Stochastic differential equations (SDEs) have been widely used to model real world random phenomena. Existing works mainly focus on the case where the time series is modeled by a single SDE, which might be restrictive for modeling time series with distributional shift. In this work, we propose a change point detection algorithm for time series modeled as neural SDEs. Given a time series dataset, the proposed method jointly learns the unknown change points and the parameters of distinct neural SDE models corresponding to each change point. Specifically, the SDEs are learned under the framework of generative adversarial networks (GANs) and the change points are detected based on the output of the GAN discriminator in a forward pass. Numerical results on both synthetic and real datasets are provided to validate the performance of the algorithm in comparison to classical change point detection benchmarks, standard GAN-based neural SDEs, and other state-of-the-art deep generative models for time series data.

Existing studies on constrained reinforcement learning (RL) may obtain a well-performing policy in the training environment. However, when deployed in a real environment, it may easily violate constraints that were originally satisfied during training because there might be model mismatch between the training and real environments. To address this challenge, we formulate the problem as constrained RL under model uncertainty, where the goal is to learn a policy that optimizes the reward and at the same time satisfies the constraint under model mismatch. We develop a Robust Constrained Policy Optimization (RCPO) algorithm, which is the first algorithm that applies to large/continuous state space and has theoretical guarantees on worst-case reward improvement and constraint violation at each iteration during the training. We show the effectiveness of our algorithm on a set of RL tasks with constraints.

The problem of robust multi-hypothesis testing in the Bayesian setting is studied in this paper. Under the$m\geq 2$hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through some moment functions, i.e., the sets contain distributions whose moments are centered around empirical moments obtained from some training data sequences. The goal is to design a test that performs well under all distributions in the uncertainty sets, i.e., a test that minimizes the worst-case probability of error over the uncertainty sets. Insights on the need for optimization-based approaches to solve the robust testing problem with moment constrained uncertainty sets are provided. The optimal (robust) test based on the optimization approach is derived for the case where the observations belong to a finite-alphabet. When the size of the alphabet is infinite, the optimization problem is infinite-dimensional and intractable, and therefore a tractable finite-dimensional approximation is proposed, whose optimal value converges to the optimal value of the original problem as the size of the dimension of the approximation goes to infinity. A robust test is constructed from the solution to the approximate problem, and guarantees on its worst-case error probability over the uncertainty sets are provided. Numerical results are provided to demonstrate the performance of the proposed robust test.

In this paper, we address the challenges of offline reinforcement learning (RL) under model mismatch, where the agent aims to optimize its performance through an offline dataset that may not accurately represent the deployment environment. We identify two primary challenges under the setting: inaccurate model estimation due to limited data and performance degradation caused by the model mismatch between the dataset-collecting environment and the target deployment one. To tackle these issues, we propose a unified principle of pessimism using distributionally robust Markov decision processes. We carefully construct a robust MDP with a single uncertainty set to tackle both data sparsity and model mismatch, and demonstrate that the optimal robust policy enjoys a near-optimal sub-optimality gap under the target environment across three widely used uncertainty models: total variation, $\chi^2$ divergence, and KL divergence. Our results improve upon or match the state-of-the-art performance under the total variation and KL divergence models, and provide the first result for the $\chi^2$ divergence model.

This paper studies first-order policy optimization for robust average cost Markov decision processes (MDPs). Specifically, we focus on ergodic Markov chains. For robust average cost MDPs, the goal is to optimize the worst-case average cost over an uncertainty set of transition kernels. We first develop a sub-gradient of the robust average cost. Based on the sub-gradient, a robust policy mirror descent approach is further proposed. To characterize its iteration complexity, we develop a lower bound on the difference of robust average cost between two policies and further show that the robust average cost satisfies the PL-condition. We then show that with increasing step size, our robust policy mirror descent achieves a linear convergence rate in the optimality gap, and with constant step size, our algorithm converges to an $\epsilon$-optimal policy with an iteration complexity of $\mathcal{O}(1/\epsilon)$. The convergence rate of our algorithm matches with the best convergence rate of policy-based algorithms for robust MDPs. Moreover, our algorithm is the first algorithm that converges to the global optimum with general uncertainty sets for robust average cost MDPs. We provide simulation results to demonstrate the performance of our algorithm.

