This study investigates the trade-off between system stability and offloading cost in collaborative edge computing. While collaborative offloading among multiple edge servers enhances resource utilization, existing methods often overlook the role of queue stability in overall system performance. To address this, a multi-hop data transmission model is developed, along with a cost model that captures both energy consumption and delay. A time-varying queue model is then introduced to maintain system stability. Based on Lyapunov optimization, a dynamic offloading algorithm (LDSO) is proposed to minimize offloading cost while ensuring long-term stability. Theoretical analysis and experimental results verify that the proposed LDSO achieves significant improvements in both cost efficiency and system stability compared to the state-of-the-art.

Polarimetric synthetic aperture radar (PolSAR) image change detection (CD) aims to accurately analyze the difference and detect changes in PolSAR images. Recently, graph transformer (GT), which combines the advantages of graph convolutional network and transformer, has increasingly attracted attention in the field of remote sensing. However, the direct application of GT for PolSAR image CD with limited training samples is challenging owing to polarimetric scattering confusion and random speckle noise. Here, we propose a novel unsupervised representation learning framework for CD in PolSAR images, named statistic-guided difference enhancement GT (SDEGT). Our motivation is that polarimetric statistics can effectively guide GT to extract robust and highly discriminative features from the raw polarimetric graphs and thus accurately detect changes. The SDEGT follows the architecture based on neighborhood aggregation GT and innovatively introduces polarimetric statistics to guide feature difference enhancement, thereby capturing the structural interaction between graph nodes and aggregating the local-to-global change correlations at low computational cost. First, SDEGT innovatively introduces noise-robust polarimetric statistics to improve its noise suppression ability and learn sufficient change-aware features from the PolSAR data. Subsequently, guided by the polarimetric statistical difference, a difference enhancement module (DEM) is designed and cleverly embedded in the SDEGT to adaptively enhance the difference between changed and unchanged nodes, thus improving the discrimination of the change-aware features. Finally, symmetric cross-entropy (SCE) is employed to facilitate the robust learning of SDEGT and attenuate the detrimental effect of label noise. Visual and quantitative experimental results on five measured PolSAR datasets with different scenes and dimensions demonstrate the competitiveness of our SDEGT over other state-of-the-art methods.

It is challenging to achieve bistatic inverse synthetic aperture radar (Bi-ISAR) imaging and scaling for maneuvering targets. In the Bi-ISAR system, high-order translational and spatial variant (SV) rotational motion errors induced by the target’s maneuvering characteristics and time-varying bistatic angle would severely blur the imaging result. Moreover, both range and cross-range scaling (2-D scaling) are needed to exploit the size information of the target in practical applications. By parametric global modeling and extracting the coupling relationship between the target’s rotational motion and time-varying bistatic angle, this article presents a new Bi-ISAR imaging framework to achieve the integration of high-order motion compensation and 2-D scaling (IHOMC-2S) for maneuvering targets. First, a multidimensional motion errors signal model is developed. Based on the established parametric global model, a joint high-order translational motion compensation and SV autofocus method (JHTSVA) is presented via parametric minimum entropy optimization with the quasi-Newton solver. Then, with the estimated optimal parameters, the effective rotational velocity (ERV) and distortion coefficient can be estimated simultaneously by solving a 1-D unconstrained optimization problem. In addition, in order to successfully perform the 2-D scaling, a data-driven initial bistatic angle estimation method based on the linked feature scatterers is given. It is worth noting that the linear geometric distortion must be corrected before 2-D scaling, otherwise the sheared Bi-ISAR image may lead to an unreliable target recognition result. Finally, underpinned by the efficient and robust approach, IHOMC-2S can achieve high-resolution Bi-ISAR imaging and scaling for maneuvering targets avoiding the selection of prominent scatterers. Several experiments confirm the feasibility and robustness of the proposed algorithm.

The imaging quality and efficiency are equally important in inverse synthetic aperture radar (ISAR) imaging. The high-order spatial variant (SV) phase errors induced by the target’s nonuniform rotational motion would seriously defocus the ISAR imaging results. The focused image can be obtained by exhaustive parameters estimation or optimization processing. However, the high-computational complexity limits its application in real-time imaging. To overcome this constraint, we propose an efficient ISAR imaging and scaling method for highly maneuvering targets by the integration of integrated cubic phase function (ICPF) and parametric spatial variant autofocus (PSVA) in this article. A novel rotational motion parameter estimation method based on ICPF, which only utilizes second-order phase term coefficients, is presented. Then, a parametric global model is established, which can achieve spatial variant (SV) autofocusing of defocused images based on estimated rotational motion parameters. Meanwhile, the cross-range scaling can also be realized using estimated effective rotational velocity (ERV). Without exhaustive parameters estimation and optimization search, the proposed ICPF-PSVA method not only achieves high-precision ISAR imaging but is also computationally efficient compared with the existing methods. Experiments using simulation data and measured data confirm the high efficiency of the proposed method in generating focused images of maneuvering targets.

It is challenging to accurately extract change features in polarimetric synthetic aperture radar (PolSAR) image change detection. Recently, many existing convolutional neural network (CNN)-based change detection algorithms show satisfactory performance, but error detection still exists in the acquired change features. In this paper, we propose an unsupervised difference-guided adaptive fusion network (DGAFN), which contains three key modules, i.e., adaptive difference extraction module (ADEM), difference feature enhancement module (DFEM), and adaptive weighted fusion module (AWFM). First, ADEM extracts initial multiscale difference features through non-local attention mechanisms guided by bitemporal feature differences, which helps the network to capture the correlation and difference between bitemporal features more accurately. Secondly, in order to further refine multiscale difference features and reduce pseudo-changes, DFEM uses class activation maps and contextual feature extraction modules (CFEM) to perceive more polarization contextual information in a larger scale range. Finally, in order to improve the recognition ability of change targets with different sizes, AWFM adaptively fuses enhanced multiscale difference features in spatial and channel dimensions by introducing attention mechanisms to obtain change features with multiscale complementary information. Comparative experimental results on five measured PolSAR datasets obtained by GaoFen-3 show that DGAFN is superior to other relevant advanced algorithms in change detection performance.

Convolutional Neural Network (CNN) still suffers from overfitting problems caused by limited samples in SAR target classification. Few-shot learning (FSL) aims to learn a classifier to classify images when only a few training examples are available for each class. Recent works on FSL demonstrate that using local descriptor representations can lead to more informative representations than using image-level representations. However, local descriptors typically capture only local information in an image, while disregarding global contextual information. Therefore, relying solely on local descriptors may not fully represent the features of an image, thus affecting the classification performance of the SAR targets. To address this problem, we propose a novel global and local descriptor-based metric network (GLMnet) for few-shot SAR target classification. The proposed GLMnet consists of global-level metric relationships and local-level metric relationships. The global-level metric relationships are computed by the Brownian distance covariance metric module to capture the relationships between image blocks. On the other hand, the local-level metric relationships are generated by the image-to-class metric module. To integrate these two metric relationships, we design an adaptive metric fusion module to achieve a more discriminative measurement performance. Furthermore, to address the issue of prototypes deviating from the true distribution due to the presence of outliers or noisy samples in the BDC metric process, we design a weighted average prototype computation module to obtain reliable prototypes. Experimental results on three SAR datasets show that the proposed GLMnet can generate reliable prototypes and achieve comparable classification results in contrast to other FSL algorithms.

Image change detection is important in polarimetric synthetic aperture radar (PolSAR) image analysis and interpretation. However, improving its accuracy is challenging because of the interference of multiplicative speckle noise. To address this issue, we propose an unsupervised PolSAR image change detection method based on a multiscale graph convolutional network (GCN). First, a Shannon entropy difference image is introduced and improved to obtain an enhanced difference image (EDI) that can effectively suppress speckle noise while preserving edge information. The generated EDI can be further utilised to construct a pseudo-label set required for unsupervised change detection. Subsequently, a difference constraint joint graph construction (DCJGC) module is proposed to obtain the object-level input information of the network. This uses the joint superpixels of multitemporal PolSAR images as graph nodes, and then introduces the difference information in the EDI to constrain the formation process of the edges between the nodes, efficiently and accurately constructing undirected graphs. Finally, a difference-guided multiscale GCN (DGMGCN) is designed for PolSAR image change detection. The network utilises difference information to eliminate the adverse effect of speckle noise on change detection and fully capture the change-aware features of multitemporal PolSAR images at fine and coarse scales, thereby improving feature discriminability. Experimental results on six real Gaofen-3 PolSAR datasets validate the superiority of the proposed approach over other state-of-the-art methods.

