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Due to the rapid development of the Intelligent Traffic System (for short, ITS), the shared information among successive vehicles can be acquired accurately and reliably. In this paper, a control scheme utilizing the successive flux difference under honk environment (SFDHE) is investigated in the lattice hydrodynamic model. Based on the Hurwitz criteria and the $H_{\infty }$ -norm, the sufficient condition for the transfer function is derived with the control theory analysis. The Bode-plot of transfer function indicates that the stability of the traffic flow is increased significantly with the novel controller. Moreover, the numerical simulation results of the new model are compared with that of Peng’s model, which demonstrates that traffic jams can be suppressed efficiently when the SFDHE control signal is taken into account.

It is greatly significant to achieve radar forward-looking region imaging. Due to the limitation of phase ambiguity and small Doppler gradient in forward-looking region, synthetic aperture radar and Doppler beam sharpening cannot work for forward-looking imaging, while real aperture radar (RAR) has arbitrary imaging geometry. Nevertheless, restricted by the antenna aperture, azimuth resolution of RAR is coarse, super-resolution technology is required to improve its azimuth resolution. Exploiting the sparse prior information of the target, the super-resolution problem can be transformed into an $L_1$ norm minimization problem mathematically. Iterative reweighted algorithm can effectively solve the $L_1$ norm minimization problem by replacing $L_1$ norm with reweighted $L_2$ norm and computing the weight in each iteration. However, it suffers from a large computational load due to the repeated multiplications and inversions of large matrices. In this article, a fast azimuth super-resolution imaging method of RAR based on iterative reweighted least squares (IRLS) with linear sketching (LS) was proposed to achieve fast super-resolution imaging of RAR. The LS theory is employed to compress echo matrix and antenna measurement matrix into much smaller matrices via multiplying them by an embedded matrix. Then, the IRLS solver was utilized to address the reconstructed objective function. Much of the expensive computation can then be performed on the smaller matrices, thereby accelerating the algorithm. Simulations and experimental data prove that the proposed algorithm can offer a time complexity reduction without loss of imaging performance.

This paper addresses the $\mathcal {H}_{2}$ , $\mathcal {H}_\infty $ and mixed $\mathcal {H}_{2}/\mathcal {H}_\infty $ formation static output control of continuous-time linear multi-agent systems with Markovian switching network topologies. It is assumed that the operation mode of the network topology cannot be directly measured but, instead, can be estimated by an imperfect detector. To model this problem, we consider a continuous-time hidden Markov model, in which the hidden component represents the real operation mode of the network topology while the observed component represents the information emitted from the detector and available for the controller. It is also assumed that only a partial information from the state variables of the multi-agent systems is available. By using an LMI (linear matrix inequality) formulation, a distributed static output controller which switches according to the detector information is designed to guarantee the stability in the mean square sense of the closed loop system, as well as an upper-bound for an index performance. Three situations are considered for the performance criteria: the $\mathcal {H}_{2}$ norm, the $\mathcal {H}_\infty $ norm, and the mixed $\mathcal {H}_{2}/\mathcal {H}_\infty $ norms. The paper is concluded with a numerical example to illustrate the effectiveness of the theoretical results.

With the rapid development of compressed sensing theories and applications, sparse signal processing has been widely used in synthetic aperture radar (SAR) imaging during the recent years. As an efficient tool for sparse reconstruction, ℓ1 optimization induces sparsity the most effectively, and the ℓ1-norm penalty is usually combined with the total variation norm (TV-norm) penalty to construct a compound regularizer in order to enhance the point-based features as well as the region-based features. However, as a convex optimizer, the analytic solution of ℓ1 regularization-based sparse signal reconstruction is usually a biased estimation. Aiming at this issue, in this article, we quantitatively analyzed the variation of reconstruction bias with respect to the complex reflectivity of targets, the undersampling ratio and the noise power. In order to reduce the bias effect and improve the reconstruction accuracy, we adopted the nonconvex regularization-based sparse SAR imaging method with a nonconvex penalty family. Furthermore, we linearly combined the nonconvex penalty and the TV-norm penalty to form a compound regularizer in the imaging model, which can improve the reconstruction accuracy of distributed targets and maintain the continuity of the backscattering coefficient. Simulation results showed that compared with ℓ1 regularization, nonconvex regularization can reduce the average relative bias from 10.88% to 0.25%; compared with the matched filtering method and ℓ1 and TV regularization, nonconvex & TV regularization can reduce the variance of the uniformly distributed targets by 80% without losing of reconstruction accuracy. Experiments on Gaofen-3 SAR data are also exploited to verify the effectiveness of the proposed method.

This paper presents a quantitative analysis of the differences between the various definitions of spatially averaged power densities ( $sIPD_{s}$ ) for localized exposure to electromagnetic near-fields at frequencies from 6 to 100 GHz. The spatially averaged modulus of the complex Poynting vector ( $sIPD_{mod}$ ) and spatially averaged norm of the real part of the complex Poynting vector ( $sIPD_{norm}$ ) were compared using numerical approaches, where their relationships with the spatially averaged absorbed power density (sAPD) and the local peak temperature elevation on skin tissue were analyzed. Our results demonstrated that outside the typical boundary of the reactive near-field, i.e., $> \lambda $ /( $2\pi$ ), which is used as a rough guide of the applicable condition for reference levels in the RF safety guidelines, but at most 10 mm from the radiation source, the maximum difference between $sIPD_{norm}$ and $sIPD_{mod}$ is smaller than 0.7 dB from 6 to 100 GHz. For the appropriate conditions recommended in the RF safety guidelines, the differences between the ratios of sAPD to $sIPD_{s}$ and those for the plane-wave normal incidence, are at most 1.4 dB and 0.9 dB for $sIPD_{norm}$ and $sIPD_{mod}$ , respectively. Under the same condition, the ratios of the temperature rise to $sIPD_{s}$ for the relatively small antennas (total dimension less than $2\lambda$ ) do not significantly exceed that for the plane-wave normal incidence, which means that the expected maximum temperature rise is lower than the temperature rise that is derived from the operational health effect threshold in terms of the temperature rise divided with the reduction factors employed in the RF safety guidelines. The above results provide suggestive evidence that the effect of the definition of $sIPD_{s}$ on the human exposure characteristics is not significant compared with those of the other factors, i.e., the antenna type (size), frequency, distance from the source, and averaging area.

