To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have been developed to construct dimension-independent algorithms. However, there are three challenges for these infinite-dimensional Bayesian methods: prior measures usually act as regularizers and are not able to incorporate prior information efficiently; complex noises, such as more practical non-i.i.d. distributed noises, are rarely considered; and time-consuming forward PDE solvers are needed to estimate posterior statistical quantities. To address these issues, an infinite-dimensional inference framework has been proposed based on the infinite-dimensional variational inference method and deep generative models. Specifically, by introducing some measure equivalence assumptions, we derive the evidence lower bound in the infinite-dimensional setting and provide possible parametric strategies that yield a general inference framework called the Variational Inverting Network (VINet). This inference framework can encode prior and noise information from learning examples. In addition, relying on the power of deep neural networks, the posterior mean and variance can be efficiently and explicitly generated in the inference stage. In numerical experiments, we design specific network structures that yield a computable VINet from the general inference framework. Numerical examples of linear inverse problems of an elliptic equation and the Helmholtz equation are presented to illustrate the effectiveness of the proposed inference framework.

Abstract. We propose a data-assisted two-stage method for solving an inverse random source problem of the Helmholtz equation. In the first stage, the regularized Kaczmarz method is employed to generate initial approximations of the mean and variance based on the mild solution of the stochastic Helmholtz equation. A dataset is then obtained by sampling the approximate and corresponding true profiles from a certain a priori criterion. The second stage is formulated as an image-to-image translation problem, and several data-assisted approaches are utilized to handle the dataset and obtain enhanced reconstructions. Numerical experiments demonstrate that the data-assisted two-stage method provides satisfactory reconstruction for both homogeneous and inhomogeneous media with fewer realizations.

Vegetation growth changes in urban areas are important for understanding ecosystem responses to climate change. In this study, a method for vegetation growth trend extraction in urban areas based on piecewise linear regression and seasonality removal from Landsat time series data is proposed. A case study in Tianjin, China indicated that considering seasonality in vegetation growth trend analysis had impact on the absolute values and even the signs of trends. Compared to piecewise linear regression without seasonality removal, the proposed method extracted more pixels with significantly monotonic growth trends.

A novel method of building damage extraction using bitemporal spectral and height data was proposed in this study. The pre-event height data were first estimated from the pre-event spectral image using Conditional Generative Adversarial Net (cGAN). The pre- and post-event spectral and height data were then used in extraction of building damages with significant changes in height and homogeneity. The experimental results demonstrated that the proposed method outperformed the existing method.

In this letter, we proposed two novel feature selection methods using sparse representation for one-class classification of remote sensing images. In the first method, a sparse reconstructive weight matrix of the data set was obtained by reconstructing samples using sparse representation. The “good” features were then selected by evaluating reconstructing errors in weight matrix. The method is called feature selection based on sample reconstruction (FSSR). In the second method, the weight matrix was obtained by reconstructing features using sparse representation. Feature selection was then conducted by evaluating correlation among features using weight matrix. The method is called feature selection based on feature reconstruction (FSFR). The proposed feature selection methods were evaluated and compared with several state-of-the-art feature selection methods in two different case studies. The experimental results indicate that the proposed methods generally outperformed the existing methods. In particular, FSFR produced stable better performance.

Winter wheat occupies an important position in agricultural production and national economy. In this study, we proposed a new method of winter wheat mapping that combined time-weighted dynamic time warping (TWDTW) and phenological rules from Landsat NDVI time series data. The proposed method was evaluated in winter wheat mapping using Landsat time series data in Beijing and Hebei Province, China. The experimental results obtained showed that the proposed method outperformed the existing method in mapping winter wheat with an acceptable accuracy.

Urbanization dynamics of small cities and towns are understudied, especially for countries in Africa. In this study, we use dense Landsat time series data to extract urban expansion dynamics of small cities and towns in Nigeria and the Democratic Republic of the Congo, and then conduct spatio-temporal analysis to characterize the obtained urban expansion. Our results show that the proposed methodology effectively extracted urban expansion of small cities with acceptable accuracy. Small cities experience patterns and rates of urban expansion that are markedly different from larger cities.