Vision Transformer (ViT) has been introduced in high-resolution synthetic aperture radar (HR SAR) image classification due to its excellent global feature extraction ability. However, small samples of SAR images make it difficult to fit the ViT with excessive trainable parameters, which easily results in over-fitting in training. Meanwhile, poor capability in capturing local features of ViT limits its accuracy in SAR image classification. To solve these problems, this letter proposes a new Lightweight Attention-Discarding Transformer (LAD Transformer) for the classification of HR SAR images. In the proposed model, the backbone of the advanced Swin transformer is used to model global information and extract hierarchical features. Moreover, the vital feature extraction part of the LAD Transformer completely discards the self-attention mechanism and extracts local features of SAR images by introducing lighter group convolution and channel shuffle (GC-CS Block). In addition, to address the estimation shift caused by consecutive batch normalization (BN) layers, a new composite normalization method consisting of Batch normalization and Layer Normalization (BLN) in GC-CS Block is proposed. The experiments show that the proposed network has fewer parameters and higher classification accuracy on two real HR SAR data.

The registration of synthetic aperture radar (SAR) and optical images is still a challenge task due to the influence of the potential nonlinear intensity differences and severe speckle noise. In this letter, we propose a feature-based SAR and optical images registration algorithm combining shearlet and sparse representation. The work consists of three main components, including the feature points detector, descriptor and matching criterion. Firstly, a new feature points detection method based on the coherence-enhancing diffusion Harris detector (CED-HD) is designed, it integrates coherence-enhancing diffusion function and shearlet-based spatial constraint on the basis of the Harris-Laplace detector, which can obtain highly repeatable feature points while suppressing speckle noise. Secondly, a multilayer complementary joint representation descriptor (MCJRD) based on shallow structural features and deep semantic features is designed. The shallow structural features are obtained jointly by Shearlet and phase congruence, while the deep semantic features are obtained by multilayer convolution sparse representation, which makes the descriptors more discriminable and robust. Finally, a feature matching criterion based on locally constrained sparse representation is designed to better reduce the reconstruction error and improve the matching ability. Experimental results on several real SAR and optical image pairs demonstrate the effectiveness of the proposed algorithm.

Compared with the rapid development of single-frequency polarimetric SAR (PolSAR) image classification technology, there is less research on the land cover classification of multi-frequency PolSAR (MF-PolSAR) images. And the deep learning methods among them are mainly based on convolutional neural networks (CNNs), only local spatiality is considered but the nonlocal relationship is ignored. Therefore, this paper proposes the MF semantics and topology fusion (MF-STF) model based on semantic interaction and nonlocal topological structure to improve MF-PolSAR classification performance. During MF-STF optimization, the semantic information-based classification (SIC) and topological property-based classification (TPC) work collaboratively, not only fully leveraging the complementarity of bands, but also combining local and nonlocal spatial information to improve the discrimination of different categories. For SIC, the designed cross-band interactive feature extraction (CIFE) module is embedded to explicitly model the deep semantic correlation among bands, thereby leveraging the complementarity of bands to make ground objects more separable. In TPC, the graph sample and aggregate network (GraphSAGE) is employed to dynamically capture the representation of nonlocal topological relations between land cover categories. In this way, the robustness of classification can be further improved by combining nonlocal spatial information. Finally, a MF weighted fusion (MFWF) strategy is proposed to merge inference from different bands, so as to make the MF joint classification decisions of SIC and TPC. Notably, its weights are adjusted based on the total model loss. The effectiveness of the proposed modules is proved by ablation experiments on three measured MF-PolSAR datasets. In addition, the comparative experiments show that MF-STF can achieve more competitive classification performance than some state-of-the-art methods.

The registration of synthetic aperture radar (SAR) and optical images is challenging due to their significant radiometric and geometric differences. Recently, popular registration algorithms based on convolutional neural networks (CNNs) have been limited to extracting local features, resulting in low registration accuracy. In this article, we propose a novel intra- and inter-modal graph attention network and contrastive learning (I2M-GAN&CL) for SAR and optical image registration to solve this problem. First, the graph construction is conducted according to positional encoding (PE), local features, and$k$-nearest neighbor (KNN) edges of keypoints from SAR and optical images. Second, based on the local features extracted by CNNs, an intra- and inter-modal graph attention network (I2MGAN) is designed. The I2MGAN mines context information and extracts global features shared between SAR and optical images, mitigating the influence of geometric and radiometric differences on registration results. The graph cross-attention (GCA) layer in I2MGAN extracts global features shared between the two images via message passing between nodes across graphs. Subsequently, the graph self-attention (GSA) layer in I2MGAN aggregates context information by conveying messages between nodes in one graph. Finally, a novel intra- and inter-modal contrastive learning (I2MCL) strategy is developed. This strategy conducts the contrastive learning of local and global features within and across modalities to explore feature similarity and increase the number of detected matching point pairs. Experimental results on the publicly available OS dataset demonstrate that the number of matching point pairs and registration accuracy of the proposed algorithm outperforms existing state-of-the-art algorithms.

In airborne forward-looking imaging, the azimuth resolution and the imaging efficiency are important. In this paper, we propose a low-dimension sparse Bayesian learning with Doppler compensation (LDSBL-DC) method to improve the azimuth resolution with a low computational complexity in airborne forward-looking imaging. First, since the variant pitching angle causes the space-variant of the Doppler centroid, the Doppler convolution matrix needs to be constructed in each range cell. We construct a Doppler compensation matrix to eliminate the space-variant of the Doppler centroid. After the Doppler centroid compensation, the Doppler convolution matrix only needs to be constructed once. Second, we propose a low-dimensional projection model based on the singular value decomposition. In the low-dimensional projection model, the high-dimension echo data is compressed to low-dimension data. Finally, combining Doppler centroid compensation and low-dimensional projection model, a new forward-looking imaging model is created, and we introduce sparse Bayesian learning (SBL) to estimate the imaging parameters. In the estimation of the targets’ scattering coefficient, we reduce the computational complexity by the matrix transformation. Several simulations are designed to evaluate the performance of the efficient forward-looking imaging method. The simulation results show the LDSBL-DC method can improve the azimuth resolution with a low computational complexity.

First, since time consumption for extracting$\alpha$will become quite tedious for very large images by pixelwise eigendecomposition, we proposed a fast$\alpha$angle's solution. Second,$\alpha$may be not unique that results in the invalidity of$\mathrm{H}/\ \alpha$decomposition. So we early proposed a sound discriminant to distinguish$\alpha$is unique or not. Third, since depolarization is serious and$\alpha$is unstable in high entropy zone, grass and flourishing canopy etc may be misclassified as double bounce scattering. Therefore we proposed a fast algorithm that$\mathrm{H}/\alpha$decomposition is combined with the model-based decomposition, which overcomes the shortcomings of the invalidity of$\mathrm{H}/\alpha$decomposition and the misclassification in high-entropy zone, and its time consumption is much shorter than$\mathrm{H}/\alpha$decomposition.

High-resolution (HR) synthetic aperture radar (SAR) image classification is a challenging task for the limitation of its complex semantic scenes and coherent speckles. Convolutional neural networks (CNNs) have been proven the superior local spatial features representation capability for SAR images. However, it is hard to capture global information of images by convolutions. To solve such issues, this letter proposes an end-to-end network named global–local network structure (GLNS) for HR SAR classification. In the GLNS framework, a lightweight CNN and a compact vision transformer (ViT) are designed to learn local and global features, and two types of features are fused in quality to mine complementary information through the fusion net. Then, our research devolves the twofold loss function to reduce the interclass distance of SAR images, which brings more compactness to classification features and less interference of coherent speckles. Experimental results on real HR SAR images indicate that the proposed method has more strong feature extraction capability and noise resistance performance. This method achieves the highest classification accuracy on both datasets compared with other related approaches based on CNN.