Infrared dim small target detection is one of the important contents in the research of military applications such as remote sensing intelligence reconnaissance, long-range precision strike, aerospace offense–defense confrontation, etc. In this article, we focus on the detection of low-flying fixed-wing unmanned aerial vehicle target based on infrared imaging. To this end, we propose a simple and effective detection model, which can be viewed as a combination of low-rank approximation and multiple sparse constraints. We first model the infrared image that to be detected as a sum of three patch matrices called background, target, and noise. Then, we put a nonconvex low-rank approximation on the background patch matrix to suppress the background edges and put a reweighted $l_{1,1}$-norm constraint on the target matrix to better preserve the dim small target. Moreover, in order to eliminate the strong residual edges left in the target image under complex background, both the $l_{1,1}$ matrix norm and the $l_{2,1}$ matrix norm are used to constrain the noise patch. Finally, we develop an alternating optimization algorithm to solve the associated minimization problem. Extensive experiments carried out on a recently released real low-flying UAV database show that the proposed approach works well in detecting infrared dim small target measured by qualitative analysis and quantitative analysis.

Hyperspectral spectral mixture analysis (SMA), which intends to decompose mixed pixels into a collection of endmembers weighted by their corresponding fraction abundances, has been successfully used to tackle mixed-pixel problem in hyperspectral remote sensing applications. As an approach of decomposing a high-dimensional data matrix into the multiplication of two nonnegative matrices, nonnegative matrix factorization (NMF) has shown its advantages and been widely applied to SMA. Unfortunately, most of the NMF-based unmixing methods can easily lead to an unsuitable solution, due to inadequate mining of spatial and spectral information and the influence of outliers and noise. To overcome such limitations, a spatial constraint over abundance and a spectral constraint over endmembers are imposed over NMF-based unmixing model for spectral-spatial constrained unmixing. Specifically, a spatial neighborhood preserving constraint is proposed to preserve the local geometric structure of the hyperspectral data by assuming that pixels in a spatial neighborhood generally fall into a low-dimensional manifold, while a minimum spectral distance constraint is formulated to optimize endmember spectra as compact as possible. Furthermore, to handle non-Gaussian noises or outliers, an $ {L}_{2,1}$-norm based loss function is ultimately adopted for the proposed spectral-spatial constrained nonnegative matrix factorization model and a projected gradient based optimization algorithm is designed for optimization. Experimental results over both synthetic and real-world datasets demonstrate that the proposed spatial and spectral constraints can certainly improve the performance of NMF-based unmixing and outperform state-of-the-art NMF-based unmixing algorithms.

To effectively solve the multi-objective motion planning problem for redundant robot manipulators, a penalty neural multi-criteria optimization (PNMCO) scheme is proposed and investigated. The scheme includes two parts: a constrained multi-criteria optimization (CMCO) subsystem, and a varying-parameter recurrent neural network combined with penalty function (VP-RNN-PF) subsystem. Specifically, the CMCO subsystem is made up of velocity two norm, repetitive motion, and infinity norm. With these criteria, it can achieve energy minimization, repetitive motion, and avoidance of speed peaks. In addition, the CMCO subsystem is then transformed into a standard quadratic programming (QP) problem, and the VP-RNN-PF subsystem is applied to solve the QP problem. Results of computer simulations based on the JACO2 robot manipulator demonstrate that the proposed PNMCO scheme is effective and feasible to plan the multi-objective motion tasks. Comparison experiments of two complex paths tracking between VP-RNN-PF and the traditional neural networks (e.g., simplified linear-variational-inequality-based primal-dual neural network, S-LVI-PDNN) shows that the proposed scheme as well as the neural network is more accurate and more efficient for solving multi-objective motion planning problem.

In this work, we propose an unsupervised multiple parametric-margin support vector clustering (MPMSVC) for noisy clustering tasks. The main idea of MPMSVC is to find a parametric-margin center hyperplane for each cluster in a manner that gathers the within-cluster instances around the corresponding center hyperplane, and keeps the between-cluster instances far away. Specifically, our MPMSVC owns the following attractive merits: i) The primal of MPMSVC is enhanced in the least squares sense, which enjoys an effective learning procedure. ii) The utilization of the linear $L_{1}$ -norm loss makes MPMSVC be more robust to noisy clustering tasks. iii) An efficient iterative algorithm is presented to optimize the non-smooth problem in MPMSVC, which only involves a set of linear equations. Also, the convergence of the proposed algorithm is guaranteed theoretically. iv) The nonlinear extension is further derived via kernel technique to deal with more complex clustering tasks. Finally, the feasibility and effectiveness of MPMSVC is validated by extensive experiments on both synthetic and real-world datasets.

Non-negative least square regression (NLS) is a constrained least squares problem where the coefficients are restricted to be non-negative. It is useful for modeling non-negative responses such as time measurements, count data, histograms and so on. Existing NLS solvers are designed for cases where the predictor variables and response variables have linear relationships, and do not consider interactions among predictor variables. In this paper, we solve NLS in the complete space of power sets of variables. Such an extension is particularly useful in biology, for modeling genetic associations. Our new algorithms solve NLS problems exactly while decreasing computational burden by using an active set method. The algorithm proceeds in an iterative fashion, such that an optimal interaction term is searched by a branch-and-bound subroutine, and added to the solution set one another. The resulting large search space is efficiently restricted by novel pruning conditions and two kinds of sparsity promoting regularization; $l_{1}$ norm and non-negativity constraints. In computational experiments using HIV-1 datasets, 99% of the search space was safely pruned without losing the optimal variables. In mutagenicity datasets, the proposed method could identify long and accurate patterns compared to the original NLS. Codes are available from https://github.com/afiveithree/inlars.