In this study, we proposed a new object-based landslide mapping method using multi-source data and One-Class Random Forest. The method was carried out by using a set of image object features, including spectral, textural and topographical features derived from bi-temporal very high resolution images and DEM data. The proposed method was evaluated using WorldView-2 multispectral images and ASTER GDEM data over Haiti area, and the importance of different features was analyzed. The results showed that the proposed method outperformed the two comparative methods, with increases of 11.58% and 5.09% in kappa coefficient, respectively. The proposed method provides a fast and reliable method for landslide mapping.

This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz decomposition, the model problem is reduced to a coupled boundary value problem of the Helmholtz equations. The relation is established between the compressional or shear far-field pattern for the elastic wave equation and the corresponding far-field pattern for the coupled Helmholtz equations. An efficient and accurate Nyström-type discretization for the boundary integral equation is developed to solve the coupled system. The translation invariance of the phaseless compressional and shear far-field patterns are proved. A system of nonlinear integral equations is proposed and two iterative reconstruction methods are developed for the inverse problem. In particular, for the phaseless data, a reference ball technique is introduced to the scattering system in order to break the translation invariance. Numerical experiments are presented to demonstrate the effectiveness and robustness of the proposed method.

This study proposed a new method of urban impervious surface extraction from very high resolution (VHR) imagery, by combining spatial and spectral unmixing and decision tree classification. Endmember classes were first defined, where two shadow endmembers were used. Spatial homogeneity and spectral purity were fused to extract endmembers, i.e., spatial and spectral endmember. A modified multiple endmember unmixing method was adopted to unmix VHR image to produce endmember fraction images. Decision rules were then created to produce final impervious surface extraction results. The experimental results using Worldview-2 multispectral image of Beijing urban area validates the proposed method, by comparing with existing methods.

Most of the decision fusion techniques developed for the remote sensing applications have the drawback of assuming the conditional independence between the classification results, whereas, usually the correlation exists due to the same measuring instrument or same area under study. Fusion of Correlated Probabilities (FCP) method has a potential to deal with conditional dependence only for two data sets. The proposed Multi-sensor Fusion of Correlated Probabilities (MFCP) algorithm is the extended version of FCP by modifying the cross conditional dependence between three or more multi-sensor information sources. The proposed MFCP method is assessed in the multi-sensor land cover classification over the Beijing area for three sensor data sets. We evaluated and validated our proposed methodology by comparing it with four existing fusion methods. The experimental results demonstrated that the proposed MFCP method outperformed all the compared fusion methods in terms of overall accuracy, kappa and class wise accuracies. Therefore, the MFCP method is adaptable to any type and any number of sensor data sets.

Urban expansion has become a major issue in many metropolitan areas with the rapid development of China. In this study, by taking Tianjin as an example, urban expansion extraction at annual frequency and spatial-temporal analysis were conducted using Landsat time series data from 1992 to 2001. Landsat data were first classified to extract urban area of different years. A temporal consistency check was then applied to improve the classification results. Overall accuracies were generally improved up to 6%, and kappa coefficient increased up to 0.08 after the consistency check. Urban expansion was obtained with post-classification comparison change detection technique. Spatial-temporal analysis was carried out to characterize the urban growth information.

Converting probability maps derived from indicator cokriging (ICK) to a specific land cover classification map is the second step of super-resolution mapping (SRM) under the geostatistical framework. In this study, two image segmentation strategies, namely mathematical morphology and region growing, were applied on the ICK-derived probability maps in order to take into account spatial characteristics such as shape and connectivity. A case study in South Carolina (USA) showed that the thematic map created by the proposed method had an overall accuracy improved by 2% and Kappa improved by 6% compared to the map derived from the existing sequential generation process. This indicates our methodology as a promising alternative that can be embedded into SRM tasks.