For maintaining the phase information in images, complex neural networks have been widely applied to PolSAR classification. However, due to constant weights of neurons, the networks may lack randomness and be potentially overfitting for complicated imaging mechanisms and random speckle noise in PolSAR images. Thus, this letter proposes a complex variational inference network (CVIN) where complex Gaussian probability distributions are introduced into the weights of neurons in complex neural networks. In CVIN, a novel evidence lower bound (ELBO) for complex network is designed to infer the variational approximation of weights through backpropagation. After training, CVIN propagates the approximate posterior distributions given the data and makes the prediction of the labels. Thus, CVIN is an ensemble of flexible models with infinite weights, where the complex weights are regularized by the Gaussian distributions. Experiments on real PolSAR images verify the feasibility of CVIN and illustrate the potential of CVIN to serve as a competitive method for PolSAR classification.

Multifrequency (MF) polarization synthetic aperture radar (PolSAR) systems can obtain more abundant and continuous earth resource information than single-frequency ones and have been widely used in the remote sensing community. However, there are relatively a few researches for the fine MF PolSAR image classification, which is an important part of remote sensing image interpretation. The main focus currently is on the single-frequency part. Therefore, for dual-frequency PolSAR image classification, this article proposes the dual-frequency attention fusion network (DFAF-Net). It is based on frequency-aware attention and adaptive feature fusion to improve classification performance. First, the dual-frequency PolSAR data is input into the joint feature extraction (JFE) module to obtain the joint feature representation. Meanwhile, two frequency-aware attention block (FAB) modules with the same structure are constructed, which, respectively, generate frequency-specific attention masks based on the guidance of different frequency data. Subsequently, these masks are used to weigh the joint features to highlight the description of different frequency-aware importance. The activated frequency-aware features can fully mine and utilize the complementary information provided by different frequencies, thereby enhancing the discrimination of similar landcover categories. Finally, the adaptive feature fusion block (AFFB) module is utilized to adaptively aggregate different frequency-aware features multiple times, which can effectively eliminate information differences. The obtained fusion features are more compact within classes and separable between classes, thereby effectively improving the classification performance. Experiments on three measured spaceborne and airborne dual-frequency PolSAR datasets verify that DFAF-Net can better perceive frequency characteristics and fully mine the complementary. Therefore, the classification accuracy is effectively enhanced, and the inaccuracy of single-frequency classification can be eliminated. Meanwhile, due to the introduction of the attention module, the classification performance of the proposed DFAF-Net is more competitive than the related deep learning networks. Quantitatively, the overall accuracy of DFAF-Net on the three datasets is respectively 98.30%, 97.42%, and 99.45%, which is better than other methods.

Bistatic inverse synthetic aperture radar (Bi-ISAR) can obtain complementary information of moving targets and overcome the inherent imaging limitations of monostatic ISAR. However, the complex motion of maneuvering targets invalidates the assumption that the imaging projection plane (IPP) is constant in conventional Bi-ISAR imaging. The 2-D spatial variant phase errors would be induced. Moreover, the phase errors have a high-order form due to the time-varying bistatic angle and the high maneuvering characteristics of the target. Meanwhile, the linear geometric distortion induced by the bistatic configuration seriously challenges target identification and classification. In this paper, we propose a novel method to compensate for the 2-D spatial variant phase errors and correct the geometric distortion simultaneously for Bi-ISAR imaging based on parametric minimum entropy optimization. First, the signal mode for maneuvering target in the bistatic configuration is developed. Second, based on the developed signal model, we analyze the coupling relationship between the 2-D high-order spatial variant phase errors and the bistatic angle, and establish a parametric minimum entropy optimization model for high-order spatial variant phase errors compensation. Then, an efficient Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is adopted to obtain the optimal solution of spatial variant coefficients. Finally, with the estimated optimal parameters, the integrated processing of 2-D spatial variant phase errors compensation and distortion correction can be realized. This method can simultaneously obtain well-focused and restored Bi-ISAR images of maneuvering targets without selecting prominent scatterers. Experiments based on scattering point simulation data and electromagnetic data verify the effectiveness of the proposed method.

Deep learning has powerful feature extraction abilities and has achieved promising results in polarimetric synthetic aperture radar (PolSAR) image classification. However, the labeled samples of PolSAR images are generally limited, which could lead to the overfitting of deep networks and the inefficiency of deep features. To overcome this problem, in this article, we propose a complex-valued enforcing population and lifetime sparsity (CV-EPLS) model to extract nonredundant sparse features from PolSAR images. CV-EPLS achieves unsupervised learning of sparse polarimetric features with limited and unlabeled samples, including amplitude and phase information in multiple polarimetric channels. Concretely, CV-EPLS defines an activation metric function to achieve strong population sparsity. Additionally, a grid search strategy is designed to ensure that activation items are evenly distributed among the sparse targets, thus forming strong lifetime sparsity. In this way, CV-EPLS constructs the complex sparse matrices and extracts discriminative sparse features in an unsupervised way, with the dependence of features being effectively reduced. Experimental results on PolSAR images demonstrate the effectiveness of CV-EPLS in the extraction of features and its application to image classification.

Deep learning (DL) methods usually need to collect a large amount of labeled data to extract deep features. However, due to the difficulty of obtaining numerous labeled data from synthetic aperture radar (SAR) images, unsupervised feature learning has been focused on SAR image processing. In this paper, we propose a three-dimensional sparse model (3-DSM) to extract deep sparse features from SAR images in an unsupervised way. Concretely, 3-DSM learns the convolution kernels by minimizing the error between the features and the constructed sparse maps, without labeled samples. Thus, the discriminative features can be extracted in an unsupervised way by the learned convolution kernels and are able to capture the main structure information of SAR images. Furthermore, to the best of our knowledge, 3-DSM firstly specifies the sparsity of convolution kernels, with each convolution kernel exhibiting its independence from the others and the redundancy of convolution kernels being diminishing. It means that each convolution kernel extracts its unique structural features of SAR images. Consequently, in the feature extraction, three-dimensional sparsities have been specified, including width, height, and depth, with the acquisition of discriminative less-redundant features. The effectiveness of 3-DSM is demonstrated by the feature extraction and segmentation of the simulated and real SAR images.

Traditional forward-looking imaging methods of real aperture radar yield unsatisfactory performance in the presence of outliers. In this article, a method based on variational Bayesian (VB) is proposed to obtain forward-looking imaging in the presence of outliers. First, considering the non-Gaussian property of the imaging noise due to the outliers, we propose to use the Student-$t$distribution to model noise. In this model, the echo signal does not need preprocessing for the outliers. Second, the Laplace hierarchical distribution is introduced to describe the sparsity of the target. Then, the forward-looking imaging problem converts to the optimal problem. Finally, we give the VB derivation to solve the imaging parameter. To illustrate the imaging performance in the presence of outliers, the outliers are randomly added to some angles and the whole scene of the echo signal in the simulations, respectively. From the simulation results, we can see that the proposed method achieves excellent performance for forward-looking imaging in the presence of outliers.

The nonstationary and non-Gaussian distribution of the high-resolution (HR) synthetic aperture radar (SAR) image provides much valuable information. However, the current methods, especially deep learning models, directly learn spatial features from HR SAR data while ignoring global statistical information. Combining the local spatial features and global statistical properties of HR SAR images is urgently needed to capture complete HR SAR characteristics. In this paper, a feature fusion network (Fusion-Net) using both deep spatial context encoder and nonstationary joint statistical model (NS-JSM) is proposed for the first time. Fusion-Net realizes the fusion description of local spatial and global statistical features in an end-to-end supervised classification framework. First, a deep spatial context encoder network (DSCEN) is designed based on multiscale group convolution (MSGC) module and channel attention (CA) module. The DSCEN expands the scope of context information extraction with few parameters and increases the interaction between high- level feature channels. Then, the NS-JSM is adopted to capture the unique SAR statistical information. Specifically, the SAR image is transformed into the Gabor wavelet domain. The produced sub-band magnitudes and phases are modeled by the log-normal and uniform distribution. The covariance matrix (CM) is calculated for mapped sub-band data to capture the interscale and intrascale nonstationary correlation. Finally, the group compression and smooth normalization units are introduced into Fusion-Net to fuse the statistical features and spatial features, which not only exploits the complementary information between different features but also optimizes the fusion feature representation. Experiments on four real HR SAR images validate the superiority of the proposed method over other related algorithms.

