Compressed sensing (CS)-based synthetic aperture radar (SAR) sparse imaging technique has been widely used in SAR reconstruction tasks, but it is limited by high computational costs and poor imaging performance. In this letter, we propose a dynamic deep unfolding network (DUN) based on content-aware shrinkage for SAR sparse imaging, called CAS-D2UN. First, an adaptive soft shrinkage mechanism is introduced to obtain a content-aware threshold and enhance the adaptability of the model. Second, a dynamic path-controllable solution is proposed to adjust the network structure based on the complexity of the input data, thereby improving inference speed. Finally, experimental results demonstrate that our proposed CAS-D2UN can achieve superior sparse reconstruction for complex scenes while shortening the imaging time.

Polarimetric synthetic aperture radar (PolSAR) images hold significant importance in applications such as crop classification. To achieve better classification performance, deep learning generally requires a large number of samples, but compared to optical remote sensing images, PolSAR image samples are relatively limited. Moreover, due to the substantial differences in scattering characteristics across different PolSAR image bands, it is challenging to train a model on samples from one band and effectively apply it to another. To address these two challenges, we propose a meta-learning classification network (MLCN) consisting of a feature learning module (FLM) and a relation learning module (RLM). The FLM employs 3-D convolution (3DConv) to fully extract spatial and scattering information from PolSAR images, thereby enhancing the model’s capability to learn correlations across different bands. The RLM integrates coordinate attention (CA) with the parametric rectified linear unit (PReLU) activation function to further enhance the model’s feature representation ability. We conduct three types of experiments on PolSAR images in the L-and C-band, including same-band same-image, same-band different-image, and different-band different-image scenarios. The results demonstrate that MLCN achieves overall accuracies (OAs) of over 96% and 90% on the Flevoland-15 and Indian Head datasets, respectively, even with only 0.2% of the sample data.

Due to its capability for all-weather, all-time information acquisition, synthetic aperture radar (SAR) plays a vital role in the field of Earth observation. However, the specificity of the radar sensor and the complexity of electromagnetic scattering imaging physics result in SAR images lacking the intuitiveness of optical images, making them unsuitable for interpretation by nonexperts. A common approach to tackle this challenge is to use a conditional generative adversarial network (cGAN) to translate SAR images into optical images, thereby enhancing readability and assisting nonexperts in interpretation while filling the gaps in optical data due to acquisition constraints. Nevertheless, traditional cGAN-based methods are limited by inadequate global semantic information extraction and poor detail preservation, leading to translated images with incoherent texture and color, and blurred edge. To address these issues, we propose a hybrid vision transformer cGAN (HVT-cGAN) for SAR-to-optical image translation (S2OIT). In our proposed HVT-cGAN, the generator utilizes a convolutional stem for patch embedding and encoding. The parallel CNN branch and vision transformer (ViT) branch are employed for the extraction and mapping of local and global information, respectively. Moreover, we propose a novel attention-based feature fusion module, named the convolutional attention fusion module (CAFM), which can adaptively aggregate local and global information from parallel branches by learning both channel-wise and spatial-wise relations. Benefiting from these improvements, our method achieves superior performance in both qualitative and quantitative comparisons with other methods on the SEN1-2 dataset. In addition, the results of multiple ablation experiments validate the effectiveness of the proposed method.

Target detection in infrared remote sensing images has important practical applications. Among the current high‐performance methods, the deep learning‐based methods require training samples, and their generalization ability is also limited by the training set. The separation of low‐rank and sparse matrix requires joint processing of multiple images with high computational complexity. The track‐before‐detect algorithms based on particle filtering also have high computational complexity. In this paper, the low‐rank and sparse matrix of a single image are proposed for target detection, and a differentiable objective function is used in the separation. At the same time, an extended multitarget tracking algorithm based on random sets is used for target filtering between frames, and the design of the filters adopts the conjugate distribution under the Bayesian framework. Finally, the practical infrared sequence images containing multiple targets and complex backgrounds were employed to verify the performance of the proposed algorithms by comparing them with state‐of‐the‐art algorithms.

