Anomaly detection is challenging with the presence of missing data. The common two-stage strategy first imputes missing values and then performs anomaly detection, making its performance highly dependent on imputation quality. When the data distribution is complex, the imputation quality may be poor, which degrades the performance of anomaly detectors. To address this issue, we propose a Missing-Kernel-based One-Class Support Vector Machine (MK-OCSVM), in which a novel missing kernel capable of handling missing data is constructed. MK-OCSVM avoids explicit imputation so that its anomaly detection performance is not affected by the imputation quality. Besides, we use the partially observed data in the observation space to model the data distribution in the latent original space, thereby enabling anomaly detection for the latent complete data. MK-OCSVM incorporates the data distribution modeling and OCSVM construction in a joint optimization framework, which alleviates the singularity issue and enhances the suitability of the missing kernel for anomaly detection. To solve the joint optimization problem of MK-OCSVM, a gradient-based alternating optimization algorithm is designed. Experimental results demonstrate the effectiveness of the proposed method.

Video anomaly detection (VAD) is important in many fields because of its theoretical and practical values. One of the challenges in VAD is the difficulty in obtaining segment-level labels due to the high annotation cost. In recent years, researchers have adopted video-level labels as a form of weak supervision, leading to the development of weakly supervised video anomaly detection (WS-VAD). Among different WS-VAD approaches, graph convolutional networks (GCNs) have attracted much attention, since they have the ability to model relationship information in video data. Typically, the relationship, represented by the graph edges, is the class label similarity, and this similarity is built based on the feature similarity and temporal consistency among video segments. Undoubtedly, the more information about class label similarity is provided, the higher the performance of GCN tends to be. In real-world scenarios of VAD, anomalies exhibit several unique properties such as diversity and rarity. These properties may lead to the following situation. Given two video segments, although their feature similarity is low and their time separation is large, both of them are anomalies, that is, they have the same class label. Likewise, normal samples also encounter such situation. However, the existing graph structures in GCN methods do not adequately account for this situation. To address this issue, this paper proposes an extended graph learning (EGL) method that incorporates additional class label similarity among video segments. The proposed EGL includes two extended graph convolutional networks (EGCNs): a spatial EGCN and a temporal EGCN. To capture more accurate information about class label similarity, EGL incorporates a feedback module to update the graph structures of EGCNs. EGL can effectively extract more information about class label similarity, thereby ensuring good performance when training data is scarce. Experimental results highlight the advantages of the proposed EGL method, particularly with limited training samples. In particular, when only 30% of the training data is used, EGL achieves the best performance of 95.55% AUC on ShanghaiTech, 81.29% AUC on UCF-Crime, and 75.31% AP on XD-Violence, outperforming the existing VAD methods by up to 6.86%, 3.23%, and 4.40%, respectively.

Anomaly localization, which involves localizing anomalous regions within images, is a significant industrial task. Reconstruction-based methods are widely adopted for anomaly localization because of their low complexity and high interpretability. Most existing reconstruction-based methods only use normal samples to construct model. If anomalous samples are appropriately utilized in the process of anomaly localization, the localization performance can be improved. However, usually only weakly labeled anomalous samples are available, which limits the improvement. In many cases, we can obtain some knowledge of anomalies summarized by domain experts. Taking advantage of such knowledge can help us better utilize the anomalous samples and thus further improve the localization performance. In this article, we propose a novel reconstruction-based method named knowledge-informed self-training (KIST) which integrates knowledge into a reconstruction model through self-training. Specifically, KIST utilizes weakly labeled anomalous samples in addition to the normal ones and exploits knowledge to yield pixel-level pseudolabels of the anomalous samples. Based on the pseudolabels, a novel loss that promotes the reconstruction of normal pixels while suppressing the reconstruction of anomalous pixels is used. We conduct experiments on different datasets and demonstrate the advantages of KIST over the existing reconstruction-based methods.