Dual-frequency polarimetric synthetic aperture radar (PolSAR) data can provide more information than single-frequency data, which can effectively improve classification accuracy. However, how to obtain sufficient and non-redundant feature representation from dual-frequency PolSAR data remains to be resolved. Besides, deep learning has shown good performance in PolSAR image classification, but it often requires a large number of labeled samples to participate in the training process, which is time-consuming and labor-intensive. In this paper, we propose a novel dual-frequency PolSAR image semi-supervised classification method that combines a dual-frequency joint feature learning (DFJFL) module with a cross label-information network (CLIN). First, the DFJFL module is developed based on the consistency and complementarity of dual-frequency data. It eliminates information redundancy by feature constraint loss function, and obtains compact dual-frequency joint feature representation. Subsequently, in order to avoid the influence of speckle noise, the proposed CLIN not only applies consistency regularization under network perturbation, but also uses the scattering mechanism of PolSAR data to find similar sample pairs to complete the consistency regularization under input perturbation, thereby achieving semi-supervised classification for PolSAR data. Experiments on four real dual-frequency PolSAR datasets verify that the proposed method can effectively extract dual-frequency PolSAR information, and make full use of unlabeled samples to improve classification accuracy. At the same time, compared with several related image classification algorithms, the proposed method could achieve the best performance.

In this letter, a joint radar scheduling and beampattern design (JRSBD) strategy is proposed to track multiple targets by a netted colocated multiple-input multiple-output (C-MIMO) radar system in clutter. The mechanism is to jointly optimize the radar scheduling and the waveform correlation matrix of each C-MIMO radar to maximize the tracking performance. First, we develop the deterministic covariance, as the performance metric, to quantify the actual target state estimate accuracy. Second, the JRSBD strategy is formulated as an optimization problem with some system constraints. The resulting optimization problem contains both binary and continuous variables and is nonconvex. Finally, we propose a sequential convex programming method to solve it. Numerical simulations demonstrate that the JRSBD strategy can effectively improve the target tracking accuracy.

Recently, convolutional neural network (CNN) has proved itself as a successful deep model and has been successfully utilized in polarimetric synthetic aperture radar (PolSAR) image classification. Most CNN-based models, however, concentrate on the correlation between the pixels and the labels in images and have fewer constraints on interclass or intraclass features. For fully utilizing the polarimetric data, we utilized complex-valued (CV) distance to learn the PolSAR features and proposed a PolSAR classification method by CV distance comparisons. First, we proposed a triplet CV network (TCVN) to learn the CV representations from PolSAR data by maximizing the interclass distance and minimizing intraclass distance. It uses the CV convolution and the CV Euclidean to maintain the phase components and applies the CV-dropout and CV$L_{2}$parameter regularization to reduce the overfitting and further improve the network performance. Subsequently, CV K nearest neighbor (CV-KNN) computes the distance of the CV representations and groups similar pixels. CV-KNN is well coupled with the TCVN because both of them are based on the Euclidean distance in the complex domain. Compared with the CNN-based methods, the proposed deep metric learning model can simultaneously extract the hierarchical features by comparing the polarimetric resolution cells in the complex domain and maintain the phase component by performing CV convolutions. The effectiveness and the superiorities of CV Euclidean distance in TCVN are demonstrated. Experiments on real PolSAR images illustrate that TCVN can deal with PolSAR data more effectively and achieve comparable performance in the PolSAR image classification even with a smaller data set.

Conditional random fields (CRFs) model is suitable for image segmentation because it can capture the dependencies of observed data and incorporate the spatial correlations into the segmentation process. In this article, to deal with the segmentation of nonstationary synthetic aperture radar (SAR) image, we combine the modeling power of the CRF model with the representation-learning ability of principal component analysis network (PCANet), and thus propose a high-order triplet CRF model based on PCANet (HOTCRF-PCANet). HOTCRF-PCANet introduces an auxiliary field to explicitly regulate nonstationary label structure patterns. Under the guidance of this auxiliary field, HOTCRF-PCANet defines a discrete quadrilateral nonstationary Markov fields model, and thus considers both the nonstationary property of image and high-order label interactions. In addition, guided by the auxiliary field, HOTCRF-PCANet proposes to use a product-of-expert (POE) potential to enforce the regions’ labeling consistency for pixels within the weak-structured region. To automatically learn rich feature representations, HOTCRF-PCANet modifies PCANet into an unsupervised mode, i.e., unsupervised PCANet (UPCANet), and constructs an UPCANet-based unary potential to effectively predict the local class probability. The effectiveness of HOTCRF-PCANet is demonstrated by the application to the unsupervised segmentation of the simulated images and real SAR images.

In this paper, we combine the modeling power of conditional random fields (CRF) model with the representation-learning ability of principal component analysis network (PCANet), and propose a high-order triplet CRF model, named as HOTCRF-PCANet, for unsupervised synthetic aperture radar (SAR) image segmentation. HOTCRF-PCANet introduces an auxiliary field to explicitly regulate label interactions of complex SAR image. In the label and auxiliary fields, HOTCRF-PCANet defines a discrete quadrilateral pairwise Markov fields (DQPMF) model, and thus constructs a high-order DQPMF potential to model the high-order label interactions in an unsupervised way. Additionally, HOTCRF-PCANet uses a product-of-expert (POE) potential to enforce the regions' labeling consistency for pixels within the weak-structured region. Moreover, HOTCRF-PCANet modifies PCANet into an unsupervised mode, i.e. UPCANet, automatically learns rich features of SAR image and constructs an UPCANet-based unary potential to predict the local class probability. The effectiveness of HOTCRF-PCANet is demonstrated by the application to the unsupervised segmentation of simulated and real SAR images.

Recently, convolutional neural network (CNN) has been successfully utilized in the terrain classification of polarimetric synthetic aperture radar (PolSAR) images. However, most CNN-based models are currently limited to handle 2-D real-valued inputs, and therefore, the physical scattering mechanism contained in the complex-valued (CV) covariance/coherency matrix cannot be extracted effectively. For this reason, CV 3-D CNN (CV-3D-CNN) is proposed for PolSAR image classification. Compared with CNN, CV-3D-CNN simultaneously extracts hierarchical features in both the spatial and the scattering dimensions by performing 3-D CV convolutions, thereby capturing the physical property from polarimetric adjacent resolution cells. Experiments on real PolSAR images classification demonstrate the effectiveness and the superiorities of CV-3D-CNN and illustrate that CV-3D-CNN can deal with scattering characteristic in a more complete manner and achieve better performance in PolSAR image classification.

A pixel-wise classification for high-resolution (HR) synthetic aperture radar (SAR) images is a challenging task, due to the limited availability of labeled SAR data, as well as the difficulty of exploring context information affected by coherent speckle. In this article, we propose a novel supervised classification method for HR SAR images, which combines a context-aware encoder network (CAEN) and a hybrid conditional random field (HCRF) model. First, a new CAEN architecture is developed based on the intrinsic property of HR SAR pixel-wise labeling. The proposed architecture follows an encoder-decoder structure, wherein the residual context encoder (RCE) block and the global context-aware (GCA) block are proposed in the encoder module to capture local to global semantic contexts. The multiscale skip connections and feature compression structures are designed in the decoder module to preserve precise object structures while improving computational efficiency. Then, a patch sampling strategy is adopted to ensure that the training and test data are completely separated. It can achieve a less-biased estimate of the test error of CAEN. In addition, the overlapped sampling and data augmentation techniques are used to solve the problem of limited labeled data. Finally, the HCRF model is constructed and combined with the previous CAEN to further enhance the spatial label consistency. Our HCRF integrates pixel-level and region-level potentials into a unified Bayesian framework, making two spatial supports come to a more accurate decision on pixel categories. Experiments on four HR SAR images validate the superiority of the proposed method over other related algorithms.