This paper presented a new method of lithological mapping using extended one-class kernel sparse representation, a new one-class classifier. In the proposed method, to address spectral variability of lithological types, learning vector quantization for novelty detection was adopted to produce several clusters before the classification process. The one-class kernel sparse representation was adopted to classify each obtained cluster. The proposed method was evaluated and validated in lithological mapping using EO-1 Hyperion hyperspectral data over an arid region in Xinjiang area, China.

We propose a new outlier generation approach for one-class random forests (OCRF), a recently developed one-class classifier. The proposed method makes use of a positive and unlabeled learning (PUL) algorithm to generate outliers from the unlabeled samples. The outlier samples generated and the target samples are then used to train an OCRF classifier for one-class classification. The proposed method is evaluated using hyperspectral data, and the results showed that the OCRF with the proposed outlier generation method provides high classification accuracy, outperforming the original OCRF, PUL and OCSVM.

In this study, a new method of extracting urban extents using relation among statistical features and decision rules was developed. Results indicate that the data from different years produced the same decision rules. The experimental results also demonstrate that the method can achieve better results than the global threshold method. A main advantage of the proposed method is that the rules derived from data of a specific year can be transferred to the data of other years, which makes it promising for rapidly monitoring urban areas regionally using DMSP/OLS NTL time series data. However, the proposed method needs further validation using more data in different geographical regions.

Urban built-up area information is pivotal to understand complex drivers and mechanisms in global climate change application. However, built-up area extraction using Landsat time series data is a challenging task due to spatial-temporal expression and modeling of land cover types. To provide insights into the intra-annual dynamics of land use change, focusing on how time series characteristics improves recognition of urban , this paper presents an alternative method to built-up area extraction using intra-annual time series of Landsat images. The central premise of the approach is that time series characteristics is firstly expressed by using spectral data, index and feature. The random forests algorithm is then used in classification process for built-up area extraction. The proposed method is further compared with methods using single temporal Landsat data, using features selected by laplacian score and using different classifiers. Results demonstrate that the proposed method improves the accuracy of urban area extraction.

Impervious surface is considered as a key indicator of urban environment quality and urbanization. Many studies have attempted to extract urban impervious surface using multispectral images of medium and high resolution, especially images acquired in summer, as they achieved higher accuracy. However, the use of summer images may underestimate impervious surface area, since some impervious surfaces are obscured by deciduous tree crowns in summer. This paper compared the results of impervious surface extracted using two-temporal Worldview-2 multispectral images acquired in summer and winter by linear spectral mixture analysis and analyzed the differences between the results. The results indicated that impervious surface extraction from winter image produced a similar accuracy with summer image. However, the area of impervious surface extracted from winter image was much higher than that from summer image by nearly 20% in study area.

A heuristic utilizing both spectral and spatial information is proposed for active learning. It addresses the issue of iteratively querying most informative training samples with a special focus on spatial-contextual image classification. With the aim to utilize all information during the learning process, the proposed heuristic queries unlabeled pixels considering spectral-spatial inconsistency (SSI), i.e., the unlabeled pixels whose spectral and spatial information indicate different class labels are favored in the active selection. To model spectral-spatial information, a Markov random field (MRF), in which the unary term is defined using the output of a support vector machine and the pairwise term is defined by a multilevel logistic model, is adopted. A new approach to the estimation of the parameters of this MRF model is also incorporated in the proposed method. It aims at taking benefit of spatial information by using the pixels which are representative of the inter-class spatial transitions. A high resolution remotely sensed image is used in the experiments, and the proposed method is proved to be feasible and accurate.