The omnichannel business has becomes a hot topic due to the fast development on e-commerce and the customers’ acquaintance with multichannel shopping mode. Various business organizations have started to work on omnichannel business issue in order to satisfy the new trend of customer demand and tend to devote their efforts to both online and offline business. Thus, there is no doubt that understanding the shopping behavior for online customers is vital for the omnichannel business. The RFM (recency, frequency, monetary) model and the k-means clustering method are commonly used to extract customers’ information and segment customers, respectively. To extend the RFM model, we divide the total frequency and monetary information into weekly level data, and as a consequence, the number of variables corresponding to one customer increases significantly, leading to the problem of high-dimensional analysis. To address this issue, in this paper we extend the regularized k-means clustering method with $L_{1}$ -norm for independent case to the clustering method with elastic net penalty with a focus on correlated variables. Our simulation results show that the proposed method performs better than the standard k-means method by providing lower error rates and can select variables simultaneously under 4 different scenarios. A real example of an online retailer is presented to illustrate the use of the proposed method and highlight its high potential in clustering high-dimensional applications. In particular, the number of variables is reduced from 108 to 98 without any loss on clustering accuracy.

We a framework for the design of low-complexity and high-performance receivers for multidimensional overloaded non-orthogonal multiple access (NOMA) systems. The framework is built upon a novel compressed sensing (CS) regularized maximum likelihood (ML) formulation of the discrete-input detection problem, in which the $\ell _{0}$ -norm is introduced to enforce adherence of the solution to the prescribed discrete symbol constellation. Unlike much of preceding literature,.g., (Assaf et al., 2020, Yeom et al., 2019, Nagahara, 2015, Naderpour and Bizaki, 2020, Hayakawa and Hayashi, 2017, Hayakawa and Hayashi, 2018, and Zeng et al., 2020), the method is not relaxed into the $\ell _{1}$ -norm, but rather approximated with a continuous and asymptotically exact expression without resorting to parallel interference cancellation (PIC). The objective function of the resulting formulation is thus a sum of concave-over-convex ratios, which is then tightly convexified via the quadratic transform (QT), such that its solution can be obtained via the iteration of a simple closed-form expression that closely resembles that of the classic zero-forcing (ZF) receiver, making the method particularly suitable to large-scale set-ups. By further transforming the aforementioned problem into a quadratically constrained quadratic program with one convex constraint (QCQP-1), the optimal regularization parameter to be used at each step of the iterative algorithm is then shown to be the largest generalized eigenvalue of a pair of matrices which are given in closed-form. The method so obtained, referred to as the Iterative Discrete Least Square (IDLS), is then extended to address several factors of practical relevance, such as noisy conditions, imperfect channel state information (CSI), and hardware impairments, thus yielding the Robust IDLS algorithm. Simulation results show that the proposed art significantly outperforms both classic receivers, such as the linear minimum mean square error (LMMSE), and recent CS-based state-of-the-art (SotA) alternatives, such as the sum-of-absolute-values (SOAV) and the sum of complex sparse regularizers (SCSR) detectors. It is also shown via simulations that the technique can be integrated with existing iterative detection-and-decoding (IDD) methods, resulting in accelerated convergence.

Discriminative subspace clustering (DSC) combines Linear Discriminant Analysis (LDA) with clustering algorithm, such as K-means (KM), to form a single framework to perform dimension reduction and clustering simultaneously. It has been verified to be effective for high-dimensional data. However, most existing DSC algorithms rigidly use the Frobenius norm (F-norm) to define model that may not always suitable for the given data. In this paper, DSC is extended in the sense of $l_{2, p}$ -norm, which is a general form of the F-norm, to obtain a family of DSC algorithms which provide more alternative models for practical applications. In order to achieve this goal. Firstly, an efficient algorithm for the $l_{p}$ -norm based KM (KM $_{\mathrm {p}}$ ) clustering is proposed. Then, based on the equivalence of LDA and linear regression, a $l_{\mathrm {2,}p}$ -norm based LDA ( $l_{\mathrm {2,}p}$ -LDA) is proposed, and an efficient Iteratively Reweighted Least Squares algorithm for $l_{\mathrm {2,}p}$ -LDA is presented. Finally, KMp and $l_{2, p}$ -LDA are combined into a single framework to form an efficient generalized DSC algorithm: $l_{2,{p}}$ -norm based DSC clustering ( $l_{2,{p}}$ -DSC). In addition, the effects of the parameters on the proposed algorithm are analyzed, and based on the theory of robust statistics, a special case of $l_{2,{p}}$ -DSC, which can show better robustness on the data sets with noise and outlier, is studied. Extensive experiments are performed to verify the effectiveness of our proposed algorithm.

Sparsity-driven synthetic aperture radar (SAR) imaging technique for frequency modulation continuous wave (FMCW) has already shown the superiority in terms of performance improvement in imaging and recovery from down-sampled data. However, restricted by the computational cost, conventional FMCW SAR sparse imaging method based on observation matrix is not able to achieve the large-scale scene reconstruction, not to mention real-time processing. To solve this problem, the FMCW SAR sparse imaging theory based on approximated observation is proposed by using an echo simulation operator to replace typical observation matrix, and recovering the scene via 2-D regularization operation. This new technology can achieve high-resolution sparse imaging of the scene with a computational cost close to that of traditional matched filtering algorithms, which makes several applications, such as early-warning and battlefield monitoring, possible by using FMCW SAR sparse imaging system. In this article, we present the recent research progress on approximated observationbased FMCW SAR sparse imaging to deal with a few key issues for practical radar systems. In particular, we describe: first, Lq-norm (0 2,q-norm regularization-based imaging technique that minimizes the azimuth ambiguities in high-resolution sparse imaging; and third, a sparse imaging technique that supports real-time applications of FMCW SAR imaging.

The maximum capacity path problem is to find a path connecting two given nodes in a network such that the minimum arc capacity on this path is maximized. The inverse maximum capacity path problem (IMCP) is to modify the capacities of the arcs as little as possible so that a given path becomes maximum capacity path in the modified network. Two cases of IMCP are considered: the capacity of the given path is preserved or not. IMCP is studied and solved both, under any sum-type (e.g., weighted $l_{k}$ norms and sum-type Hamming distance) and max-type distance (e.g., weighted $l_{\infty }$ norm or bottleneck Hamming distance). The obtained algorithms for IMCP are applied to solve a real road transportation network optimization problem.