Anomaly detection (AD) techniques are widely used in various fields. Existing techniques primarily focus on learning a normal region from single-view data, which may be not suitable for multiview data that provides more comprehensive information from multiple perspectives. Therefore, AD techniques designed for multiview data are necessary. Straightforwardly, one can concatenate the features learned from multiple single-view data into a joint representation to conduct AD. However, this may overlook the inevitable overlaps between views, potentially masking view-specific information due to the repetitive calculations of these overlaps. Among the various possible methods, one way to address this is to compress redundant information while maintaining comprehensive information across views. Following this way, in this article, we leverage the principle of information bottleneck (IB) to extract concise and comprehensive representations for multiview data. But it is problematic to directly use these representations for AD, since the multiview fusion process may disturb the intrinsic structure of the original data. That is, samples distributed at the edges/center of the original normal data distribution are mapped closer to the center/edges. This might cause abnormal samples (close to the normal data at the edges) to be incorrectly mapped into the normal region during inference. In the AD scenario, the absence of abnormal training samples makes it unfeasible to preserve this structure using supervised information. In this article, we design a topology-preserved regularization that unsupervisedly constrains the latent representations to preserve the original data's intrinsic structure, to improve the AD performance. Overall, we propose a topology-preserved multiview information bottleneck (TMVIB) feature extraction method to extract concise, comprehensive, and topology-preserved latent representations from multiview data. Interestingly, we find that the TMVIB feature extraction method itself can be viewed as a regularized anomaly detector, allowing it to output anomaly scores directly. Experiments on synthetic and real-world multiview datasets demonstrate the effectiveness of the proposed TMVIB.

Neural architecture search (NAS) has shown great promise in automatically designing neural network models. Recently, block-wise NAS has been proposed to alleviate deep coupling problem between architectures and weights existed in the well-known weight-sharing NAS, by training the huge weight-sharing supernet block-wisely. However, the existing block-wise NAS methods, which resort to either supervised distillation or self-supervised contrastive learning scheme to enable block-wise optimization, take massive computational cost. To be specific, the former introduces an external high-capacity teacher model, while the latter involves supernet-scale momentum model and requires a long training schedule. Considering this, in this work, we propose a resource-friendly deeply supervised block-wise NAS (DBNAS) method. In the proposed DBNAS, we construct a lightweight deeply-supervised module after each block to enable a simple supervised learning scheme and leverage ground-truth labels to indirectly supervise optimization of each block progressively. Besides, the deeply-supervised module is specifically designed as structural and functional condensation of the supernet, which establishes global awareness for progressive block-wise optimization and helps search for promising architectures. Experimental results show that the DBNAS method only takes less than 1 GPU day to search out promising architectures on the ImageNet dataset with less GPU memory footprint than the other block-wise NAS works. The best-performing model among the searched DBNAS family achieves 75.6% Top-1 accuracy on ImageNet, which is competitive with the state-of-the-art NAS models. Moreover, our DBNAS family models also achieve good transfer performance on CIFAR-10/100, as well as two downstream tasks: object detection and semantic segmentation.

Pedestrian detection plays a critical role in computer vision as it contributes to ensuring traffic safety. Existing methods that rely solely on RGB images suffer from performance degradation under low-light conditions due to the lack of useful information. To address this issue, recent multispectral detection approaches have combined thermal images to provide complementary information and have obtained enhanced performances. Nevertheless, few approaches focus on the negative effects of false positives (FPs) caused by noisy fused feature maps. Different from them, we comprehensively analyze the impacts of FPs on detection performance and find that enhancing feature contrast can significantly reduce these FPs. In this article, we propose a novel target-aware fusion strategy for multispectral pedestrian detection, named TFDet. The target-aware fusion strategy employs a fusion-refinement paradigm. In the fusion phase, we reveal the parallel- and cross-channel similarities in RGB and thermal features and learn an adaptive receptive field to collect useful information from both features. In the refinement phase, we use a segmentation branch to discriminate the pedestrian features from the background features. We propose a correlation-maximum loss function to enhance the contrast between the pedestrian features and background features. As a result, our fusion strategy highlights pedestrian-related features and suppresses unrelated ones, generating more discriminative fused features. TFDet achieves state-of-the-art performance on two multispectral pedestrian benchmarks, KAIST and LLVIP, with absolute gains of 0.65% and 4.1% over the previous best approaches, respectively. TFDet can easily extend to multiclass object detection scenarios. It outperforms the previous best approaches on two multispectral object detection benchmarks, FLIR and M3FD, with absolute gains of 2.2% and 1.9%, respectively. Importantly, TFDet has comparable inference efficiency to the previous approaches and has remarkably good detection performance even under low-light conditions, which is a significant advancement for ensuring road safety. The code will be made publicly available at https://github.com/XueZ-phd/TFDet.git.