Markov random field (MRF) is one of most powerful tools for description of spatial information. Utilizing spatial information characterized by MRF, classification of remote sensing image becomes more reliable and accurate. At the same time, however, MRF also results in the loss of image details such as fine scaled objects and the wrong boundaries. For this reason, we propose a potential calculation method in which spatial dependence in spectral feature is taken into consideration. To assess its performance, HYDICE of Washington is utilized. Results exhibits, compared with traditional MRF, the proposed one achieves better performance both in accuracy assessment and visual inspection.

This paper is concerned with an inverse surface scattering problem in near-field optical imaging, which is to reconstruct the scattering surface of a dielectric medium with a resolution beyond the diffraction limit. It is a nontrivial extension of the authors' work on near-field imaging of infinite rough surfaces from impenetrable to penetrable media [G. Bao and P. Li, SIAM J. Appl. Math., 73 (2013), pp. 2162--2187], where a more sophisticated transmission problem needs to be considered. The scattering surface is modeled as a small and smooth deformation of a plan surface. Based on a transformed field expansion, an analytic solution, which is given as a power series, is derived for the direct scattering problem. By neglecting high order terms in the power series, the original nonlinear inverse problem is linearized; explicit and unified reconstruction formulas are deduced for both reflection and transmission configurations. A spectral cut-off regularization is adopted to suppress the exponential growth of the noise in the evanescent wave components, which carry high spatial frequency of the scattering surface and contribute to the superresolution in the near-field regime. The method requires only a single illumination at a fixed frequency and is realized efficiently by the fast Fourier transform. Numerical results show that the method is simple, stable, and effective in reconstructing scattering surfaces of dielectric media with subwavelength resolution.

In recent years, sparse representations have been widely studied in the context of remote sensing image analysis. In this paper, we propose to exploit sparse representations of morphological attribute profiles for remotely sensed image classification. Specifically, we use extended multiattribute profiles (EMAPs) to integrate the spatial and spectral information contained in the data. EMAPs provide a multilevel characterization of an image created by the sequential application of morphological attribute filters that can be used to model different kinds of structural information. Although the EMAPs' feature vectors may have high dimensionality, they lie in class-dependent low-dimensional subpaces or submanifolds. In this paper, we use the sparse representation classification framework to exploit this characteristic of the EMAPs. In short, by gathering representative samples of the low-dimensional class-dependent structures, any given sample may by sparsely represented, and thus classified, with respect to the gathered samples. Our experiments reveal that the proposed approach exploits the inherent low-dimensional structure of the EMAPs to provide state-of-the-art classification results for different multi/hyperspectral data sets.

This paper proposed a novel urban building extraction method to address the problems with shadow and spectral confusion using LiDAR data and very high resolution (VHR) imagery. The buildings were first extracted using height from LiDAR data and normalized difference vegetation index (NDVI) from VHR image. A refinement step was then adopted to reduce the errors caused by shadow and spectral similarity between the buildings with color roofs and vegetated roofs and the trees. A post processing step was finally conducted to further improve the result. The proposed method was quantitatively evaluated and compared with existing method using airborne LiDAR data and Quickbird image. The results indicated that the proposed method significantly outperformed the existing method. The proposed method is applicable for building extraction using VHR image and LiDAR data over complex urban areas with tall buildings and buildings with color roofs or vegetated roofs.

Image Segmentation is an essential step for object-based analysis using very high resolution (VHR) images. A segmentation method by combined spectral and structural information was proposed in this paper for VHR multispectral images. The method consists of three steps. Structural information is first extracted and combined with spectral information to define pixel similarity. A region growing strategy using gradient image to determine seed points is then employed to produce initial segmentation results. A region merging step is finally performed to improve the initial results. Both visual inspection and quantitative measures are used to evaluate the performance of the proposed method. The experimental results of a Beijing area Quickbird image indicate that the proposed method achieves a better performance than existing morphological method and it is comparable with the widely used eCognition multi-resolution method.