The problem of quickest change detection (QCD) in autoregressive (AR) models is investigated. A system is being monitored with sequentially observed samples. At some unknown time, a disturbance signal occurs and changes the distribution of the observations. The disturbance signal follows an AR model, which is dependent over time. Before the change, observations only consist of measurement noise, and are independent and identically distributed (i.i.d.). After the change, observations consist of the disturbance signal and the measurement noise, are dependent over time, which essentially follow a continuous-state hidden Markov model (HMM). The goal is to design a stopping time to detect the disturbance signal as quickly as possible subject to false alarm constraints. Existing approaches for general non-i. i.d. settings and discrete-state HMMs cannot be applied due to their high computational complexity and memory consumption, and they usually assume some asymptotic stability condition. In this paper, the asymptotic stability condition is firstly theoretically proved for the AR model by a novel design of forward variable and auxiliary Markov chain. A computationally efficient Ergodic CuSum algorithm that can be updatedrecursivelyis then constructed and is further shown to be asymptotically optimal. The data-driven setting where the disturbance signal parameters are unknown is further investigated, and an online and computationally efficient gradient ascent CuSum algorithm is designed. The algorithm is constructed by iteratively updating the estimate of the unknown parameters based on the maximum likelihood principle and the gradient ascent approach. The lower bound on its average running length to false alarm is also derived for practical false alarm control. Simulation results are provided to demonstrate the performance of the proposed algorithms.

The problem of robust binary hypothesis testing is studied. Under both hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through moments; in particular, the sets contain distributions whose moments are centered around the empirical moments obtained from training observations. The goal is to design a test that performs well under all distributions in the uncertainty sets, i.e., minimize the worst-case error probability over the uncertainty sets. In the finite-alphabet case, the optimal test is obtained. In the infinite-alphabet case, a tractable approximation to the worst-case error is derived that converges to the optimal value A test is further constructed to generalize to the entire alphabet. An exponentially consistent test for testing batch samples is also proposed. Numerical results are provided to demonstrate the performance of the proposed robust tests.

The problem of quickest change detection in Markov models is studied. A sequence of samples are generated from a Markov model, and at some unknown time, the transition kernel of the Markov model changes. The goal is to detect the change as soon as possible subject to false alarm constraints. The data-driven setting is investigated, where neither the pre-nor the post-change Markov transition kernel is known. A kernel based data-driven algorithm is developed, which applies to general state space and is recursive and computationally efficient. Performance bounds on the average running length and worst-case average detection delay are derived. Numerical results are provided to validate the performance of the proposed algorithm.

The problem of quickest change detection in hidden Markov models (HMMs) is investigated. A sequence of samples are generated from a HMM, and at some unknown time, the transition kernel and/or the emission probability of the HMM changes. The goal is to detect the change as soon as possible subject to false alarm constraints. The data-driven setting is investigated, where none of the pre-, post-change Markov transition kernels or the emission probabilities are known. In this paper, a kernel based data-driven algorithm is developed. Performance bounds on its average running length (ARL) to false alarm and worst-case average detection delay (WADD) are theoretically characterized, where the WADD is at most of the order of the logarithm of the ARL. Numerical results are provided to validate the performance of the proposed algorithm.

The problem of robust hypothesis testing is studied, where under the null and the alternative hypotheses, the data-generating distributions are assumed to be in some uncertainty sets, and the goal is to design a test that performs well under the worst-case distributions over the uncertainty sets. In this paper, uncertainty sets are constructed in a data-driven manner using kernel method, i.e., they are centered around empirical distributions of training samples from the null and alternative hypotheses, respectively; and are constrained via the distance between kernel mean embeddings of distributions in the reproducing kernel Hilbert space, i.e., maximum mean discrepancy (MMD). The Bayesian setting and the Neyman-Pearson setting are investigated. For the Bayesian setting where the goal is to minimize the worst-case error probability, an optimal test is firstly obtained when the alphabet is finite. When the alphabet is infinite, a tractable approximation is proposed to quantify the worst-case average error probability, and a kernel smoothing method is further applied to design test that generalizes to unseen samples. A direct robust kernel test is also proposed and proved to be exponentially consistent. For the Neyman-Pearson setting, where the goal is to minimize the worst-case probability of miss detection subject to a constraint on the worst-case probability of false alarm, an efficient robust kernel test is proposed and is shown to be asymptotically optimal. Numerical results are provided to demonstrate the performance of the proposed robust tests.

Phase unwrapping is a key step in interferometric synthetic aperture radar (InSAR) data processing. The deterioration of the phase continuity caused by noise or special topography in the interference data often brings challenges to the unwrapping work. When the phase is separated by low coherence samples, it is difficult to extract continuous phase across the closed discontinuity loops. We propose a two-dimensional phase unwrapping method based on region residues derived from continuous regions with higher continuity. The separated continuous regions generate phase differences and expanded boundaries between the regions. There may be region residues at the intersection of the boundaries, and dual residues are coupled for branch-cuts. According to the branch-cuts, the proposed method realizes the phase aligning of the separated regions. The aligned region phase provides a global continuity framework, which guides the unwrapping outside. The proposed method is validated with a block of airborne InSAR interferometric phase data.

