Given the raw time series, we want to output the denoised one. We denote the input InSAR time series as , where n is the length, and for each , represents the t-th observation of the time series. Since the SAR data is expected to be acquired regularly, the time interval between two consecutive observations of X is constant. A masking vector
Experiments
We demonstrate the performance of our proposed GRU model on both synthetic data and Hong Kong International Airport (HKIA) real-world data and compare it to the commonly used Gaussian filtering and other RNN baseline methods.
Robustness to different noise levels
In Section 4.4, the synthetic testing data share the same noise level as the training data in the experiment. However, in real applications, we can not estimate the noise level in advance, the robustness of a denoising model to different noise conditions matters. Therefore, we conduct experiments on five groups of testing datasets with different noise levels range from 2 mm to 9 mm (STD). Other settings keep the same as in Section 4.4 (missing rate is 15%, oscillation amplitude ranges in [0,
Conclusion
In this paper, we propose a deep bidirectional GRU model for atmospheric noise removal from the InSAR time series. For generating sufficient synthetic training data, we develop a simulation method based on the physical mechanisms of typical deformations. For handling missing values in the InSAR time series, we introduce a bidirectional GRU-D layer in our proposed GRU model. By incorporating the seasonal factor (SF) signal as an auxiliary input, our proposed GRU model shows advantages in dealing
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by National Natural Science Foundation of China (41971278) and the Research Grants Council (RGC) of Hong Kong (CUHK14504219).
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