Urban built-up area information is required by many applications, such as research of urbanization rate. Urban built-up area extraction using moderate resolution remotely sensed data (e.g. Landsat TM/ETM+) presents numerous challenges, such as very heterogeneous spectral features of urban areas, spectral confusion between built-up class and others. Considering that image texture is one of the important spatial information for identifying urban land cover, a new methodology to address these issues is proposed. This approach involves processes as the following, as a first step, multivariate texture is computed through multivariate variogram. Spectral bands and multivariate texture are then combined in classification process for built-up area extraction. One-Class Support Vector Machine (OCSVM) classifier was used in this process. A comprehensive evaluation is present with Landsat TM data of Beijing, China. Results demonstrate that the proposed method significantly improves the accuracy of urban area extraction.

This paper proposed a decision fusion method based on Tau model for land cover classification. The method explicitly takes into account conditional correlation existed between different classification results from multi-sensor data. The proposed method was evaluated and compared with an existing decision fusion method using Landsat TM/ETM+ and ENVISAT ASAR data from Beijing urban area. The results showed that the proposed method produced comparable with or slightly better than the traditional fusion methods.

This paper proposed a method that uses shadow change information in bi-temporal images to improve accuracy of urban building damage detection. The initial building damage detection was conducted by object-based bitemporal classification using One-Class Support Vector Machine (OCSVM). The shadow changes extracted from the images were then used to refine the results produced in previous step. The experimental results using bitemporal Quickbird images acquired in Dujiangyan, Sichuan of China showed the proposed method significantly improved the detection accuracy. In particular, the commission error of the building damage was significantly reduced. Further work is required to make more sophisticated rule sets to obtain better results.

In this paper, we propose a method for urban building damage detection from multitemporal high resolution images using spectral and spatial information combined. Given the spectral similarity between damaged and undamaged areas in the images, two spatial features are used in the damage detection, i.e. invariant moments and LISA (local indicator of spatial association) index. These two spatial features were computed for each image object, which is produced by image segmentation. The One-Class Support Vector Machine (OCSVM), a recently developed one-class classifier was used to classify the multitemporal data to obtain building damage information. The uses of spectral data alone and plus obtained spatial features for building damage detection were separately evaluated using bitemporal Quickbird images acquired in Dujiangyan area of China, which was heavily hit by the Wenchuan earthquake. The results show that the combined use of spectral and spatial features significantly improved the damage detection accuracy, compared to that of using spectral information alone.

Most existing multitemporal classification researches use spectral information alone. However, adding spatial structure and temporal correlation in the classification could improve the classification accuracy. This paper proposed a new method to extract multitemporal texture by the Pseudo Cross Variogram (PCV). The derived texture features were combined with the original spectral information for multitemporal classification. The performance of the proposed multitemporal texture was evaluated in land cover classification using bi-temporal hyperspectral CHRIS/PRBOA images. The experiments showed that CHIRS/PROBA data is applicable in multitemporal classification, and including multitemporal texture in multitemporal classification could lead to a significant increase in overall classification accuracy, compared to the classification using spectral information alone.

Monitoring the sowing area and the crops growth are the two basic aspects of agricultural remote sensing. With the advantage of DMC+4 simultaneously providing mid-resolution multispectral image and high-resolution panchromatic image, we choose winter wheat as investigated object, establish a vegetation canopy radiation model on the consider of sun-target-sensor geometry and clumping effect to monitor the spatial distribution of the growth condition of winter wheat, and then validate the model through mathematical simulation and field experiment. The work indicates that the model and retrieval method used are available. The spatial scaling effect of LAI is to be further studied.

Most existing multitemporal change detection methods use the spectral information alone. However, the inclusion of spatial and temporal information in change detection could improve the accuracy of change detection. This study proposes a new method which includes the multivariate texture in change detection by the direct multitemporal classification. The multivariate texture was extracted from two multispectral images, by the Pseudo Cross Multivariate Variogram (PCMV), which is an extension of the traditional Pseudo Cross Variogram (PCV). The experiments showed that the inclusion of multivariate texture could significantly improve the overall accuracy of change detection, compared to that of using the spectral information alone.