The selection of training samples is important for the accuracy and efficiency of the synthetic aperture radar (SAR) image change detection task. However, training samples are traditionally extracted from the whole image, which leads to longer training time and an unbalanced number of pixels in the changed and unchanged classes. To overcome this problem, we propose a novel change detection method combining saliency detection with a principal component analysis network, named SDPCANet. To enhance the reliability of the training samples and reduce the amount of training samples, the SDPCANet uses context-aware saliency detection to obtain the salient region, from which the training samples are extracted. In addition, to alleviate the gap between the numbers of training samples in two classes, we regulate the candidate samples using the uniform-selecting strategy to enhance the reliability of the training samples for the SDPCANet. Then, the SDPCANet is trained with the extracted training samples and the remaining pixels are classified in the salient region to obtain the final change map. The experimental results on four sets of multitemporal SAR images demonstrate that the SDPCANet outperforms the reference methods proposed recently.

Dominant scattering mechanism (DSM) obtained by Freeman decomposition is significant for polarimetric synthetic aperture radar (PolSAR) image classification. To preserve the purity of scattering characteristics, it restricts pixels in a scattering category to be classified with other pixels in the same scattering category. However, due to the speckle and the limited image resolution, it is difficult to obtain the DSMs of some pixels, which are defined as the fuzziness of polarized scattering mechanisms. Therefore, we first consider a particular-and pertinent-auxiliary field, and then propose the fuzzy triplet discriminative random fields (FTDF) model to describe the fuzziness of polarized scattering mechanisms, thus categorizing the scattering mechanisms into four classes: surface scattering, double-bounce scattering, volume scattering, and mixed scattering. The pixels in the first three categories are with specific DSMs, and the FTDF model introduces an exponential kernel distance to combine the multiple features of PolSAR data into classification. For the pixels in the mixed scattering, FTDF introduces a fuzzy clustering algorithm regularized by Kullback-Leibler information to consider the fuzzy DSMs, thus enhancing the classification. Then the fuzziness modeling of polarized scattering mechanisms can guide the classification of PolSAR images. The experimental results on real PolSAR images demonstrate the effectiveness of the FTDF model, and illustrate that it can improve the classification accuracy, and simultaneously preserve the purity of scattering mechanisms.

The registration of synthetic aperture radar (SAR) and optical images is a challenging task due to the potential nonlinear intensity differences between the two images. In this paper, a novel image registration method, which combines nonlinear diffusion and phase congruency structural descriptor (PCSD), is proposed for the registration of SAR and optical images. First, to reduce the influence of speckle noise on feature extraction, a uniform nonlinear diffusion-based Harris (UND-Harris) feature extraction method is designed. The UND-Harris detector is developed based on nonlinear diffusion, feature proportion, and block strategy, and explores many more well-distributed feature points with potential of being correctly matched. Then, according to the property that structural features are less sensitive to modality variation, a novel structural descriptor, namely, the PCSD, is constructed to robustly describe the attributes of the extracted points. The proposed PCSD is built on a PC structural image in a grouping manner, which effectively increases the discriminability and robustness of the final structural descriptor. Experimental results conducted on SAR and optical image pairs demonstrate that the proposed method is more robust against speckle noise and nonlinear intensity differences and improves the registration accuracy effectively.

The WGΓ model has been validated as an effective model for the characteristic of polarimetric synthetic aperture radar (PolSAR) data statistics. However, due to the complexity of natural scene and the influence of coherent wave, the WGΓ model still needs to be improved to fully consider the polarimetric information. Then, we propose the WGΓ mixture model (WGΓMM) for PolSAR data to maintain the correlations among statistics in PolSAR data. To further consider the spatial-contextual information in PolSAR image classification, we propose a novel mixture model, named mixture WGΓ-Markov random field (MWGΓMRF) model, by introducing the MRF to improve the WGΓMM model for classification. In each law of the MWGΓ-MRF model, the interaction term based on the edge penalty function is constructed by the edge-based multilevel-logistic model, while the likelihood term being constructed by the WGΓ model, so that each law of the MWGΓ-MRF model can achieve an energy function and has its contribution to the inference of attributive class. Then, the mixture energy function of the MWGΓ-MRF model has the fusion of the weighted component, given the energy functions of every law. The mixture coefficient and the corresponding mean covariance matrix of the MWGΓ-MRF model are estimated by the expectation-maximization algorithm, while the parameters of the WGΓ model being estimated by the method of matrix log-cumulants. Experiments on simulated data and real PolSAR images demonstrate the effectiveness of the MWGΓ-MRF model and illustrate that it can provide strong noise immunity, get smoother homogeneous areas, and obtain more accurate edge locations.

Triplet Markov fields (TMF) model is widely used to deal with non‐stationary synthetic aperture radar (SAR) images. However, its ability to capture global information remains limited due to the non‐causal property. A hierarchical TMF model is proposed in this study based on the non‐linear diffusion (ND) strategy, which is denoted as ND‐hierarchical TMF (HTMF). ND is adopted to generate multiscale decomposition according to local image content, and that is superior to traditional wavelet decomposition in reflecting hierarchical nature of image structure and detailed features. The auxiliary field in ND‐HTMF is redefined and initialised on the finest scale to characterise edge information and that enhances the prior modelling ability for non‐stationary local image features. The multiscale likelihood and multiscale causal prior energy functions are then defined respectively in bottom‐up and top‐down procedures to capture local and global information for performing segmentation. Segmentation experiments on simulated and real SAR images demonstrate the effectiveness of ND‐HTMF in both edge characterisation accuracy and robustness against speckle noise.

In this study, the authors present an efficient time‐dimension‐reduced track‐before‐detect (TR‐TBD) processor for slow‐moving weak multi‐targets detection in strong clutter environment. In their proposed framework, they elaborate observations from multiple frames (or scans) and resample them in time direction, then distinguish the slow‐moving targets from the clutter in the radon parameter domain by exploiting the fact that different velocities of targets have different skewing angles corresponding to their tracks in the range–time (range–pulse) plane. To further enlarge the skewing angles differences between the slow‐moving targets and the clutter, TR‐TBD is proposed by incorporating the time‐dimension reduction operator. This is very helpful to amplify the skewing angle of slow‐moving targets, while the improvement is very small for the clutter. Therefore, it is much convenient to figure out the slow‐moving weak targets from heavy clutter environment based on their amplified skewing angle differences by setting proper threshold. After detecting the targets, CLEAN‐based track recovery method is proposed to eliminate the false tracks and recover the true tracks. Experimental results on real‐data demonstrate that the proposed algorithm can detect the closely spaced targets and eliminate the false tracks under low signal‐to‐noise ratio and signal‐to‐clutter ratio.

This letter addresses the problem of cross-range superresolution in Doppler beam sharpening (DBS). The coherence of echoes in the azimuth direction and the sparsity of the DBS image in the Doppler domain are fully exploited; thus, a superresolution DBS imaging framework using aperture-extrapolated sparse representation (SR) is proposed. In this framework, aperture extrapolation based on the autoregressive model is utilized to predict the forward and backward information in the azimuth direction, and SR is exploited to extract the Doppler spectrum information. In addition, the resolution ability with different coherent processing intervals is analyzed. The sharpening ratio in this proposed algorithm can be improved by a factor of two or four theoretically in comparison with the conventional DBS imaging method. Experimental results demonstrate that the proposed framework can lead to noticeable performance improvement.

The recently proposed triplet Markov fields (TMF) model enhances the nonstationary image prior modeling ability by introducing an auxiliary field. Motivated by the TMF model, we propose a generalized TMF model based on ambiguity label information fusion (ALF-TMF) for synthetic aperture radar (SAR) image segmentation. The redefined auxiliary field in ALF-TMF indicates the dominant direction of local image contents and gives explicit nonstationary divisions of SAR images. To reduce the influence of unreliable observations caused by speckle noise, the original label field is adaptively generalized by introducing ambiguity class based on image observation and local nonstationary contextual information. Given the extended label field, prior and likelihood terms are constructed and merged to provide the posterior segmentation decision via the Bayesian fusion rule. Real SAR images are utilized in the experimental analysis, and the effectiveness of the proposed method is validated accordingly.