Federated learning (FL) has attracted widespread attention in the Internet of Things domain recently. With FL, multiple distributed devices can cooperatively train a global model by transmitting model updates without disclosing the original data. However, the distributed nature of FL makes it vulnerable to data poisoning attacks. In practice, malicious clients can launch the label-flipping attack (LFA) by simply tampering with the labels of local data, thus causing the global model to misclassify the samples of a selected class as the target class. Although some defense mechanisms have been proposed, they rely on specific assumptions about data distribution, and their performance degrades significantly when the data on clients are non-IID. Besides, most existing methods require clients to upload model updates in plaintext so that the server can identify and remove the malicious updates. But, direct transmission of model updates may still reveal private information. Considering these issues, we develop a label-flipping-robust and privacy-preserving FL (LFR-PPFL) algorithm, which is applicable to both independent and identically distributed (IID) and non-IID data. We first propose a detection method based on temporal analysis on cosine similarity to distinguish malicious clients from benign clients. Then, we propose a privacy-preserving computation protocol based on homomorphic encryption to implement this detection method and perform federated aggregation while protecting the privacy of clients. Besides, a detailed theoretical analysis is given to demonstrate the privacy guarantee of the proposed protocol. Experimental results on real-world data sets show that the proposed algorithm can effectively defend against LFAs under various data distributions.

Ordinal regression (OR) is a multi-class classification problem with ordered labels. The objective functions of most OR methods are based on the misclassification error. The volume under the ROC surface (VUS) is a measure of OR that quantifies the ranking ability of OR models. It can also be used as an objective function in OR. In practice, data may be collected by multiple nodes in a distributed and online manner, and is difficult to process centrally. In this paper, we intend to develop a VUS-based distributed online OR method. Computing VUS requires a sequence of data from all categories, but the available online data may not cover all categories and the required data may distribute across different nodes. Besides, the existing approximation methods of VUS are inappropriate for using in OR. To address these issues, we first propose two new surrogate losses of the VUS in OR. We then derive their decomposed formulations and propose distributed online OR algorithms based on VUS maximization (dVMOR). The experimental results demonstrate their effectiveness.

Anomaly detection is widely used in many fields to reveal the abnormal process of a system. Typical model-based anomaly detection methods work well in general anomaly detection problems. However, in some application-specific scenarios, the anomalies of interest are "direction-related," that is, only deviation in certain directions of the data space is abnormal. Most existing anomaly detection methods do not work well in these scenarios, especially when there is no abnormal data information during training. Considering that in many real anomaly detection applications such as medical disease detection and industrial device faults diagnosis, the normal data have several ordinal levels, and the anomalies can be regarded as an unseen level distributed roughly along the ordinal direction outside the normal levels. Notice that the ordinal information is inherently "direction-related," and we can use the ordinal information to assist in finding a "direction-related" boundary for the normal data to detect anomalies of interest. A typical type of methods utilizing the ordinal information is ordinal regression. However, to the best of our knowledge, the existing ordinal regression methods are unable to be directly applied to anomaly detection. In this article, to detect the aforementioned "direction-related" anomalies, we propose an ordinal regression algorithm for direction-related anomaly detection (ORAD). Specifically, we first formulate ORAD as an optimization problem. Then, we apply the difference of convex functions (DC) programming to solve the problem to obtain a "direction-related" boundary. After that, we calculate the outlier scores based on the deviation from the boundary. Theoretically, we analyze the ordinal properties and the convergence of ORAD. We carry out experiments on both synthetic data and real datasets to demonstrate the effectiveness of the proposed ORAD.

Training neural network classifiers (NNCs) usually requires all instances to be correctly labeled, which is difficult and/or expensive to satisfy in some practical applications. When label noise is present, mislabeled data will severely mislead the training of NNCs, resulting in poor generalization performance. In this work, we address the label noise issue by removing mislabeled instances from the training data. A COnsistence-based Mislabeled Instances REmoval (COMIRE) method is proposed. The main idea is based on the observation that during the training of the NNC, the training loss and the model's prediction uncertainty of correctly labeled instances show similar trends, while those of mislabeled instances have quite different trends. Thus, the consistency between the two trends can be used to distinguish correctly labeled instances from mislabeled ones. On this basis, an iteration scheme is introduced to further increase the separability between the two types of data. Experimental results show that COMIRE can effectively identify the mislabeled instances. Moreover, the classification performance is significantly improved after removing the identified instances from the noisy training data.