High-resolution multispectral remote sensing image provides both spectral and structural information about land cover/land use types. In segmentation of such complex image scenes with obvious texture, the efficient image segmentation is required. In this study, a method for high resolution image segmentation based on the extended morphological profiles is proposed. First, fundamental morphological vector operations (erosion and dilation) are defined by the extension, taking into account the spatial and spectral information in simultaneous fashion. Theoretical definitions of extended morphological operations are used in the formal definition of the concept of extended morphological profiles, which is constructed based on the repeated use of openings and closings by reconstruction with a structuring element (SE) of increasing size. Then, the morphological multiscale characteristic (MMC) of each pixel is gained through the derivative of the extended morphological profiles (DEMP). A modified method was proposed to obtain the right morphological characteristics of the pixel, which will be used for the final segmentation results. Finally, a simple region merging method based on the distance between two centroids of the neighboring regions was adopted to further improve the segmentation result. The proposed approach is applied to high- resolution QuickBird multispectral images from urban, agricultural and forest areas for evaluation and comparison with existing methods, in terms of qualitative visual inspection and quantitative criteria. The proposed method demonstrated better performance than the classical morphological segmentation approaches.

Super low frequency remote sensing technique introduced here is, with the use of natural electromagnetic waves, used to explore the apparent resistivity of strata on the surface of the Earth, and then to reduce the degree of enrichment of gas underground and indicate the depth of the gas-bearing stratum. The simple theory, exploration method and device are presented in the text. Contrasts are made between the results obtained from experiments and those extracted by drilling at the same location for validating this technique.

Local Binary Pattern is a new texture measure which is theoretically simply but powerful. When used in remote sensing multi-channel image processing, the multivariate version of LBP operator should be considered. In this paper, a multivariate LBP operator was proposed to calculate multivariate texture for multi-spectral remote sensing image. Both single-band texture and multivariate texture were employed in the classification process. Segmented Minimum Noise Fraction transform was conducted before classification to reduce features. Experiment shows that compared to spectral classification, the classification accuracy can be significantly improved when the proposed classification scheme was used.

The analysis of spatial structure features in high resolution imagery is one of the most important research fields in remote sensing information processing. In this study, we attempt to quantitativ ...

This paper investigates segmentation of multispectral images using multiscale watershed transformation for land cover classification with SPOT 5 multispectral data. The multiscale gradient operator was computed separately for each band, and then resulting multiple gradient images were combined by averaging of magnitude of the gradient components to create a single-value gradient image. The gradient image was filtered to eliminate local minima. The watershed transformation was used for segmentation of the filtered gradient image. The results indicate that the use of multiscale gradients for watershed segmentation could overcome the over-segmentation effect and achieve more accurate segmentation result. The incorporation of contextual information from multiscale morphological segmentation in image classification substantially improves the classification accuracy, compared to pixel-wise classification.

Multispectral airborne data from the NASA MODIS/ASTER airborne simulator (MASTER) were acquired in Kochang area, Korea, during the PACRIM II mission in 2000. The objective of this study was to evaluate the effectiveness of MASTER data for mapping land cover classes. The 25 bands, including 11 visible and near infrared (VNIR) bands and 14 shortwave Infrared (SWIR) bands, were selected for land cover mapping in the area. Data was calibrated using the flat field method. Various methods, such as Principal Component Analysis (PCA), Minimum Noise Fraction (MNF), were used for feature extraction to determine the inherent dimensionality of the data and to reduce the computational requirement. Spatial texture was extracted from some components obtained from above transforms. Vegetation Index was also computed from the calibrated data. Selected components, texture, and vegetation Index were combined for land cover mapping. Maximum likelihood was utilized for classification using different data combinations. The study showed that different land cover classes could be discriminated from MASTER data using contemporary data processing strategies. Further work is planned to fuse MASTER data and KOMPSAT EOC data as well as other available data for land cover classification.