The dictionary learning algorithm is an effective image classification algorithm. To tackle with the problems including noise, occlusion, small sample problem, and so on, many discriminative dictionary learning models have been proposed. However, the performance of these algorithms might not be satisfactory, the main reason is that some useful features are not effectively disclosed. For example, the coding coefficients of the samples have row sparsity consistency and the block structure property. Maintaining the inherent features of the samples (e.g. the block structure, local characteristics of atoms) is beneficial to enhance the discriminative ability of the model. In addition, a powerful discriminative constraint is also essential to improve the performance of image classification. In the paper, we propose a new structural constraint and discriminative constraint based dictionary pair learning for image classification. In the model, the L21 norm constraint is applied on the analysis sub-dictionary to ensure the row sparsity consistency of the coding coefficients as much as possible. A new discriminative constraint is designed to enforce the representation matrix to be more discriminative, which can be acquired by minimizing the intra-class scatter and maximizing the inter-class scatter of the samples. Besides, we define a new atomic locality constraint, which forces the atoms to preserve the structure information of the samples. Finally, seven benchmark data sets are selected to evaluate the performance of the proposed method in comparison with popular methods. The experimental results outperform the state-of-the-art methods, which demonstrates the efficacy of the proposed model.

The Received Signal Strength (RSS) fingerprint-based indoor localization method in Wireless Local Area Network (WLAN) environment has been widely used due to its low hardware requirements and high positioning accuracy. However, the positioning system requires enormous effort to collect fingerprint at each reference point in positioning area, which is time-consuming and laborious. For the practicability of the method, it is essential to reduce the workload of fingerprint collection in the offline phase and construct a fingerprint database efficiently and accurately. Utilizing the high spatial correlation of RSS, in this paper, an efficient fingerprint database construction method is proposed based on low-rank matrix completion. In the meanwhile, different from the traditional matrix completion model, we propose an improved optimization model by converting to the weighted nuclear norm and introducing l1-norm and Frobenius norm to recover unknown data accurately and reduce the influence of outliers and Gaussian noise simultaneously. Furthermore, we combine the K-Nearest Neighbor (KNN) method to solve the problem that matrix completion cannot deal with all unknown rows or columns in the matrix. The experiment results indicate that the proposed algorithm can recover the fingerprint database completely through a few RSS information and has higher accuracy than other algorithms in various scenarios.

Feature selection and feature transformation are the two main approaches to reduce dimensionality, and they are often presented separately. In this study, a novel robust and efficient feature selection method, called FS-VLDA-L2,1 (feature selection based on variant of linear discriminant analysis and L2,1-norm), is proposed by combining a new variant of linear discriminant analysis and L2,1 sparsity regularization. Here, feature transformation and feature selection are integrated into a unified optimization objective. To obtain significant discriminative power between classes, all the data in the same class are expected to be regressed to a single vector, and the important task is to explore a transformation matrix such that the squared regression error is minimized. Therefore, we derive a new discriminant analysis from a novel view of least squares regression. In addition, we impose row sparsity on the transformation matrix through L2,1-norm regularized term to achieve feature selection. Consequently, the most discriminative features are selected, simultaneously eliminating the redundant ones. To address the L2,1-norm based optimization problem, we design a new efficient iterative re-weighted algorithm and prove its convergence. Extensive experimental results on four well-known datasets demonstrate the performance of our feature selection method.

The iterative algorithms of computed tomography (CT) reconstruction derived from the dictionary learning (DL) regularization have been developed to make high quality recovery from the under-sampled data acquired by a low dose protocol. However, when they are applied to noisy data with low sampling rate, streaking artifacts and bias tends to appear in early iteration results. Since the dictionary is over-complete, the artifacts and bias can also be represented well by the dictionary, resulting in the reservation of these unexpected structures in the final image. We proposed a smoothed L0 norm-constraint dictionary learning (SL0-DL) algorithm to deal with these unexpected structures. For the proposed algorithm, we introduce smoothed-L0 norm regularization to the objective function. In each iteration process, the intermediate image generated by the DL representation will be smoothed using SL0 norm, and then the smoothed image is used to update the output of this iteration. The raw data from both the numerical simulation and actual CT acquisition are used to test the performances of the proposed SL0-DL method. Experimental results demonstrate that the proposed method performs better than other competing algorithms with better noise and artifacts suppression performance while preserving image texture details. And the results show a significant improvement in the quality of the reconstructed image, which demonstrates that the proposed algorithm is really effective.

Most of the existing cross-modal retrieval methods make use of labeled data to learn projection matrices for different modal data. These methods usually learn the original semantic space to bridge the heterogeneous gap, ignoring the rich semantic information contained in unlabeled data. Accordingly, a semantic consistency cross-modal retrieval with semi-supervised graph regularization (SCCMR) algorithm is proposed, which integrates the prediction of labels and the optimization of projection matrices into a unified framework to ensure that the solution obtained is globally optimal. At the same time, the method uses graph embedding to consider the nearest neighbors in the potential subspace of paired images and texts as well as images and texts with the same semantics. ${l_{21}}$ -norm constraint is applied to the projection matrices to select the discriminative features for different modal data. The results show that our method outperforms several advanced methods on four commonly used cross-modal retrieval datasets.

Deep learning has demonstrated state-of-the-art performance for a variety of challenging computer vision tasks. On one hand, this has enabled deep visual models to pave the way for a plethora of critical applications like disease prognostics and smart surveillance. On the other, deep learning has also been found vulnerable to adversarial attacks, which calls for new techniques to defend deep models against these attacks. Among the attack algorithms, the black-box schemes are of serious practical concern since they only need publicly available knowledge of the targeted model. We carefully analyze the inherent weakness of deep models in black-box settings where the attacker may develop the attack using a model similar to the targeted model. Based on our analysis, we introduce a novel gradient regularization scheme that encourages the internal representation of a deep model to be orthogonal to another, even if the architectures of the two models are similar. Our unique constraint allows a model to concomitantly endeavour for higher accuracy while maintaining near orthogonal alignment of gradients with respect to a reference model. Detailed empirical study verifies that controlled misalignment of gradients under our orthogonality objective significantly boosts a model's robustness against transferable black-box adversarial attacks. In comparison to regular models, the orthogonal models are significantly more robust to a range of $l_p$ norm bounded perturbations. We verify the effectiveness of our technique on a variety of large-scale models., Comment: Accepted in IEEE Access

We propose an Lp -norm-based sparse regularization model for license plate deblurring, which is motivated by distinctive properties of license plate images. For the blurred images, general deblurring methods may restore a good overall visual effect. However, in real-life traffic surveillance system, the deblurring results may be not good for license plates. The main reason lies in that general deblurring methods do not give sufficient thought to the features of license plate, which could be important priors for deblurring. Focusing on this issue, analysis on the statistical distribution characteristics of the license plates are launched, based on which an Lp-norm-based regularization model is proposed. Furthermore, alternating direction method of multipliers are introduced to solve the model. Experimental results demonstrate that the proposed model performs favorably against the state-of-the-art license plate image deblurring methods.