Image registration is an important preprocessing step in many synthetic aperture radar (SAR) image applications. A key issue in image registration is to reliably establish the correspondences between the feature points extracted from the reference and sensed images. A new point matching algorithm is proposed in this paper to align two SAR images. In the proposed method, by considering image patches as the basic units, a novel local descriptor including the intensity and geometric information is assigned to each feature point, which is more robust to speckle noise. Furthermore, a correspondence establishment scheme is introduced based on the reconstruction errors between feature points calculated by the sparse representation (SR) technique, which is designed for achieving accurate matches. Based on the obtained SR coefficients, a coordinate correction procedure is further proposed for improving the localization accuracy of the obtained correspondences. Both simulated deformed and real SAR images are utilized to evaluate the performance. The experimental results indicate that the proposed method yields a better registration performance in terms of both accuracy and robustness.

For random-field-based image segmentation, the conditional random field (CRF) model offers theoretic advantages over the generative Markov random field one, since it directly models the posterior distribution of label field conditioned on an observable image. In this paper, we propose an adaptive hybrid CRF (AHCRF) model for synthetic aperture radar (SAR) image segmentation. Based on the generation of superpixels and their boundary feature analysis, the proposed method adaptively divides SAR image into different parts, namely, homogeneous regions, heterogeneous regions, and edges. In homogeneous regions, the regional-level CRF is defined on superpixels, and the pixels within each superpixel force to have the same segmentation label. Oppositely, the pixel-level CRF is defined on pixels within heterogeneous regions or edges, and local autocovariance features are extracted for constructing the unary and pairwise potentials to incorporate effective local contextual information. The integration of regional-level and pixel-level CRFs gives the proposed AHCRF model, and it is validated by experiments on several real SAR images. The experimental analysis indicates that the AHCRF is robust to speckle noise and preserves detailed features well in segmentation.

Performance of the k-means clustering algorithm for synthetic aperture radar (SAR) image change detection is usually worsened by the inherent existence of the speckle noise. Therefore, in this letter, an unsupervised multiple kernel k-means clustering algorithm with local-neighborhood information (LIMKKM algorithm) is proposed for SAR image change detection. The LIMKKM algorithm contributes in two aspects. First, it fuses various features through a weighted summation kernel by automatically and optimally computing the kernel weights. Here, the intensity and texture features of the ratio image are fused. Second, it incorporates the local-neighborhood information into its clustering objective function for providing strong noise immunity. The LIMKKM change detection algorithm is carried out in a train-test way to lighten the computational burden. Experimental results on real images demonstrate the effectiveness, especially the strong noise immunity, of the LIMKKM method and illustrate that it is suitable for SAR image change detection.

Designing a kernel function with good discriminating ability and a highly application-adaptive kernelized classifier is the key of many kernel methods. However, not many kernel functions combining directly the bitemporal images' information are designed specifically for change detection tasks. In addition, extreme learning machine (ELM) has not found wide applications in change detection tasks, even though it is a potential kernel method possessing outstanding approximation and generalization capabilities as well as great classification accuracy and efficiency. Therefore, an approach relying on a difference correlation kernel (DCK) and a multistage ELM (MS-ELM) is proposed in this paper for synthetic aperture radar (SAR) image change detection. First, a DCK function is constructed specifically for change detection by measuring the “distance” between any two pixels. The DCK function depicts the cross-time similarities between couples of bitemporal image patches at any cyclic shifts with a kernel correlation operation and the high-order spatial distances between two differently located pixels with an algebraic subtraction. The DCK function possesses strong noise immunity and good identification of changed areas simultaneously. Second, an MS-ELM classifier is constructed for obtaining the change detection result. In MS-ELM, the hidden nodes and weights between the hidden and output layers are updated stage by stage by improving the kernel functions that compose them. Each stage of the MS-ELM is a standard kernel-ELM, and the DCK function is utilized in the first stage. The regenerative kernel functions incorporate the output spatial-neighborhood information of the previous stage for enhancing remarkably the MS-ELM's discriminating ability and noise resistance. The converged result at the last stage of MS-ELM is the final change detection result. Experiments on real SAR image change detection demonstrate the effectiveness of the DCK function and the MS-ELM algorithm, particularly its good identification of changed areas and strong robustness against noise in SAR images.

How to produce the difference data of the two temporal images is a crucial factor in image change detection. In this letter, we propose multicontextual mutual information data (MMID) based on the bivariate Gaussian distribution (BGD) for synthetic aperture radar (SAR) image change detection and illustrate their superiorities over the classical difference data. MMID, which are an improved form of image spatial mutual information, are constructed based on the quadrilateral Markov random field (QMRF) and can be factored into the linear combination of the entropies. Then to adapt MMID to the change detection, we construct the 2-D entropies based on the BGD. In this way, MMID are able to capture the intertemporal statistical dependence of the two temporal images and thus can be taken as the feature-level difference data rather than the pixel-level data. The maximum-likelihood method, the automatic threshold method, and the Markov random field method are performed on the MMID of the real two temporal SAR images for the change detection. Experimental results demonstrate the superiorities of MMID over the traditional difference data.

The scale-invariant feature transform (SIFT) algorithm has been widely applied to optical image registration. However, mostly because of multiplicative speckle noise, SIFT has a limited performance when directly applied to synthetic aperture radar (SAR) image. In this letter, a novel SAR image registration method is proposed, which is based on the combination of SIFT, nonlinear diffusion, and phase congruency. In our proposed algorithm, the multiscale representation of a SAR image is generated by nonlinear diffusion, since it better preserves edges in the image as opposed to Gaussian smoothing, which is used in the original SIFT. To reduce the influence of multiplicative speckle noise, the ratio of exponential weighted average operator is used to compute the gradient information in the construction of nonlinear diffusion scale space. Moreover, phase congruency information is utilized to remove the erroneous keypoints within the initial keypoints. Experimental results on multipolarization, multiband, and multitemporal SAR images indicate that our algorithm can improve the match performance compared to the SIFT-based method, which leads to a subpixel accuracy for all the tested image pairs.

In this letter, we propose a hybrid conditional random field (HCRF) model for synthetic aperture radar (SAR) image change detection. The HCRF model is constructed by incorporating the statistics of the log-ratio image derived from the two-temporal SAR images into conditional random field model. In this way, it is able to integrate the SAR images information, including the texture features of the two-temporal SAR images, the statistics, and the spatial interactions of the log-ratio image, into the change detection. Moreover, to achieve the integration of the information, the HCRF model consists of three parts, namely, the unary potential, the pairwise potential, and the data term modeled by the statistics of the log-ratio image. The unary potential is modeled by a support vector machine using the texture features extracted from the two-temporal SAR images, and the pairwise potential is constructed by the multilevel logistical model to capture the spatial interactions of the log-ratio image. Generalized Gamma distribution (GΓD) is utilized to model the statistics of the intensity data in the log-ratio image. Finally, experimental results on three sets of two-temporal SAR images validate the effectiveness of the proposed HCRF model.

Statistical modeling for the statistics of polarimetric synthetic aperture radar (SAR) data is a critical factor in polarimetric SAR data processing. In this letter, we utilize the complex Wishart-generalized Gamma (WGΓ) distribution to model multilook polarimetric SAR data, in which the complex Wishart distribution and generalized Gamma distribution model the speckle and texture components, respectively. Moreover, we derive a closed-form expression for the WGΓ distribution based on the product model and propose a parameter estimation technique of the WGΓ distribution in this letter. We perform the experiments on the polarimetric SAR data acquired by the AIRSAR and ESAR to verify the superiority and effectiveness of the WGΓ distribution over the K and KummerU distributions in the goodness of fit of polarimetric SAR data histograms and the polarimetric SAR image classification. The experimental results demonstrate that the WGΓ distribution has a greater flexibility than the K and KummerU distributions in the statistical modeling of multilook polarimetric SAR data.