Hashing has been widely used for nearest neighbors search over big data. Hashing encodes high dimensional data points into binary codes. Most hashing methods use the single-bit quantization (SBQ) strategy for coding the data. However, this strategy often encodes neighboring points into totally different bits. Recently, a double-bit quantization (DBQ) strategy was proposed, which can better preserve the similarity of the data. The hashing problems are generally NP-hard, due to the discrete constraints. For tractability, some relaxation methods were proposed by discarding the discrete constraints. However, such a manner makes the hash codes less effective, due to the large quantization error. To obtain high-quality hash codes, some discrete hashing methods were proposed, which directly solve the hashing problem without any relaxations. However, the existing discrete hashing methods can only deal with single-bit hashing. In this paper, we propose a discrete hashing method to solve double-bit hashing problems. To address the difficulty brought by the discrete constraints, we propose a method to transform the discrete hashing problem into an equivalent continuous optimization problem. Then, we devise algorithms based on DC (difference of convex functions) programming to solve the problem. Numerical experiments are provided to show the superiority of the proposed methods.

Multilabel classification (MLC) has received much attention recently. The existing MLC algorithms usually learn multiple classifiers simultaneously by exploiting the correlations among different labels. However, it is difficult and/or expensive to collect a large amount of multilabeled data in practice. The lack of labeled data significantly deteriorates the performance of classification. Moreover, the existing algorithms belong to centralized learning, that is, all the data with their labels must be transmitted to a fusion center for processing. But in many real applications, data may be dispersedly collected/stored in distributed nodes of networks. Due to the concerns of communication cost, processing ability, and data privacy, it is impossible to transmit and/or process the data centrally at one node. Considering this, the problem of distributed MLC over networks is studied, and two distributed information-theoretic semisupervised multilabel learning (dITS2ML2) algorithms are proposed, which are, respectively, used for solving linear and nonlinear MLC problems. In the proposed algorithms, a cost-sensitive objective function is designed, in which a new label correlation term defined on some anchor data is suggested. Besides, to decentralize the global objective function, a distributed matrix completion algorithm is developed to distributively complete the label matrix of the anchor data. Then, by exchanging and combining a few intermediate quantities instead of the original data for both linear and nonlinear cases, the model parameters can be adaptively estimated. The convergence of the proposed dITS2ML2algorithms is analyzed, and their effectiveness in MLC is verified by simulations on various real datasets.

Anomaly detection plays an important role in industry, especially in ensuring system safety and product quality. Due to the unavailability of anomalous data in many practical cases, anomaly detection is usually solved by one-class classification (OCC) methods using only normal data. As a classical OCC method, one-class support vector machine (OCSVM) is a popular discriminative approach for anomaly detection, which detects abnormal data points by establishing a decision boundary in the kernel space. However, the performance of OCSVM heavily relies on kernel parameters, whose selection is not trivial for anomaly detection problems. Moreover, for some uneven and complex data distributions, different data regions may have quite different densities and shapes, making it difficult for OCSVM to obtain good boundaries in all regions using a global kernel parameter. To address the above two issues, in this article, we propose a hybrid algorithm incorporating vector quantization and OCSVM (VQ-OCSVM). Specifically, vector quantization is used to extract distribution information of normal data, and the results are used to construct an explicit mapping function to map data into a high-dimensional feature space. Then, OCSVM is performed in the feature space to build a classifier. By introducing the explicit mapping into OCSVM, the proposed method can effectively bypass the kernel parameter selection problem of the classical OCSVM method. Furthermore, the constructed mapping carries the data distribution information, and the VQ-OCSVM model can be regarded as an integration of generative learning and discriminative learning. The complementary properties of these two paradigms make the proposed VQ-OCSVM algorithm have better generalization capacity for complex data distribution. Both qualitative and quantitative experimental results demonstrate the effectiveness and advantages of the proposed method.

Hashing-based approximate nearest neighbors search has attracted broad research interest, due to its low computational cost and fast retrieval speed. The hashing technique maps the data points into binary codes and, meanwhile, preserves the similarity in the original space. Generally, we need to solve a discrete optimization problem to learn the binary codes and hash functions, which is NP-hard. In the literature, most hashing methods choose to solve a relaxed problem by discarding the discrete constraints. However, such a relaxation scheme will cause large quantization error, which makes the learned binary codes less effective. In this paper, we present an equivalent continuous formulation of the discrete hashing problem. Specifically, we show that the discrete hashing problem can be transformed into a continuous optimization problem without any relaxations, while the transformed continuous optimization problem has the same optimal solutions and the same optimal value as the original discrete hashing problem. After transformation, the continuous optimization methods can be applied. We devise the algorithms based on the idea of DC (difference of convex functions) programming to solve this problem. The proposed continuous hashing scheme can be easily applied to the existing hashing models, including both supervised and unsupervised hashing. We evaluate the proposed method on several benchmarks and the results show the superiority of the proposed method compared with the state-of-the-art hashing methods.