This article presents an image deblurring method using ℓ0-norm-based deblurring and ℓ2-norm-based texture-aware image fusion for remote sensing images. To restore the details of blurred texture, the proposed method first performs texture restoration by fusing the restored results using Richardson-Lucy deconvolution and unsharp masking. Next, we analyzed the intensity and dark channel properties of remote sensing images and perform the ℓ0-norm-based deblurring using the intensity and dark channel priors. Although the ℓ0-norm-based deblurring can provide a significantly restored result, it cannot overcome the loss of the texture region. On the other hand, the proposed ℓ2-norm-based image fusion method can preserve both sharp edges and texture details. In the experiments, we demonstrate that the proposed method can provide better restored results than existing state-of-the-art deblurring methods without oversmoothing and undesired artifact.

This paper presents a few innovations towards learning a discriminative block-structured dictionary. The learning process of such a dictionary is broadly divided into two steps: block formation and dictionary update. In the existing works on block structure estimation, it is assumed that the maximum block size is known a priori. In real-world problems, such an assumption may be sub-optimal. For addressing that, a genetic algorithm optimized K-means clustering based block formation approach is proposed in this work. We also propose a novel dictionary learning approach that incorporates three attributes, namely, reconstruction and discriminative fidelities, block-wise incoherence, and ℓ2,1-norm regularization. To further enhance the discriminative ability of the sparse codes, the class-specific and class-common information are modeled separately in the dictionary. The ℓ2,1-norm regularization enhances the consistency among sparse codes belonging to the same-class data. In the proposed approach, the dictionary is updated block-wise by employing the singular value decomposition of the composite error matrix obtained through the weighted combination of the component errors. The proposed innovations are evaluated on several public image databases for super-resolution and classification tasks. Along with those image databases, speech based speaker verification task is also evaluated the proposed approach in a few different domains to validate the generalizability. The experimental results obtained on these different databases demonstrate the effectiveness of the proposed approaches when compared with the respective state-of-the-art.

This paper is concerned with a comparative study of biped walking on rough terrains. Given a bipedal robot capable of walking on a flat ground with periodic behavior, whose motion can be described by a limit cycle with the Poincare map, we consider whether the robot remains stable on rough terrain, in which geometrical uncertainties of the terrain are assumed to be persistent and bounded. More precisely, the $l_\infty $ -induced norm is defined on the Poincare map and taken as a performance measure evaluating a robot walking with the bounded persistent uncertainties. To minimize the performance measure and achieve an optimal walking performance, we further provide a systematic controller design scheme consisting of a inner-loop continuous-time controller and a outer-loop event-based controller, in which the latter is described as a sort of the $l_{1}$ optimal controller. Finally, the validity as well as the effectiveness of our proposed methods in biped walking on a rough terrain are demonstrated through simulation studies.

In this paper, a class of diffusion zero-attracting stochastic gradient algorithms with exponentiated error cost functions is put forward due to its good performance for sparse system identification. Distributed estimation algorithms based on the popular mean-square error criterion have poor behavior for sparse system identification with color noise. To overcome this drawback, a class of stochastic gradient least exponentiated (LE) algorithms with exponentiated error cost functions were proposed, which achieved a low steady-state compared with the least mean square (LMS) algorithm. However, those LE algorithms may suffer from performance deterioration in the spare system. For sparse system identification in the adaptive network, a polynomial variable scaling factor improved diffusion least sum of exponentials (PZA-VSIDLSE) algorithm and an lp-norm constraint diffusion least exponentiated square (LP-DLE2) algorithm are proposed in this work. Instead of using the l1-norm penalty, an lp-norm penalty and a polynomial zero-attractor are employed as a substitution in the cost functions of the LE algorithms. Then, we perform mean behavior model and mean square behavior modal of the LP-DLE2 algorithm with several common assumptions. Moreover, simulations in the context of distributed network sparse system identification show that the proposed algorithms have a low steady-state compared with the existing algorithms.

Global quadratic stabilization in probability is considered for both switched linear certain stochastic systems and switched linear uncertain stochastic systems where there are norm bounded uncertainties. Under the assumption that every single subsystem is NOT globally quadratically stable in probability (GQS-P), we propose both static and dynamic output based switching laws such that the switched system on hand is GQS-P. In the case of static output based switching, the condition is expressed by a set of matrix inequalities, while the design of dynamic output based switching is proposed with a convex combination of subsystems and a robust Luenberger observer for each subsystem. Numerical examples are presented to show validity of the design conditions and switching algorithms.

In this paper, we propose a derivative free algorithm for solving non-linear monotone equations with convex constraints. The proposed algorithm combines the method of spectral gradient and the projection method. We also modify the backtracking line search technique. The global convergence of the proposed method is guaranteed, under the mild conditions. Further, the numerical experiments show that the large-scale non-linear equations with convex constraints can be effectively solved with our method. The $L_{1}$ -norm regularized problems in signal reconstruction are studied by using our method.

In multi-label learning, instances can be associated with a set of class labels. The existing multi-label feature selection (MLFS) methods generally adopt either of these two strategies, namely, selecting a subset of features that is shared by all labels (common features) or exploring the most discriminative features for each label (label-specific features). However, both of them can play a key role in the discrimination of different labels. For example, common features can distinguish all labels, and label-specific features contribute to discriminating label's differences. They are important for the discriminability of selected features. On the other hand, it is well-known that exploiting label correlations can advance the performance of MLFS, and label correlations are local and only shared by a data subset in most cases. How to effectively learn and exploit local label correlations in the selection process is significant. In this paper, to address these problems, we propose a novel MLFS framework. Specially, common and label-specific features are simultaneously considered by introducing both $l_{2,1}$ -norm and $l_{1}$ -norm regularizers, local label correlations are automatically learned with probability and learned correlation information is efficiently exploited to help feature selection by constraining label correlations on the output of labels. A comparative study with seven state-of-the-art methods manifests the efficacy of our framework.