Image fusion (IF) aims to integrate valuable information from multiple sources, and the fusion of optical image and synthetic aperture radar is at the core of remote sensing IF. Despite the remarkable capability of deep learning in IF, it often depends on costly datasets, lacks explicit interpretability, and has instable training process. Diffusion models, such as diffusion denoising probabilistic model and its continuous form (i.e., score-based diffusion model), exhibit powerful generative ability and offers novel ideas to address the hurdles above. To this end, it is kernel and challenge to robustly estimate the posterior distribution of ground truth w.r.t given measurements. In this letter, we propose a variational diffusion IF method for robust estimation of posterior distribution. First of all, an optimization model is developed in the framework of variational inference, where the fidelity term comes from traditional optimization fusion model and the regularization term is actually a weighted integral form of the score function matching. And then, a fast numerical algorithm is designed via first-order stochastic optimization, significantly reducing computational complexity. Finally, the proposed method is validated in experiments with WHU-OPT-SAR and SEN1-2 real datasets, and the results show that the proposed method not only outperforms the state-of-the-art methods in terms of fused image quality, but also almost has half of computational complexity of existing diffusion model IF methods.

In real-world applications, not all instances in the multiview data are fully represented. To deal with incomplete data, incomplete multiview learning (IML) rises. In this article, we propose the joint embedding learning and low-rank approximation (JELLA) framework for IML. The JELLA framework approximates the incomplete data by a set of low-rank matrices and learns a full and common embedding by linear transformation. Several existing IML methods can be unified as special cases of the framework. More interestingly, some linear transformation-based complete multiview methods can be adapted to IML directly with the guidance of the framework. Thus, the JELLA framework improves the efficiency of processing incomplete multiview data, and bridges the gap between complete multiview learning and IML. Moreover, the JELLA framework can provide guidance for developing new algorithms. For illustration, within the framework, we propose the IML with the block-diagonal representation (IML-BDR) method. Assuming that the sampled examples have an approximate linear subspace structure, IML-BDR uses the block-diagonal structure prior to learning the full embedding, which would lead to more correct clustering. A convergent alternating iterative algorithm with the successive over-relaxation optimization technique is devised for optimization. The experimental results on various datasets demonstrate the effectiveness of IML-BDR.

Different views of multiview data share certain common information (consensus) and also contain some complementary information (complementarity). Both consensus and complementarity are of significant importance to the success of multiview learning. In this paper, we explicitly formulate both of them for multiview classification. On the one hand, a cohesion-increasing loss term with a learnable label-adjusting matrix is designed to facilitate consensus among views in the training stage. With this kind of loss, the learned classifiers of all views are more likely to obtain the correct classification, thereby maximizing the agreement among views. On the other hand, an independence measurement is adopted as the diversity-promoting regularization to encourage classifiers to be diverse such that more complementary information can be captured by these "diversified" classifiers. Overall, the resultant model is capable of achieving more comprehensive and accurate classification by exploring and exploiting the common and complementary information across multiple views more thoroughly. An iterative optimization algorithm with proved convergence is proposed for training the model. Extensive experimental results on various datasets have demonstrated the efficacy of the proposed method.

Multi-view subspace clustering has been applied to applications such as image processing and video surveillance, and has attracted increasing attention. Most existing methods learn view-specific self-representation matrices, and construct a combined affinity matrix from multiple views. The affinity construction process is time-consuming, and the combined affinity matrix is not guaranteed to reflect the whole true subspace structure. To overcome these issues, the Latent Complete Row Space Recovery (LCRSR) method is proposed. Concretely, LCRSR is based on the assumption that the multi-view observations are generated from an underlying latent representation, which is further assumed to collect the authentic samples drawn exactly from multiple subspaces. LCRSR is able to recover the row space of the latent representation, which not only carries complete information from multiple views but also determines the subspace membership under certain conditions. LCRSR does not involve the graph construction procedure and is solved with an efficient and convergent algorithm, thereby being more scalable to large-scale datasets. The effectiveness and efficiency of LCRSR are validated by clustering various kinds of multi-view data and illustrated in the background subtraction task.