Data classification is usually challenged by the difficulty and/or high cost in collecting sufficient labeled data, and unavoidability of data missing. Besides, most of the existing algorithms belong to centralized processing, in which all of the training data must be stored and processed at a fusion center. But in many real applications, data are distributed over multiple nodes, and cannot be centralized to one node for processing due to various reasons. Considering this, in this article, we focus on the problem of distributed classification of missing data with a small proportion of labeled data samples, and develop a distributed semi-supervised missing-data classification (dS2MDC) algorithm. The proposed algorithm is a distributed joint subspace/classifier learning, that is, a latent subspace representation for missing feature imputation is learned jointly with the training of nonlinear classifiers modeled by the$\chi ^{2}$kernel using a semi-supervised learning strategy. Theoretical performance analysis and simulations on several datasets clearly validate the effectiveness of the proposed dS2MDC algorithm from different perspectives.

Fault diagnosis, which aims to identify the root cause of the observed abnormality, is essential for the control and optimization of industrial processes. Many existing data-driven fault diagnosis methods require all the training samples to be correctly labeled. However, label noise is ubiquitous in practical industrial data, and the performance of these methods may be severely affected. In this article, we address the fault diagnosis issue in the presence of label noise. A probabilistic information-theoretic discriminant analysis (PITDA) algorithm is proposed, which consists of two iterative steps. First, a probabilistic feature extractor based on information theory is presented to extract discriminative features from industrial data. Second, a robust mixture discriminant analysis method is applied to build label noise-tolerant classifier in the feature space and produce the probability used in the first step. Iteration of these two steps gives the PITDA algorithm, which is able to perform fault diagnosis for complex and high-dimensional industrial data in the presence of label noise. Experimental results on synthetic data, Tennessee Eastman benchmark process, and a real-world air compressor working process demonstrate the effectiveness and advantages of the proposed algorithm.

Recently, broad learning system (BLS) has been introduced to solve industrial fault diagnosis problems and has achieved impressive performance. As a flat network, BLS enjoys a simple linear structure, which enables BLS to train and update the model efficiently in an incremental manner, and it potentially has better generalization capacity than deep learning methods when training data are limited. The basic BLS is a supervised learning method that requires all the training data to be labeled. However, in many practical industrial scenarios, data labels are usually difficult to obtain. Existing semisupervised variant uses manifold regularization framework to capture the information of unlabeled data, however, such a method will sacrifice the incremental learning capacity of BLS. Considering that in many practical applications, training data are sequentially generated, in this article, an online semisupervised broad learning system (OSSBLS) is proposed for fault diagnosis in these cases. The proposed method not only can efficiently construct and incrementally update the model, but also can take advantage of unlabeled data to improve the model's diagnostic performance. Experimental results on the Tennessee Eastman process and a real-world air compressor working process demonstrate the superiority of OSSBLS in terms of both diagnostic performance and time consumption.

Multispectral imaging plays a vital role in the area of computer vision and computational photography. As spectral band images can be misaligned due to imaging device movement or alternation, image registration is necessary to avoid spectral information distortion. The current registration measures specialized for multispectral data are typically robust yet complex, requiring excessive computation. The common measures such as sum of squared differences (SSD) and sum of absolute differences (SAD) are computationally efficient whereas they perform poorly on multispectral data. To cope with this challenge, we propose a structure consistency boosting (SCB) transform that aims at boosting the structural similarity of multispectral images. With SCB, the common measures can be employed for multispectral image registration. The SCB transform exploits the fact that inherent edge structures maintain relative saliency locally despite the nonlinear variation between band images. A statistical prior of the natural image, which is based on the gradient-intensity correlation, is explored to build a parametric form of SCB. Experimental results validate that the SCB transform outperforms current similarity enhancement algorithms, and performs better than the state-of-the-art multispectral registration measures. Thanks to the generality of the statistical prior, the SCB transform is also applicable to various multimodal data such as flash/no-flash images and medical images.