Impervious surface extraction from remote sensing images has become a promising technology to measure the urban ecological environment and monitor human activity. However, due to the complex characteristics of impervious landscapes, most researches on impervious surface extraction hardly identify the scattered and small objects especially in difficult areas, which severely affect the accuracy of mapping impervious surface. In this work, we propose a channel and spatial attention mechanism (CSAM) to extract impervious surface in difficult areas, which includes a channel attention module to learn the relationship in the multi-channel remote sensing images and a spatial attention module to capture the features of the inconspicuous objects. Experiments with the Sentinel-2 dataset in South Africa demonstrate that CSAM can outperform the state-of-the-art methods.

In this paper, the robust hypothesis testing problem is investigated, where under the null and the alternative hypotheses, the distributions are assumed to be in some uncertainty sets. The uncertainty sets are constructed in a data-driven manner, i.e., they are centered around empirical distributions. The distance between kernel mean embeddings of distributions in the reproducing kernel Hilbert space is used as the distance metric of uncertainty sets. The Bayesian setting is studied, where the goal is to minimize the worst-case error probability. An optimal test is firstly obtained for the case with a finite alphabet. For the case with an infinite alphabet, a tractable approximation is proposed to quantify the worst-case error probability, and a kernel smoothing method is further applied to design test that generalizes to unseen samples. A heuristic robust kernel test is also proposed and proved to be exponentially consistent. Numerical results are provided to demonstrate the performance of the proposed tests.

The problem of quickest change detection in anonymous heterogeneous sensor networks is studied. The sensors are clustered into$K$groups, and different groups follow different data generating distributions. At some unknown time, an event occurs in the network and changes the data generating distribution of the sensors. The goal is to detect the change as quickly as possible, subject to false alarm constraints. The anonymous setting is studied, where at each time step, the fusion center receives unordered samples without knowing which sensor each sample comes from, and thus does not know its exact distribution. In [1], an optimal algorithm was provided, which however is not computational efficient for large networks. In this paper, a computationally efficient test is proposed and a novel theoretical characterization of its false alarm rate is further developed.

The problem of quickest dynamic anomaly detection in anonymous heterogeneous sensor networks is studied. The$n$heterogeneous sensors can be divided into$K$types with different data generating distributions. At some unknown time, an anomaly emerges in the network and changes the data generating distribution of the sensors. The goal is to detect the anomaly as quickly as possible, subject to false alarm constraints. The anonymous setting is studied, where the fusion center does not know which sensor that each sample comes from, and thus does not know its exact distribution. Firstly, the static setting is investigated where the sensor affected by the anomaly does not change with time. A generalized mixture CuSum algorithm is constructed and is further shown to be asymptotically optimal. The problem is then extended to a dynamic setting where the sensor affected by the anomaly changes with time. An asymptotically optimal weighted mixture CuSum algorithm is proposed. Numerical results are also provided to validate the theoretical results.

The problem of robust hypothesis testing is studied, where under the null and alternative hypotheses, data generating distributions are assumed to belong to some uncertainty sets. In this paper, uncertainty sets are constructed in a data-driven manner, i.e., they are centered around empirical distributions of training samples from the null and alternative hypotheses, respectively; and are constrained via the distance between kernel mean embeddings of distributions in the reproducing kernel Hilbert space. The Neyman-Pearson setting is investigated, where the goal is to minimize the worst-case probability of miss detection subject to the constraint on the worst-case probability of false alarm. An efficient robust kernel test is proposed and is further shown to be asymptotically optimal. Numerical results are further provided to demonstrate the performance of the proposed robust test.

The problem of quickest change detection (QCD) in anonymous heterogeneous sensor networks is studied. There are n heterogeneous sensors and a fusion center. The sensors are clustered into K groups, and different groups follow different data generating distributions. At some unknown time, an event occurs in the network and changes the data generating distribution of the sensors. The goal is to detect the change as quickly as possible, subject to false alarm constraints. The anonymous setting is studied in this paper, where at each time step, the fusion center receives n unordered samples. The fusion center does not know which sensor each sample comes from, and thus does not know its exact distribution. In this paper, a simple optimality proof is derived for the Mixture Likelihood Ratio Test (MLRT), which was constructed and proved to be optimal for the non-sequential anonymous setting in [1]. For the QCD problem, a mixture CuSum algorithm is constructed in this paper, and is further shown to be optimal under Lorden's criterion [2].