Algorithms for dictionary learning aim to learn a dictionary under which training data have sparse representations. This paper addresses the dictionary update sub-problem, the goal of which is to update the dictionary and the corresponding sparse coefficients given a fixed sparsity pattern. It is a non-convex bilinear inverse problem, and hence challenging to solve. Inspired by a recent work by Ling and Strohmer, we re-formulate the dictionary update problem as a linear least squares problem, which is convex and easy to solve. Necessary bounds on the number of training samples required for a unique solution are derived when exact sparsity pattern is known. Further, for dictionary update with unknown sparsity patterns, an efficient iterative algorithm based on total least squares is developed. Embedding the new dictionary update procedure into an overall dictionary learning algorithm achieves better numerical performance compared to state of the art algorithms.

To reduce the size of spectral data, compressive sensing imaging systems are developed to sample fewer measurements than the Nyquist‐rate ones, from which the original data can be recovered by the optimisation model and algorithm. However, this is not a cheap option for the case where the real‐time acquisition of spectral information is required. To solve this problem, the authors propose a novel sensing approach for spectral features by combining the sampling, recovery and feature extraction. Inspired by the spectral feature representation, the sampling (sensing) matrix is designed from the training spectral samples to sense the spectral features of the imaging scene, which can be utilised for classification and recognition directly. Besides, the physical realisation of the sensing matrix for compressive spectral imaging systems is demonstrated by designing new modulation patterns of the digital micro‐mirror device. The experimental results on real spectral data show the feasibility of the proposed scheme and the robustness to the quantisation error and the measurement noise. Moreover, the proposed sensing approach can reduce the cost of computation and time greatly by removing the sparse recovery and feature extraction..

Parameter retrieval of ocean internal waves from synthetic aperture radar (SAR) images is an important issue of oceanography; however, the extraction precision is usually limited by the complex waveforms and the noise. To improve the performance of parameter extraction, traditional methods usually focus on removing the noise on SAR images by exploiting its statistical character, but the structure character of ocean internal waves does not draw enough attentions to improve the image quality for parameter extraction. This study presents a local low‐rank approach to extract the parameters robustly by associating the noise removing and parameter extraction together. An optimisation model is first developed by associating the speckle suppression and the exploration of the structural prior of internal wave, where the local low‐rank prior is utilised. Also then, a numerical algorithm based on alternating optimisation scheme is designed to solve the proposed model. The proposed approach not only improves the extraction precision, but is also robust to the non‐ideal cases such as the deformed waveforms. In experiments, both simulations and real data are used to demonstrate the efficiency and robustness of the proposed method.

With the advent of multi-view data, multi-view learning (MVL) has become an important research direction in machine learning. It is usually expected that multi-view algorithms can obtain better performance than that of merely using a single view. However, previous researches have pointed out that sometimes the utilization of multiple views may even deteriorate the performance. This will be a stumbling block for the practical use of MVL in real applications, especially for tasks requiring high dependability. Thus, it is eager to design reliable multi-view approaches, such that their performance is never degenerated by exploiting multiple views.This issue is vital but rarely studied. In this paper, we focus on clustering and propose the Reliable Multi-View Clustering (RMVC) method. Based on several candidate multi-view clusterings, RMVC maximizes the worst-case performance gain against the best single view clustering, which is equivalently expressed as no label information available. Specifically, employing the squared χ2 distance for clustering comparison makes the formulation of RMVC easy to solve, and an efficient strategy is proposed for optimization. Theoretically, it can be proved that the performance of RMVC will never be significantly decreased under some assumption. Experimental results on a number of data sets demonstrate that the proposed method can effectively improve the reliability of multi-view clustering.