Kernel methods with specifically designed kernel function are suitable for dealing with practical nonlinear problems. However, kernel methods have found limited applications to synthetic aperture radar (SAR) image change detection in that their performances are affected by the inherent multiplicative speckle noise of SAR images. It is known that the spatial-contextual information is helpful in suppressing the degrading effects of the noise. Therefore, a label-information composite kernel (LIC kernel) constructed on the basis of the spatial-contextual information is proposed in this paper for SAR image change detection. A typical spatial information, the output-space label-neighborhood information that is extracted using all labels in the neighborhood of each pixel, may enhance noise immunity, but with inaccurate edge locations simultaneously. Consequently, the anisotropic Gaussian kernel model is utilized for analyzing anisotropic textures of the bitemporal images, and then, a comparison scheme acting on the input-space textures of the bi-temporal images is proposed to supervise the extraction of the output-space label-neighborhood information in the construction of the LIC kernel. The constructed LIC kernel is of good preservation of edge locations of changed areas as well as strong noise immunity. The LIC kernel is updated iteratively with the newest change map outputted from the support vector machine, until the change map converges. Experiments on real SAR images demonstrate the effectiveness of the LIC kernel method and illustrate that it has both strong noise immunity and good preservation of edge locations of changed areas for SAR image change detection.

The conditional random field (CRF) model is suitable for the image segmentation because this model relaxes the assumption of conditional independence of the observed data and models the data-dependent label interaction in the image modeling. However, this model has a limited ability to capture the global and local image information from the perspective of multiresolution analysis. Moreover, for synthetic aperture radar (SAR) image segmentation, SAR scattering statistics that are essential to SAR image processing are not considered in the CRF model. In this paper, we propose a hierarchical CRF (HIECRF) model for SAR image segmentation. The HIECRF model belongs to the discriminative models according to the semantic structure. While inheriting the advantages of the CRF model, the HIECRF model achieves the integration of the image features and SAR scattering statistics and captures the contextual structure information in the spatial and scale spaces. Moreover, we derive a hierarchical inference algorithm for the HIECRF model in virtue of the mean-field approximation (MFA) to provide the maximization of the posterior marginal (MPM) estimate of the HIECRF model. Then, by the bottom-up and the top-down recursions in the hierarchical inference procedure, the HIECRF model effectively exploits the global and local image information, including the contextual structures, the image features, and the scattering statistics, to achieve the MPM segmentation. The effectiveness of the HIECRF model is demonstrated by the application to the semisupervised segmentation of the simulated images and the real SAR images.

The recently proposed triplet Markov random fields (TMF) model is very suitable for dealing with non‐stationary image segmentation. However, influenced by multiplicative speckle noise, synthetic aperture radar image (SAR) is dim and blurred in the boundaries of different areas, making it difficult to locate boundary accurately in the segmentation process. Thus, in this study, the authors propose a new segmentation algorithm using fuzzy label field‐based TMF model for SAR images. In the proposed algorithm, the value of each site in the label field is extended from a finite discrete set in the classical TMF model to a continuous one, in order to describe the memberships of each pixel to different classes. A fuzzy energy function is constructed to describe the joint prior distribution of the fuzzy label field and the auxiliary field. The construction of fuzzy energy function also takes into account four direction information and degree of difference between neighbouring pixels. Iterative conditional estimation method and maximum posterior mode criterion are applied to implement parameter estimation and segmentation. Experimental results on simulated data and real SAR images demonstrate the effectiveness of the proposed algorithm.

Change detection can be performed in a supervised manner. However, supervised methods for synthetic aperture radar (SAR) image change detection may suffer from lack of training samples. Therefore, in this letter, a semisupervised support vector machine classifier based on a cluster-neighborhood (CN) kernel is proposed for SAR image change detection. In the proposed method, samples are categorized into two neighborhoods with kernel k-means clustering algorithm. In addition, a CN kernel is constructed based on the composite-ratio kernel using the neighborhood-based statistical features. When a few labeled samples are available, the proposed CN kernel explores the information of unlabeled samples to enhance its discriminative ability and enhance its robustness against speckles. Experimental results on real SAR image change detection demonstrate the effectiveness of the proposed method when a few labeled samples are available.

Conditional random field (CRF) has been widely used in optical image and remote sensing image segmentation because of the advantage of directly modeling the posterior distribution and capturing arbitrary dependencies among observations. However, for nonstationary SAR images, applications of CRF often fail because of their nonstationary property. The triplet Markov field (TMF) model is well appropriate for nonstationary SAR image processing, owing to the introduction of an auxiliary field which reflects the nonstationarity. Therefore, we introduce an auxiliary field to describe the nonstationarity of the posterior distribution and propose an unsupervised SAR image segmentation algorithm based on a conditional TMF (CTMF) framework which combines the advantages of both CRF and TMF. The proposed CTMF framework explicitly takes into account the nonstationary property of SAR images, directly models the posterior distribution, and considers the interactions among the observed data. Experimental results on real SAR images validate the effectiveness of the algorithm proposed in this letter.

The triplet Markov field (TMF) can obtain more promising classification results of nonstationary images than the Markov random field (MRF). However, TMF has limitedly specialized applications to polarimetric synthetic aperture radar (PolSAR) images with nonstationarity properties. In addition, it is difficult to interpret the meaning of the auxiliary field derived by TMF. This implies that the auxiliary field may not have the physical meaning. We propose Wishart TMF with a specific auxiliary field for PolSAR image classification. We define a smoothness characteristic, which describes the extent of pixel smoothness in its neighborhood. This characteristic acts on the energy of the proposed TMF to supervise the classification of the auxiliary field. The auxiliary field can distinguish the smoothness stationarity and nonsmoothness stationarity of PolSAR images, which indicates that the auxiliary field has the specific physical meaning. The effectiveness of the proposed TMF is demonstrated by real PolSAR image classification experiments.

The motivation of this letter is to resolve the nonnegative eigenvalue constraint (NNEC) problem of four-component decomposition (FCD). It is analyzed that the NNEC is an essential requirement for remainder coherency matrices in the FCD, however the measured polarimetric synthetic aperture radar (POLSAR) data experiment shows there exits the NNEC problem that some remainder coherency matrices of the FCD do not satisfy the NNEC, which means these matrices are not positive semi-definite. In addition, it is analyzed that the scheme using the nonnegative eigenvalue decomposition (NNED) for three-component decomposition (TCD) cannot be directly extended to the FCD to overcome the NNEC problem, so a scheme using the NNED for the FCD is proposed as follow. From matrix theory, we draw a conclusion that if the last remainder coherency matrix satisfies the NNEC, then all remainder coherency matrices also satisfy the NNEC; we successively analyze that the NNEC problem of the last remainder coherency matrices results from the overestimation of scattering powers. Then a shrinkage coefficient is used to depress all possible overestimations of scattering powers, and the overestimation case with the minimum remainder power is chosen to resolve the NNEC problem. Moreover, we have simplified the solution to NNED, which is used to calculate the shrinkage coefficient. The measured POLSAR data experiment shows that the proposed FCD can further enhance double-bounce scattering and depress volume scattering for urban areas.

Due to the characteristic of the synthetic aperture radar (SAR) image's sensitivity to the target aspect angles, a multiple sparse representation (MSR) method for SAR target configuration recognition is proposed. Making use of the prior information, dictionaries are constructed by using the samples of each configuration to better capture the detail information of the SAR images. The advantage of MSR over sparse representation for detail feature extraction is analyzed. Moreover, to achieve better recognition results, the Dempster–Shafer fusion is carried out to get comprehensive description of the target for configuration recognition. Two mass functions are constructed based on MSR and the sample statistical property. The combined mass function has the advantages of both the detail and global features of the target. Experiments on the moving and stationary target acquisition and recognition data sets validate the effectiveness and superiority of the proposed algorithm.