Wireless sensor networks (WSNs) act as the backbone of Internet of Things (IoT) technology. In WSN, field sensing and fusion are the most commonly seen problems, which involve collecting and processing of a huge volume of spatial samples in an unknown field to reconstruct the field or extract its features. One of the major concerns is how to reduce the communication overhead and data redundancy with prescribed fusion accuracy. In this paper, an integrated communication and computation framework based on meta-learning is proposed to enable adaptive field sensing and reconstruction. It consists of a stochastic-gradient-descent (SGD)-based base-learner used for the field model prediction aiming to minimize the average prediction error, and a reinforcement meta-learner aiming to optimize the sensing decision by simultaneously rewarding the error reduction with samples obtained so far and penalizing the corresponding communication cost. An adaptive sensing algorithm based on the above two-layer meta-learning framework is presented. It actively determines the next most informative sensing location, and thus considerably reduces the spatial samples and yields superior performance and robustness compared with conventional schemes. The convergence behavior of the proposed algorithm is also comprehensively analyzed and simulated. The results reveal that the proposed field sensing algorithm significantly improves the convergence rate.

Anomaly detection has attracted much attention in recent years since it plays a crucial role in many domains. Various anomaly detection approaches have been proposed, among which one-class support vector machine (OCSVM) is a popular one. In practice, data used for anomaly detection can be distributively collected via wireless sensor networks. Besides, as the data usually arrive at the nodes sequentially, online detection method that can process streaming data is preferred. In this paper, we formulate a distributed online OCSVM for anomaly detection over networks and get a decentralized cost function. To get the decentralized implementation without transmitting the original data, we use a random approximate function to replace the kernel function. Furthermore, to find an appropriate approximate dimension, we add a sparse constraint into the decentralized cost function to get another one. Then we minimize these two cost functions by stochastic gradient descent and derive two distributed algorithms. Some theoretical analysis and experiments are performed to show the effectiveness of the proposed algorithms. Experimental results on both synthetic and real datasets reveal that both of the proposed algorithms achieve low misdetection rates and high true positive rates. Compared with other state-of-the-art anomaly detection methods, the proposed distributed algorithms not only show good anomaly detection performance, but also require relatively short running time and low CPU memory consumption.

Recently, hashing-based approximate nearest neighbors search has attracted considerable attention, especially in big data applications, due to its low computation cost and fast retrieval speed. In the literature, most of the existing hashing algorithms are centralized. However, in many large-scale applications, the data are often stored or collected in a distributed manner. In this situation, the centralized hashing methods are not suitable for learning hash functions. In this paper, we consider the distributed learning to hash problem. We propose a novel distributed graph hashing model for learning efficient hash functions based on the data distributed across multiple agents over network. The graph hashing model involves a graph matrix, which contains the similarity information in the original space. We show that the graph matrix in the proposed distributed hashing model can be decomposed into multiple local graph matrices, and each local graph matrix can be constructed by a specific agent independently, with moderate communication and computation cost. Then, the whole objective function of the distributed hashing model can be represented by the sum of local objective functions of multiple agents, and the hashing problem can be formulated as a nonconvex constrained distributed optimization problem. For tractability, we transform the nonconvex constrained distributed optimization problem into an equivalent bi-convex distributed optimization problem. Then we propose two algorithms based on the idea of alternating direction method of multipliers to solve this problem in a distributed manner. We show that the proposed two algorithms have moderate communication and computational complexities, and both of them are scalable. Experiments on benchmark datasets are given to demonstrate the effectiveness of the proposed methods.

Distributed data processing over networks has received a lot of attention due to its wide applicability. In this paper, we consider the multitask problem of in-network distributed estimation. For the multitask problem, the unknown parameter vectors (tasks) for different nodes can be different. Moreover, considering some real application scenarios, it is also assumed that there are some similarities among the tasks. Thus, the intertask cooperation is helpful to enhance the estimation performance. In this paper, we exploit an additional special characteristic of the vectors of interest, namely, joint sparsity, aiming to further enhance the estimation performance. A distributed jointly sparse multitask algorithm for the collaborative sparse estimation problem is derived. In addition, an adaptive intertask cooperation strategy is adopted to improve the robustness against the degree of difference among the tasks. The performance of the proposed algorithm is analyzed theoretically, and its effectiveness is verified by some simulations.

Image registration is a fundamental issue in multispectral image processing, and is challenged by two main characteristics of multispectral images. First, the regional intensities can be essentially different between band images. Second, the local contrasts of two difference band images are inconsistent or even reversed. Conventional measures can align images with different regional intensity levels, but may fail in the circumstance of severe local intensity variation. In this paper, a new measure called normalized total gradient is proposed for multispectral image registration. The measure is based on the key assumption (observation) that the gradient of the difference between two aligned band images is sparser than that between two misaligned ones. A registration framework, which incorporates image pyramid and global/local optimization, is further introduced for affine transform. Experimental results validate that the proposed method is not only effective for multispectral image registration, but also applicable to general unimodal/multimodal image registration tasks. It performs better than or comparable to the existing methods, both quantitatively and qualitatively.