Compressive sensing (CS) theory enables single‐pixel compressive imaging (SPCI) popular in optical remote sensing imaging, since single‐pixel imager not only realises the acquisition and recovery of sparse images at the sampling rates significantly below the classical Nyquist rate, but also makes use of special detectors to improve sensitivity, dynamic range, spectral range and so on. However, its requirement of static imaging condition for the time‐sequential measurements makes it difficult to apply in remote sensing, since the imaging platform is always in motion relative to the imaging scene. In this study, the authors develop a new method for SPCI on moving platform in optical remote sensing. Instead of ignoring the motion during sampling, the proposed method first builds the compressive sampling model based on motion compensation during sampling, and then reconstructs the image by frame‐by‐frame recovery method and joint recovery method, respectively, in the framework of CS theory, where the recovery condition is also analysed. To validate the basic principle and the physical feasibility of motion compensation, the authors implement the numerical simulations and optical experiments, where different conditions are exploited sufficiently. In addition, the proposed method for SPCI can be also extended into other applications, such as 360° annular imaging, multi‐pixel compressive imaging as well as super‐resolution imaging.

Recently, a tight frame, called convolution framelets (CFs) and constructed by convolving local and non‐local bases, is proposed to provide valuable insights in understanding the patch‐based processing approaches in the viewpoint of sparse representation (SR). However, it is still unclear how to represent signals with energy concentration guarantee in its lifted space and how to optimise the local base for a given non‐local base. To address these issues, the equivalence between the signal space and its lifted space is established by the Hankel operator. In the lifted space, the energy concentration property of signals is measured by the sparsity instead of the Euclidean norm and the rank. With the new objective function, an optimisation model is built to train the optimal local base for a given nonlocal base from the training samples, motivating us to propose the optimal matching convolution framelets (OMCFs). In addition, a numerical algorithm is also designed to solve the proposed model using alternating optimisation strategy. The OMCF for SR is tested on the speech signals, and the comparisons with traditional popular SR tools, such as discrete cosine transform (DCT) and Haar wavelets, demonstrate its better performance.

Multi-view clustering, which aims to improve the clustering performance by exploring the data’s multiple representations, has become an important research direction. Graph based methods have been widely studied and achieve promising performance for multi-view clustering. However, most existing multi-view graph based methods perform clustering on the fixed input graphs, and the results are dependent on the quality of input graphs. In this paper, instead of fixing the input graphs, we propose Multi-view clustering with Adaptively Learned Graph (MALG), learning a new common similarity matrix. In our model, we not only consider the importance of multiple graphs from view level, but also focus on the performance of similarities within a view from sample-pair level. Sample-pair-specific weights are introduced to exploit the connection across views in more depth. In addition, the obtained optimal graph can be partitioned into specific clusters directly, according to its connected components. Experimental results on toy and real-world datasets demonstrate the efficacy of the proposed algorithm.

Speckle suppression is extremely important for understanding and utilising synthetic aperture radar (SAR) images, while the emphasis of the traditional methods for speckle suppression is usually focused on removing the noise instead of keeping the scattering character of imaging objects, which has caused serious interference to the subsequent applications of SAR images. The authors aim to develop sparse partial differential equation (PDE) for speckle suppression of SAR image, where the PDE model is associated with the sparse prior of objects and the statistical property of speckle. The PDE model has been proved to have the ability of denoising and edge‐preserving by proper design, and the sparse prior of the point‐ and line‐like objects on SAR images has been also illustrated, both of which help for keeping the scattering characters. To solve the proposed sparse PDE model, a numerical algorithm is designed and the sparse constraint is realised in each step of the diffusion process. In experiments, several real SAR images are utilised to validate the performance of the proposed method.

With the advent of multi-view data, multi-view learning has become an important research direction in machine learning and image processing. Considering the difficulty of obtaining labeled data in many machine learning applications, we focus on the multi-view semi-supervised classification problem. In this paper, we propose an algorithm named multi-view semi-supervised classification via adaptive regression (MVAR) to address this problem. Specifically, regression-based loss functions with ℓ2,1matrix norm are adopted for each view and the final objective function is formulated as the linear weighted combination of all the loss functions. An efficient algorithm with proved convergence is developed to solve the non-smooth ℓ2,1-norm minimization problem. Regressing to class labels directly makes the proposed algorithm efficient in calculation and can be applied to large-scale data sets. The adaptively optimized weight coefficients balance the contributions of different views automatically, which makes the performance robust against the existence of low-quality views. With the learned projection matrices and bias vectors, predictions for out-of-sample data can be easily made. To validate the effectiveness of MVAR, comparisons are made with some benchmark methods on realworld data sets and in the scene classification scenario as well. The experimental results demonstrate the effectiveness of our proposed algorithm.