The scenario that the moving range spread target (RST) contains the complicated motion is assumed in this letter, which means that its motion includes different nonconstant elements. Based on sparse representation, a new coherent integration method is proposed to improve the detection performance of the moving RST in Gaussian noise. Here, the sinc basis is introduced to sparsely represent the high-range-resolution profile (HRRP). Basis pursuit denoising (BPDN) recovers the HRRPs from their noisy measurements; hence, aligning the range bins can be implemented at low signal-to-noise ratios via the entropy minimization of adjacent coefficient vectors of the sparse HRRPs. Then, phase compensation is achieved by the recursive multiple-scatterer algorithm (RMSA) in order to acquire the coherent integration gain. Using the sinc basis, the adaptive subspace detector (ASD) is adopted to realize RST detection. Finally, the experimental results on raw data demonstrate the effectiveness of the proposed method.

The salient region, which is a basic feature in the early stage of the human vision system, has been utilized to solve the problems of image analysis and interpretation nowadays. Although there are several salient-region detection methods for optical images, it is a hard work for synthetic aperture radar (SAR) images, which has large multiplicative speckle noise. Based on the statistical distribution of speckle noise and the local intensity variation, this letter presents a novel multiple-scale salient-region detection method for intensity SAR images. In this method, via constructing a 2-D local-intensity-variation histogram, the self-dissimilarity metric curve over scale is computed first to determine the saliency of the local region and its salient scale. Then, based on the Gamma statistical distribution of speckle noise, a new local complexity metric is proposed to obtain the saliency metric at the salient scale. After collecting all the salient regions in the image, a simple iterative algorithm is presented to refine the stable salient regions. Experimental results show the noise robustness, the accuracy, and the stability of the proposed method for SAR images.

Wideband radars transmit wideband linear frequency modulated (FM) pulses to achieve the high range resolution. The scenario that the echo is down-converted by a mixer with a reference signal that is a replica of the transmitted pulse is assumed in this letter. Here, the complex sinusoidal signal basis (CSSB) is introduced to sparely represent the received echo. Then the compressed sensing (CS) radar receiver is designed to reduce the sampling rate; hence, the high resolution range profile (HRRP) can be acquired from low dimensional CS measurements via L1 norm-minimization. Using the statistical characteristic and the dominant scatterer, a constant false alarm rate (CFAR) detector is proposed to detect the range spread target in the complex Gaussian noise. In the new detector, the cross quasi-ambiguity function (CQAF) is selected to acquire the target feature to distinguish the range spread target from the Gaussian noise, thus constructing a close connection between the sparse basis and the target detection. Finally the proposed method is evaluated by the raw data.

The triplet Markov fields (TMF) model has been successfully applied to statistical segmentation of nonstationary images by introducing the auxiliary field, which represents the different stationarities of images. Commonly, the TMF adopts a four-nearest neighborhood. This limits the modeling ability for complex priors. Therefore, this paper suggests using a higher order neighborhood-based TMF (HN-TMF). In the HN-TMF, the autocovariance analysis is applied to reveal the local fluctuation at each site. The auxiliary field is then redefined based on the local fluctuation information to denote homogeneity or heterogeneity. Based on the auxiliary field, the local energy function in HN-TMF is constructed either in a homogeneous or heterogeneous way, and hence, the local structure can be embedded in the energy function to improve the prior modeling ability. Along with the newly constructed energy function, new initializations of HN-TMF parameters are given to fulfill the physical interpretation of the energy function. The experiments performed on both synthetic and real synthetic aperture radar images demonstrate the effectiveness of the proposed HN-TMF in both speckle noise reduction and heterogeneous region segmentation accuracy.

Feature extraction is the key step of synthetic aperture radar (SAR) target configuration recognition. A statistical model embedding the locality preserving property is presented to extract the maximum amount of desired information from the data, which is of crucial help to recognition. The noise, or error, of the SAR image samples is described by a Gaussian mixture distribution, and the locality preserving property is embedded into the statistical model to focus on the problem of configuration recognition. Along with the extraction of the information of interest through the use of the statistical model, also, the preservation of the local structure of the data set is achieved. Parameter estimation is implemented through the expectation–maximization algorithm. Experimental results on the Moving and Stationary Target Acquisition and Recognition data set validate the effectiveness of the proposed method. SAR target configuration recognition is realized with satisfactory accuracy.

The triplet Markov field (TMF) model is powerful in the nonstationary synthetic aperture radar (SAR) image analysis. Taking the speckle noise and the correlation of nonstationarities in two multitemporal SAR images into account, we propose a change-detection method based on the TMF model in this letter. The third fieldUin the TMF model is redefined to describe the nonstationary textural similarity between the two images for change detection. The corresponding prior energy of (X,U) is reconstructed. The adaptive weight parameter in prior energy is introduced to cope with the detection tradeoff issue. An automatic estimation of the parameter is obtained with low level of complexity. The Bayesian maximum posterior marginal criterion is utilized with the TMF model to obtain change detection. Experimental results on real SAR images validate the superiority of the proposed TMF method over the Markov random field method.

The triplet Markov field (TMF) model recently proposed is suitable for tackling the nonstationary image segmentation. In this letter, we propose a hierarchical TMF (HTMF) model for unsupervised synthetic aperture radar (SAR) image segmentation. In virtue of the Bayesian inference on the quadtree, the HTMF model captures the global and local image characteristics more precisely in the bottom-up and top-down probability computations. In this way, the underlying spatial structure information is effectively propagated. To model the SAR data related to radar backscattering sources, generalized Gamma distribution is utilized. The effectiveness of the proposed HTMF model is demonstrated by application to simulated data and real SAR image segmentation.

The echo scattered from a slow-moving weak target on sea surface is nonstationary due to the influence of waves. Time-frequency distributions are good tools to analyze it. In this paper, we propose a method for detecting slow-moving weak targets in sea clutter, which is based on time-frequency iteration decomposition. This method consists of three stages. First, we present a fast signal synthesis method (FSSM) based on eigenvalue decomposition. The FSSM can synthesize a signal faster and more accurately from the Wigner distribution (WD). Then, we present a signal iteration decomposition method (IDM) from the masked WD and the FSSM. By the IDM, the small component of a signal can be obtained, even when it is very close to a large component in the time-frequency plane. Finally, the proposed method results from the IDM and two criteria. Here the two criteria are defined to select the target signal. The proposed method is evaluated by X-band sea echo with a weak simulated target or a real target. The results demonstrate that it not only detects the slow-moving weak target but also shows its instantaneous state.

The triplet Markov field (TMF) model recently proposed is suitable for dealing with nonstationary synthetic aperture radar (SAR) image segmentation. In this letter, we propose a multiscale TMF model in wavelet domain, named as the wavelet-domain TMF (WTMF) model. In the WTMF model, a multiscale causal WTMF energy function is constructed to capture the intra- and interscale dependences in random fields$(X, U)$. Moreover, multiscale likelihoods of the WTMF model are derived based on a wavelet hidden Markov tree to capture the statistical properties of wavelet coefficients. The proposed model can integrate the global and local information in terms of spatial configuration and image features in a more complete manner. The coarser scale information is utilized to guide the finer scale segmentation, and the coarse-to-fine causal interactions are considered using a Markov chain. Experimental results prove that the proposed model can segment SAR images better than several models previously proposed.

A new method is developed to merge two spatially registered images with diverse focus based on multiresolution wavelet decomposition and evolutionary strategy (ES). At first, the wavelet decomposition without down-sampling is used to perform an addition of wavelet high-frequency components of each image. Then, in terms of difference of area-based energy feature in two original images, ES is adopted to partition the region and perform the fusion. The experimental results show that the proposed method can achieve better fusion performance than wavelet transform (WT) method.

A new algorithm is developed to merge a high-resolution panchromatic image and a low-resolution multispectral image based on the combination of multiresolution wavelet decomposition, evolutionary strategy and the IHS transform. The high-resolution panchromatic image is firstly decomposed to the wavelet planes, then the regions are partitioned by evolutionary strategy in terms of difference of edge information from wavelet planes and the merging algorithm is done by adding edge influence factor in different region. The proposed method is compared with the IHS and the MWT methods. The results of the comparison show the proposed merger performing the best in combining and preserving spectral-spatial information for the test images.