Spectral built-up indices are considered promising to map impervious surface area (ISA) distribution at regional and global scales due to their easy implementation, parameter-free and convenience in practical applications. The objective of this study is to explore and compare the potential of different impervious surface indices for mapping urban area from Landsat imagery. By sharpening a thermal-band image and integrating it in a current index, a modified normalized difference impervious surface index (MNDISI) is proposed. Additionally, an automatic Gaussian-based threshold selection method is proposed to identify the optimal MNDISI threshold for separating impervious surface from background features. To evaluate the effectiveness of MNDISI, comparison analysis is conducted between MNDISI and other built-up indices using Landsat TM/ETM+/OLI-TIRS imagery acquired in the four different seasons. With reduced uncertainties from automatic threshold selection, the MNDISI has highest performance of ISA mapping with an overall accuracy of 87% and an overall Kappa coefficient of 0.74. This study reveals that the proposed MNDISI with automatic threshold selection is an effective index for impervious surface extraction, which could be applied for rapid and automatic ISA mapping at regional and global scales.

Poyang Lake is the largest freshwater lake in China and one of the most important wetlands in the world. Vegetation, an important component of wetland ecosystems, is one of the main sources of the carbon in the atmosphere. The backscatter coefficients (HH, HV and VV), the Pope biophysical indices, the polarimetric parameters from Freeman-Durden decomposition, Cloude-Pottier decomposition, TSVM decomposition were derived from RADARSAT-2 PolSAR data and used to analysis the relationship between them and the wetland vegetation biomass. After the polarization parameters optimization, we find that these 6 parameters, σ0HV, VSI, PV, PD, PSand Anisotropy (A) can be used to retrieve the Poyang Lake Wetland vegetation biomass. The R2and RMSE of the wetland vegetation biomass inversion for the combination of SVM and backscatter coefficients are 0.49, 118.3g/m2; that for the combination of SVM and polarimetric parameters are 0.71, 76.1g/m2.

Forests are simplified as homogeneous volumes constituted of randomly uniform particles, characterized by a constant extinction coefficient in the random volume over ground (RVoG) model, which has been extensively applied to polarimetric synthetic aperture radar (SAR) interferometry for forest height estimation. This letter takes into account the heterogeneous vertical structure reflected by the vertically varying extinction coefficient curve in the forest volume layer, and modifies the RVoG model to make it be more suitable for height inversion of forests with complex structures. For this purpose, the normalized extinction coefficient curve is fit by large-footprint light detection and ranging full waveform data using the Gaussian function. Finally, the varying extinction RVoG model is applied to forest height estimation using airborne L-band SAR data acquired by the E-SAR system. The results are compared with in situ measurements, which indicate that the varying extinction RVoG model can obtain more accurate results for forest height inversion.

The fusion of low-spatial-resolution multispectral (MS) bands and a high-spatial-resolution (HSR) panchromatic (PAN) band obtained by the same sensor is desirable to produce high quality, HSR MS images. Due to the significant effect of haze values on spectral direction of pixels in the fused images, a fusion method taking into account haze, which is referred as Haze- and Ratio- based (HR) method, is demonstrated to yield better performance than some other methods. In this HR method, haze values are determined by the minimal gray values of each of the MS bands and the PAN band. Obviously, these minimal values correspond to different pixels in different bands, which may cause unstable performance of the method. In order to yield a reasonable and stable approach for the determination of haze values, an improved dark-pixel subtraction method is proposed to determine the haze values used in the HR method in this study.

Water extraction in arid regions such as north Xinjiang is particularly important due to their lack of water. During the last decades, water resources in north Xinjiang have been seriously impacted by more and more coal-mining activities. Accurate extraction of rivers and broad waters in this region is becoming requisite. However, there are some limitations for existing methods to extract small rivers whose width is less than the resolution of optical imagery because most river-pixels are mixed-pixels in this region. Additionally, rivers there often share similar spectral characteristics with hill shadows, bringing more challenges to their extraction. As typical arid mountain regions, the coal-mining regions of north Xinjiang were selected as the study area in our research. In addition to a cloud removal project, the paper proposed a Blue and Near Infrared Band based Water Index (BNWI) and built the water index model using the Normalized Difference Water Index (NDWI), the Modified Normalized Difference Water Index (MNDWI) and BNWI. Based on the introduced method, the long time series of small-river and broad-water products were extracted from the Landsat MSS/TM/OLI imagery. Experiments proved the proposed method was appropriate for small rivers delineation and the MNDWI threshold method was available to broad waters extraction. The overall accuracy (OA) was above 90%. Results showed that water body was decreasing affected by human activities in coal-mining regions in the period 2002-2014.