This paper aims at the feature enhancement for the multichannel synthetic aperture radar (SAR) images. A novel non-local vectorial total variation approach, which is an extension of the non-local vectorial total variation approach for the multichannel SAR images, is proposed. It contains the vectorial data fidelity term and the non-local vectorial total variation term. The non-local vectorial total variation term contains the structure information and is constructed by high-dimensional non-local gradient. Experiments on the measured multichannel SAR images shows that the proposed approach can efficiently suppress speckle noise and enhance features especially edges.

In the single‐image dehazing problem, it is critical that the transmission is accurately estimated. However, the extracted transmission in the dark channel model cannot effectively deal with the edge and the sky area because of the poor applicability of the dark channel prior to these areas. This study aims to solve that problem by proposing a novel variational model (VM) to optimise the transmission. This VM introduces a smoothness term and a gradient‐preserving term to mitigate the false edge and the distorted sky area in the recovered image. Further, a fast algorithm to solve the VM is proposed on the basis of the additional operator splitting algorithm. This algorithm is an effective linear time algorithm and has excellent performance on optimising the transmission. The average running time of the algorithm shows an improvement of over 20 times that of the guided image filtering in these experiments. Experimental results also show that the proposed algorithm is both effective and efficient for optimising the transmission.

The authors focus on the minimum sampling rate and the exact recovery condition in the sampling of multiple signals with finite rate of innovation (FRI) and sparse common support (SCS). The authors first propose the subspace‐based recovery method and analyse its relation with the annihilating filter; then the proposed method is used for sampling the multiple signals with FRI and SCS. It is observed that the minimum sampling rate for the exact recovery heavily depends on the signal structure described by the defined characteristic matrix, based on which a sufficient and necessary condition is also presented. The numerical simulations show that the proposed recovery method and the recovery condition are feasible for the sampling of multiple signals with FRI and SCS.

In multichannel image processing, many tasks, such as image denoising, image deblurring, and image inpainting, can be included in the fields of inverse problems and high-dimensional data processing. To get better performance, there are two key points that should be considered seriously. On the one hand, most of these inverse problems are ill-posed, and the prior constraints are necessary to transform them into well-posed problems by reducing the solution space. On the other hand, the information of the coupling among different channels is important in multichannel image processing, where each channel of the image is usually processed separately. In this paper, we propose the fidelity-Beltrami-sparsity (FBS) model for the inverse problems in multichannel image processing, which can simultaneously exploit two important priors, i.e., the smoothness prior and the sparsity prior. As we know, the smoothness prior and the sparsity prior have been widely validated for an image, respectively, so inverse problems with these two priors in image processing are more likely to be well-posed. In addition, the proposed model can also utilize the coupling among different channels of the image by building these constraints on the image manifold. More importantly, the FBS model is numerically calculable, although the model associated with the fidelity term, the smoothness constraint, and the sparsity constraint is not convex or differentiable. Finally, we present the numerical results of the proposed method as well as the comparative results for different inverse problems, namely, image denoising, image deblurring, and image inpainting, in multichannel image processing. Quantitative comparisons by the peak signal-to-noise ratio as well as the visual effect indicate the better performance of the proposed method.

The fast algorithm for satellite visibility is very important in many applications, particularly in the real-time simulation environments. In this paper, a novel algorithm, true anomaly iteration compensation (TAIC) algorithm, is proposed to predict the visibility of the elliptical orbits' satellites. A main property of our algorithm is that it could avoid solving the transcendental equation: Kepler Equation, therefore the computation of the algorithm is very small. Furthermore, a compensation method is used to yield more accurate results. The excellent performance of the algorithm is illustrated by the numerical results. For TAIC algorithm, the error of visibility- time is about 0.21% and the error of the entry-access time instant and the exit-access time instant is about 0.79 seconds.