In this paper, we consider a distributed robust optimization (DRO) problem, where multiple agents in a networked system cooperatively minimize a global convex objective function with respect to a global variable under the global constraints. The objective function can be represented by a sum of local objective functions. The global constraints contain some uncertain parameters which are partially known, and can be characterized by some inequality constraints. After problem transformation, we adopt the Lagrangian primal-dual method to solve this problem. We prove that the primal and dual optimal solutions of the problem are restricted in some specific sets, and we give a method to construct these sets. Then, we propose a DRO algorithm to find the primal-dual optimal solutions of the Lagrangian function, which consists of a subgradient step, a projection step, and a diffusion step, and in the projection step of the algorithm, the optimized variables are projected onto the specific sets to guarantee the boundedness of the subgradients. Convergence analysis and numerical simulations verifying the performance of the proposed algorithm are then provided. Further, for nonconvex DRO problem, the corresponding approach and algorithm framework are also provided.

Photometric stereo estimates surface normals from multiple images captured under different light directions using a fixed camera. To deal with non-Lambertian reflections, the recent photometric stereo methods employ iterative or optimization frameworks that are computationally expensive. This paper proposes an efficient photometric stereo method using kernel regression, which can be transformed to an eigendecomposition problem. The kernel parameter is variable for each surface point so that it can cope with the variety of general reflectances. The best kernel parameter is automatically determined by leave-one-out cross validation. To improve computational efficiency, the leave-one-out process is accelerated by fast matrix computation and proper normal initialization. The proposed photometric stereo method is extensively evaluated on synthetic and real surfaces with various reflectances. Experimental results validate that the method is computationally efficient and achieves the state-of-the-art accuracy in surface normal estimation.

Multispectral imaging system is of wide application in relevant fields for its capability in acquiring spectral information of scenes. Its limitation is that, due to the large number of spectral channels, the imaging process can be quite time-consuming when capturing high-resolution (HR) multispectral images. To resolve this limitation, this paper proposes a fast multispectral imaging framework based on the image sensor pixel-binning and spectral unmixing techniques. The framework comprises a fast imaging stage and a computational reconstruction stage. In the imaging stage, only a few spectral images are acquired in HR, while most spectral images are acquired in low resolution (LR). The LR images are captured by applying pixel binning on the image sensor, such that the exposure time can be greatly reduced. In the reconstruction stage, an optimal number of basis spectra are computed and the signal-dependent noise statistics are estimated. Then the unknown HR images are efficiently reconstructed by solving a closed-form cost function that models the spatial and spectral degradations. The effectiveness of the proposed framework is evaluated using real-scene multispectral images. Experimental results validate that, in general, the method outperforms the state of the arts in terms of reconstruction accuracy, with additional 20× or more improvement in computational efficiency.

The L1-norm cost function of the low-rank approximation of the matrix with missing entries is not smooth, and also cannot be transformed into a standard linear or quadratic programming problem, and thus, the optimization of this cost function is still not well solved. To tackle this problem, first, a mollifier is used to smooth the cost function. High closeness of the smoothed function to the original one can be obtained by tuning the parameters contained in the mollifier. Next, a recurrent neural network is proposed to optimize the mollified function, which will converge to a local minimum. In addition, to boost the speed of the system, the mollifying process is implemented by a filtering procedure. The influence of two mollifier parameters is theoretically analyzed and experimentally confirmed, showing that one of the parameters is critical to computational efficiency and accuracy, while the other not. A large number of experiments on synthetic data show that the proposed method is competitive to the state-of-the-art methods. In particular, the experiments on large matrices and a real application in the structure from motion indicate that the memory requirement of the proposed algorithm is mild, making it suitable for real applications that often involve large-scale matrix decomposition.