Plane clustering methods, typically, $k$ plane clustering ( $k$ PC), play conclusive roles in the family of data clustering. Instead of point-prototype, they aim to seek multiple plane-prototype fitting planes as centers to group the given data into their corresponding clusters based on L2 norm metric. However, they are usually sensitive to outliers because of square operation on the L2 norm. In this paper, we focus on robust plane clustering and propose a L1 norm plane clustering method, termed as $\text{L}1k$ PC. The leading problem is optimized on the L1 ball hull, a non-convex feasible domain. To handle the problem, we provide a new strategy and its related mathematical proofs for L1 norm optimization. Compared to state-of-the-art methods, the advantages of our proposed lie in 4 folds: 1) similar to $k$ PC, it has clear geometrical interpretation; 2) it is more capable of resisting to outlier; 3) theoretically, it is proved that the leading non-convex problem is equivalent to several convex sub-problems. To our best knowledge, this opens up a new way for L1 norm optimization; 4) the $k$ fitting planes are solved by $k$ individual linear programming problems, rather than higher time-consuming eigenvalue equations or quadratic programming problems used in the conventional plane clustering methods. Experiments on some artificial, benchmark UCI and human face datasets show its superiorities in robustness, training time, and clustering accuracy.

The estimation of sequence or symmetrical components and frequency in three-phase unbalanced power system is of great importance for protection and relay. This paper proposes a new H∞ filter based on sparse model to track the sequence components and the frequency of three-phase unbalanced power systems. The inclusion of sparsity improves the error convergence behavior of estimation model and hence short-duration non-stationary PQ events can easily be tracked in the time domain. The proposed model is developed using l1 norm penalty in the cost function of H∞ filter, which is quite suitable for estimation across all the three phases of an unbalanced system. This model uses real state space modeling across three phases to estimate amplitude and phase parameters of sequence components. However, frequency estimation uses complex state space modeling and Clarke transformation generates a complex measurement signal from the unbalanced three-phase voltages. The state vector used for frequency estimation consists of two state variables. The proposed sparse model is tested using distorted three-phase signals from IEEE-1159-PQE database and the data generated from experimental laboratory setup. The analysis of absolute and mean square error is presented to validate the performance of the proposed model.

Nuclear norm and $l_{1}$ norm are the common regularization in salient object detection. However, existing literatures show that these terms either 1) are very slow for large scale problems due to singular value decomposition (SVD) on full matrix in every iteration, or 2) over-penalize the large singular values. In this paper, we propose to use respectively the non-convex weighted Schatten- $p$ quasi-norm and ${l_{p}}$ -norm $(0 for characterizing background and salient object. By matrix factorization, the optimization process, associated with the alternating direction method of multiplier (ADMM), is based on a unified convex surrogate which is only required to handle some small size matrices. Simultaneously, the convergence of algorithm is analyzed and validated. Experimental results indicate the new method usually outperform the state-of-the-art methods.

Sparse representation has been widely used over the past decade in computer vision and signal processing to model a wide range of natural phenomena. For computational convenience and robustness against noises, the optimization problem for sparse representation is often relaxed using convex or nonconvex surrogates instead of using the l0-norm, the ideal sparsity penalty function. In this paper, we pose the following question for nonconvex sparsity-promoting surrogates: What is a good sparsity surrogate for general nonconvex systems? As an answer to this question, we suggest that the difficulty of handling the l0-norm does not only come from the nonconvexity but also from its gradient being zero or not well-defined. Accordingly, we propose desirable criteria to be a good nonconvex surrogate and suggest a corresponding family of surrogates. The proposed family of surrogates allows a simple regularizer, which enables efficient computation. The proposed surrogate embraces the benefits of both l0 and l1-norms, and most importantly, its gradient vanishes slowly, which allows stable optimization. We apply the proposed surrogate to wellknown sparse representation problems and benchmark datasets to demonstrate its robustness and efficiency.

This article introduces a new hyperspectral image (HSI) denoising method that is able to cope with additive mixed noise, i.e., mixture of Gaussian noise, impulse noise, and stripes, which usually corrupt hyperspectral images in the acquisition process. The proposed method fully exploits a compact and sparse HSI representation based on its low-rank and self-similarity characteristics. In order to deal with mixed noise having a complex statistical distribution, we propose to use the robust ℓ1 data fidelity instead of using the ℓ1 data fidelity, which is commonly employed for Gaussian noise removal. In a series of experiments with simulated and real datasets, the proposed method competes with state-of-the-art methods, yielding better results for mixed noise removal.

Subspace segmentation assumes that data comes from the union of different subspaces and the purpose of segmentation is to partition the data into the corresponding subspace. Low-rank representation (LRR) is a classic spectral-type method for solving subspace segmentation problems, that is, one first obtains an affinity matrix by solving a LRR model and then performs spectral clustering for segmentation. This paper proposes a group norm regularized factorization model (GNRFM) inspired by the LRR model for subspace segmentation and then designs an Accelerated Augmented Lagrangian Method (AALM) algorithm to solve this model. Specifically, we adopt group norm regularization to make the columns of the factor matrix sparse, thereby achieving a purpose of low rank, which means no Singular Value Decompositions (SVD) are required and the computational complexity of each step is greatly reduced. We obtain affinity matrices by using different LRR models and then performing cluster testing on different sets of synthetic noisy data and real data, respectively. Compared with traditional models and algorithms, the proposed method is faster and more robust to noise, so the final clustering results are better. Moreover, the numerical results show that our algorithm converges fast and only requires approximately ten iterations.