Until now, most polarimetric synthetic aperture radar interferometry (PolInSAR) research has been based on full-polarization (HH + HV + VH + VV) SAR data, which can provide complete polarimetric information but usually have a smaller swath and lower spatial resolution than dual-polarization (dual-pol) data. Some existing researches concern the dual-pol PolInSAR; however, these works did not perform the coherence optimization process which may make the inversion unstable. In this paper, the PolInSAR technique based on dual-pol (HH + HV) SAR data is investigated in order to demonstrate its validity for forest height retrieval and thus show that PolInSAR is better able to meet the requirements of global-scale research. We extend the three-stage inversion process and coherence optimization algorithm to dual-pol PolInSAR. In addition, based on the random volume over ground model, a search method for finding the volume-only coherence on ambiguous line segments is proposed. Finally, the dual-pol PolInSAR technique is applied to forest height estimation using airborne L-band SAR data acquired by the E-SAR system over the Traunstein test site in Germany. The forest heights estimated by dual-pol PolInSAR are compared with those estimated using the full-pol mode and also with measurements made in situ. The results show that dual-pol PolInSAR can obtain similar estimated forest heights to the full-pol mode and also that the search method for volume-only coherence retrieval can improve the inversion accuracy. The coefficient of determination (r2) for the relation between the dual-pol PolInSAR and the in situ measurements is 0.7287.

Various multispectral (MS) and panchromatic (PAN) fusion (or pan-sharpening) algorithms were developed to produce an enhanced MS image of high spatial resolution. Regarding the novelty in both the PAN and MS bands of the WV-2 imagery, the objective of this study is to assess the performance of nine state-of-the-art pan-sharpening methods for the WV-2 imagery, using both image quality indices and information indices that used for urban information extraction. The comparison of the four quality indices (RASE, ERGAS, SAM, and Q4) demonstrated that the HR method performed the best for the WV-2 MS and PAN images. However, the comparison of the four information indices showed that a higher quality at data level does not signify better information preservation for object recognition.

Global climate change has caused sea level rise, and one of the most extremely consequences are the increased frequency and hazards of the storm surge disasters, therefore, how to effectively assess the risk of storm surge disaster is of importance to hazard reduction and mitigation. However, the storm surge forecast models have complex parameters, which computational inefficiency. Traditional large-scale assessment usually takes elevation-area method based on GIS software, which result in large errors. The present study is attempted to: (1) Select proper two-dimensional hydraulic storm surge inundation model. This model not only has the physical realism but simple and efficient. (2)The present study will focus on the method to extract the required surface parameters based on the remote sensing data to integrate remote sensing data into the model. This project aims to provide the theoretical basis and methodologies for flood risk assessment in coastal zone of China.

The objective of this paper is to map large-area impervious surfaces in bohai ring megalopolis areas from Landsat imagery using SVM method. Then, combined with the sixth population census data, the map of the impervious surface area (ISA) per person is derived. Finally, this paper analyses the relationship between the impervious surfaces and population census data, and gross domestic product (GDP) data. Our results indicated that the density of ISA in Beijing and Tianjin were great higher than in other administrative regions. By comparing the ISA with population census and GDP data, our results also indicated that the ISA was highly correlated with population census and GDP data. A strong relationship (R2= 0.879) was observed between the ISA and the population census data in the whole study area. In addition, a strong and positive relationship was observed between the ISA and GDP data (correlation coefficient R2= 0.779 for the whole study area). This research can provide a simple method for policy makers to assess potential urbanization impacts of future urban planning and development activities.

The main objective of this paper is to examine and evaluate the performance of the airborne SAR system through interferometric processing and error analysis. Firstly, the paper describes how high-precision DEMs are derived from the airborne dual-antenna InSAR data. Based on airborne dual-antenna InSAR bore-sight model, this paper summarizes the main factors which influence the accuracy of DEM in data processing, and analyses the error of those factors. Then, the POS/AV510 system parameters are used for analyzing the quantitative relationship between the platform height, baseline length, baseline angle, look angle and DEM error. The experimental data used is airborne dual-antenna X-band InSAR data, and the measured GCPs are used to validate the accuracy of DEM. Evaluation results in terms of the standard deviation (SD) and the average mean error (AME) are derived by comparing the reconstructed InSAR DEM with the reference GCPs. The AME of the DEM is up to 1.7628 m. The SD of the DEM are up to±1.0858 m.