A random submatrix method (RSM) is proposed to calculate the low-rank decomposition U(m×r)V(n×r)(T) (r < m, n) of the matrix Y∈R(m×n) (assuming m > n generally) with known entry percentage 0 < ρ ≤ 1. RSM is very fast as only O(mr(2)ρ(r)) or O(n(3)ρ(3r)) floating-point operations (flops) are required, compared favorably with O(mnr+r(2)(m+n)) flops required by the state-of-the-art algorithms. Meanwhile, RSM has the advantage of a small memory requirement as only max(n(2),mr+nr) real values need to be saved. With the assumption that known entries are uniformly distributed in Y, submatrices formed by known entries are randomly selected from Y with statistical size k×nρ(k) or mρ(l)×l , where k or l takes r+1 usually. We propose and prove a theorem, under random noises the probability that the subspace associated with a smaller singular value will turn into the space associated to anyone of the r largest singular values is smaller. Based on the theorem, the nρ(k)-k null vectors or the l-r right singular vectors associated with the minor singular values are calculated for each submatrix. The vectors ought to be the null vectors of the submatrix formed by the chosen nρ(k) or l columns of the ground truth of V(T). If enough submatrices are randomly chosen, V and U can be estimated accordingly. The experimental results on random synthetic matrices with sizes such as 13 1072 ×10(24) and on real data sets such as dinosaur indicate that RSM is 4.30 ∼ 197.95 times faster than the state-of-the-art algorithms. It, meanwhile, has considerable high precision achieving or approximating to the best.

A class of recovering algorithms for 1-bit compressive sensing (CS) named Soft Consistency Reconstructions (SCRs) are proposed. Recognizing that CS recovery is essentially an optimization problem, we endeavor to improve the characteristics of the objective function under noisy environments. With a family of re-designed consistency criteria, SCRs achieve remarkable counter-noise performance gain over the existing counterparts, thus acquiring the desired robustness in many real-world applications. The benefits of soft decisions are exemplified through structural analysis of the objective function, with intuition described for better understanding. As expected, through comparisons with existing methods in simulations, SCRs demonstrate preferable robustness against noise in low signal-to-noise ratio (SNR) regime, while maintaining comparable performance in high SNR regime.

In this paper, we consider the training of complex-valued filter based on the information theoretic method. We first generalize the error entropy criterion to complex domain to present the complex error entropy criterion (CEEC). Due to the difficulty in estimating the entropy of complex-valued error directly, the entropy bound minimization (EBM) method is used to compute the upper bounds of the entropy of the complex-valued error, and the tightest bound selected by the EBM algorithm is used as the estimator of the complex-error entropy. Then, based on the minimization of complex-error entropy (MCEE) and the complex gradient descent approach, complex-valued learning algorithms for both the (linear) transverse filter and the (nonlinear) neural network are derived. The algorithms are applied to complex-valued linear filtering and complex-valued nonlinear channel equalization to demonstrate their effectiveness and advantages.

Understanding the underlying mechanism of the propagation of neuronal activities within the brain is a fundamental issue in neuroscience. Traditionally, communication and information processing have been exclusively considered as the province of synaptic coupling between neurons. Astrocytes, however, have recently been acknowledged as active partners in neuronal information processing. So, it is more reasonable and accurate to study the nature of neuronal signal propagation with the participation of astrocytes. In this paper, we first propose a feedforward neuronal-astrocytic network (FNAsN), which includes the mutual neuron-astrocyte interaction. Besides, we also consider the unreliability of both the synaptic transmission between neurons and the coupling between neurons and astrocytes. Then, the performance of firing rate propagation through the proposed FNAsN is studied through a series of simulations. Results show that the astrocytes can mediate neuronal activities, and consequently improve the performance of firing rate propagation, especially in a weak and noisy environment. From this point of view, astrocytes can be regarded as a realistic internal source of noise, which collaborates with an externally applied weak noise to prevent synchronous neuron firing within the same layer and thus to ensure reliable transmission.

In this letter, we propose a Student's t-hidden Markov model with truncated stick-breaking priors (TSB-SHMM). In the TSB-SHMM, the priors for elements in the initial state vector and the state transition matrix are constructed by stick-breaking procedure with a truncation level, and the observation emission distributions are the Student's t-mixtures. Then we derive an inference algorithm for estimating the parameters of the proposed TSB-SHMM. Experimental results on the synthetic data and text-dependent speaker identification illustrate that the TSB-SHMM can automatically determine the number of states and are robust to untypical observed data.

To improve the classification performance of k-NN, this paper presents a classifier, called k -NS, based on the Euclidian distances from a query sample to the nearest subspaces. Each nearest subspace is spanned by k nearest samples of a same class. A simple discriminant is derived to calculate the distances due to the geometric meaning of the Grammian, and the calculation stability of the discriminant is guaranteed by embedding Tikhonov regularization. The proposed classifier, k-NS, categorizes a query sample into the class whose corresponding subspace is proximal. Because the Grammian only involves inner products, the classifier is naturally extended into the high-dimensional feature space induced by kernel functions. The experimental results on 13 publicly available benchmark datasets show that k-NS is quite promising compared to several other classifiers founded on nearest neighbors in terms of training and test accuracy and efficiency.