In recent years, the application of renewable energy resources (RES) with DC output has increased, and RES integration as DC islanded microgrids (DC ImGs) has attracted the attention of many researchers. However, DC ImGs face many challenges, and voltage stability is extremely critical for efficient power distribution. This challenge becomes more prominent when exogenous disturbances, as well as time-delay, exist in the system mainly because of the communication network. In this study, we develop a mathematical model of the time-delay DC ImG. To compensate for the effect of the time-delay, three control strategies are introduced—stabilizing, robust, and robust-predictor. The controller’s stability is guaranteed based on the Lyapunov-Krasovskii theorem, whereas for the exogenous disturbance rejection, the $\mathcal {L}_{2}$ -norm of the system is reduced. Furthermore, to obtain the proposed controllers’ gains, linear-matrix-inequality constraints are formulated. The performances of the controllers are investigated through numerous simulations, and a detailed analysis is presented.

Feature extraction (FE) plays an important role in machine learning. In order to handle the “dimensionality disaster”problem, the usual approach is to transform the original sample into a low-dimensional target space, in which the FE task is performed. However, the data in reality will always be corrupted by various noises or interfered by outliers, making the task of feature extraction extremely challenging. Thence, we propose a novel image FE method via approximate orthogonal low-rank embedding (AOLRE), which adopts an orthogonal matrix to reserve the major energy of the samples, and the introduction of the ℓ2,1-norm makes the features more compact, differentiated and interpretable. In addition, the weighted Schatten p-norm is adopted in this model for fully exploring the effects of different ranks while approaching the original hypothesis of low rank. Meanwhile, as a robust measure, the correntropy is applied in AOLRE. This can effectively suppress the adverse influences of contaminated data and enhance the robustness of the algorithm. Finally, the introduction of the classification loss item allows our model to effectively fit the supervised scene. Five common datasets are used to evaluate the performance of AOLRE. The results show that the recognition accuracy and robustness of AOLRE are significantly better than those of several advanced FE algorithms, and the improvement rate ranges from 2% to 15%.

The generalization performance of deep learning models for medical image analysis often decreases on images collected with different devices for data acquisition, device settings, or patient population. A better understanding of the generalization capacity on new images is crucial for clinicians' trustworthiness in deep learning. Although significant research efforts have been recently directed toward establishing generalization bounds and complexity measures, still, there is often a significant discrepancy between the predicted and actual generalization performance. As well, related large empirical studies have been primarily based on validation with general-purpose image datasets. This paper presents an empirical study that investigates the correlation between 25 complexity measures and the generalization abilities of supervised deep learning classifiers for breast ultrasound images. The results indicate that PAC-Bayes flatness-based and path norm-based measures produce the most consistent explanation for the combination of models and data. We also investigate the use of multi-task classification and segmentation approach for breast images, and report that such learning approach acts as an implicit regularizer and is conducive toward improved generalization., 15 pages, 4 figures

LP (Linear Prediction) analysis is the most commonly used and successful speech analysis implemented in smartphones. We have been proposing time-varying complex AR (TV-CAR) speech analysis for an analytic signal to solve the shortcomings of the LP. Recently, we proposed l 2 -norm regularization TV-CAR analysis that penalizes rapid spectral changes in time-domain and frequency-domain, called hybrid RLP (Regularized LP) and TRLP (Time-RLP) method, and we have already evaluated performance using F 0 estimation for noise corrupted speech. The IRAPT (Instantaneous RAPT) for the estimated complex residual realizes the F 0 estimation. This paper proposes an improved F 0 estimation introducing a pre-filter as pre-processing and evaluates the performance.

The acquisition of a discrete-time signal is an important part in compressive sensing problem. Instead of using $\ell_{0}$ -norm optimization, much attention is paid to $\ell_{p}$ -norm formulation for $p\in(0,1)$ due to its fast convergence and comparable accuracy. Iteratively reweighted least squares (IRLS) minimization is known as an improved algorithm of the typical basis pursuit with $\ell_{1}$ -norm criterion. In this work, an alternative enhancement of the IRLS criterion is presented. The proposed method invokes a descending sort of the absolute values of all elements in the solution and updates the nonzero indices in each iteration. Numerical examples illustrate that the proposed nonzero index update can help the IRLS minimization to recover the sparse signal with lower normalized root mean square error.

This paper addresses the globally non - overshooting/ undershooting (NOUS) tracking control problem of linear-time invariant (LTI) multi-input/output (MIMO) systems by utilizing state feedback control with a minimal Frobenius norm feedback gain matrix. An algorithm is proposed that synthesizes such a minimal-norm feedback controller, which ensures the desired convergence rate in all the outputs of the closed-loop system. The key idea is to utilize the additional freedom arising from eigenvalue placement in a disk region in the complex plane characterized by a linear matrix inequality (LMI). A numerical example is presented to compare the effectiveness of the proposed algorithm with the existing approach.

Battery prognostics is a promising area that aids in managing potential risks in times of failure of an event. One common way of estimating battery health is to monitor its capacity continuously. Traditionally, several methods like Kalman filter, Extended Kalman filter and data-driven models have been studied extensively. However, support vector machines offer a better generalization ability around every training sample and obtain a sparse solution, we leverage this to our capacity estimation problem. In this manuscript, the class of Support vector regressors (SVR) is utilized to predict battery capacity using multi-channel profiles of voltage, current and temperature. Publicly available battery dataset from NASA is utilized to model a capacity estimation problem and models like classical $\varepsilon$ -SVR, Least square support vector regression (LSSVR), Twin support vector regression (TSVR), Huber-SVR and $\mathcal{L}_{1}$ -norm support vector regression are tested on three different battery sets. Results indicate superior performance of TSVR in terms of root mean squared error (RMSE) which is found as low as 0.0235 when compared to existing studies. Further, to qualitatively analyze the regression methods, a residual analysis in the form of the Durbin-Watson test is carried out.

In this paper, different interaction analysis techniques are compared. Four different methods considered are: the conventional relative gain array (RGA) method, participation matrix (PM) method, hankel interaction index array (HIIA) method and H 2 -norm based interaction. A transformer-less dual-input dual-output DC/DC converter is utilized as an example to compare various interaction measures among the plant output and input for obtaining suitable combination of pairs for the input and output. MATLAB platform is used for validating the analytical findings.

The aim of this work is to create an application that uses the ISO 643:2012 norm for the physical characterization of materials. This application, with its well adapted graphical interface offers the user a better processing of micrographic images, which allows an easy use; it will lead directly to reliable and reproducible results. In this paper, we are interested in determining the mean grain size in material using LSM (the level set method) based on FCM (fuzzy c-means clustering) to get the mean grains size of interest (types of surfaces) and to improve the precision of segmentation with a specified micrographic method. There are two steps in the proposed method. The first step involves using the fuzzy c-means algorithm to generate a clustered image. The second step is based on extracting the grains boundaries by using the appropriate class of the clustered image as an initial condition of the level set method. To achieve this objective, an application has been developed in the OpenCV library to make it easier for the expert to calculate grain sizes.

The $\ell_{0}$ gradient regularization is an inverse problem which penalizes the $\ell_{0}$ norm of the reconstructed image's gradient; it has several applications in image processing, ranging from edge extraction, clip-art JPEG artifact removal to X-ray CT reconstruction. Current state-of-the art algorithms for solving these problems are ADMM based since the proximal operator resulting from a direct gradient-based approach is non-trivial. In this paper we propose to use a quadratic envelope relaxation to the $\ell_{0}$ gradient regularization problem, which results in a novel edge-preserving filtering model. To develop our new fast gradient-based algorithm we combine the use of convex envelopes for non-convex functionals along with the accelerated proximal gradient methodology. Our initial numerical results (Python based) show that our proposed algorithm, which currently targets the denoising problem, is competitive with the state-of-the-art.

Monitoring of wild animals has taken different approaches with an aim to provide vital information used in animal protection in their natural habitats. To recognize animal species without human trackers requires machine learning models that extract specie's features from an image. This project proposes a method of counting animals in an image and specifying the species of each animal using Unet and a variant of the SqueezeNet model. To train the Unet model, images and corresponding masks are used as the training data. Different optimizers are applied to each model. During inference, Unet outputs a binary mask with ones where an animal is detected and zeros elsewhere. SqueezeNet model is trained with images corresponding to six classes: bushbuck, impala, llama, warthog, waterbuck, and zebra. Three variants of the SqueezeNet model have been trained. The first contains the original backbone while the other two have the original backbone with an additional fire module. In one model the Fire module is similar to the Fire modules of the original backbone while in the other model, the extra fire module contains batch normalization layers. The trained models show that Unet trained with Nadam optimizer achieves the highest dice coefficient while the SqueezeNet with an extra Fire module containing batch norm layers and RMSprop optimizer achieves the highest training accuracy. The combined system containing the two models takes an image and outputs the image with bounding boxes around each animal and the corresponding animal species. The system achieves both counting and recognition of the species for each image placed at the input.

Synthetic transmit aperture (STA) can achieve very high spatial resolution thanks to its dynamic focusing in both transmit and receive. However, because each element is activated individually and sequentially to transmit a spherical wave, the imaging frame rate is low. In addition, the low transmitted energy leads to low signal-to-noise ratio (SNR) echoes. In our previous study, we proposed to use compressed sensing (CS) algorithm to recover full STA dataset from fewer apodized plane wave (PW) transmissions (CS-STA). In this way, the frame rate and SNR of STA imaging can be significantly improved. However, owing to the iterative nature of CS algorithms, the reconstruction of STA dataset is very time consuming, which hampers its real application. In this study, the minimal $l$ 2 -norm least square method is used to recover the STA dataset with significantly reduced computational time. Simulation shows that the proposed method can achieve ~5×103times acceleration for STA dataset reconstruction, compared with CS-STA. Simulated B-mode images show that the proposed method is capable of achieving higher generalized contrast-to-noise ratios (gCNRs) for anechoic inclusions than STA, with maintained spatial resolution. Simulated strain images show that the proposed method could preserve the phase information of radio-frequency data during the reconstruction, and achieve acceptable quality in strain estimation in noise-free condition.

Collecting salient and relevant information from many images and merging this to generate a quality image is the main goal of image fusion technique. Because of the camera's characteristics while photographing a scene, multi focus images will be produced. Each image of the scene has a different set of features and the merging leads to a good capture of the scene. Activity level measurement and fusion strategy are the critical areas of study in multi focus fusion. To find various focused information in transformed and spatial domains, there have been a lot of algorithms developed. Convolutional neural networks are excellent at representing deep features in an easier format and this property is used to represent multi focus images. Each pixel's activity map is used as a parameter in the fusion strategy. Euclidian norm are a good tool to find the similarities between a set of values. l2 Euclidian norm along with activity map performs the fusion of feature maps collected by residual network. When compared to other fusion algorithms, the presented technique is efficient and improves the image quality. The merged images correlate with human visual perception. The algorithm is suitable for applications like remote sensing, surveillance, and medical diagnosis, etc.

This paper investigates Vector Fitting (VF) algorithm variants for frequency-domain impedance modelling of converters in different control modes. The VF variants are obtained by varying the error norm used for minimizing the error between approximated fitting function and the measurement data. Consequently, in addition to the L2 norm minimized in the standard VF, L1 and H2 norms are minimized and their fitting accuracy is compared. Furthermore, a comparison of accuracy is also carried out by minimizing these three norms in the modified standard VF known as Relaxed Vector Fitting (RVF). The results show that an additional degree of freedom introduced in RVF leads to higher accuracy fitting compared to standard VF. The accuracies of VF between the three norms differ only marginally. Minimizing the H2 norm results in high accuracy, but it requires pre-defined measurement frequency points, which can lead to an impractical definition of input data. L1 norm minimization results in large deviations at a few measurement points due to an additional weighting factor introduced in the error minimization function. Moreover, RVF minimizing L2 norm shows the highest VF accuracy.

Compressed sensing (CS) allows accelerated magnetic resonance imaging (MRI) by highly undersampling k-space data. The key to high quality CS-MRI reconstruction is rational utilization of the sparsity of image in a certain transform domain. Existing CS-MRI methods commonly uses l 0 norm or l 1 norm to enforce the sparsity of image coefficients but lack parameter adaptation. In this work, a patch level sparse representation is derived from the joint maximum a posteriori (MAP) estimation under a probabilistic model, which adopts a hierarchical prior to characterize sparse image coefficients. The corresponding image reconstruction model is efficiently optimized by alternating direction method of multipliers (ADMM). Simulation results reveal that the proposed approach achieves higher reconstruction performance than competing CS-MRI methods, and is proven to be superior to general I p norm based methods.