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Sparse representation (SR) of a signal aims at finding the minimum number of atoms for its representation. In several practical scenarios, the signal is vulnerable to outliers and thus robustness is required for SR based algorithms. However, most existing robust schemes are designed on the assumption that the anomalies are independently distributed, which may not perform well encountering complex interferences, especially the correlated ones. To deal with this drawback, a robust SR model is proposed, where both independent and correlated outliers are considered. Specifically, the fitting error is decomposed as the combination of a low-rank component and a sparse part, corresponding to the correlated gross error and independent outlier, respectively. Then, the group sparsity of the representation coefficient is utilized. Moreover, ℓ 0 -norm and ℓ 2 , 0 -norm are adopted as the sparsity regularization for the sparse outlier and representation coefficients, respectively. The solutions to ℓ 0 / ℓ 2 , 0 -norm minimization are generated by the hard-thresholding strategy, where the decision threshold is adaptively determined using median absolute deviation operator. As for the low-rank regularization, due to the NP-hardness of rank minimization, we employ matrix logarithmic norm as the rank surrogate to lessen the approximation gap. Finally, we apply the proposed model to face recognition task, and the excellent performance demonstrates its effectiveness. [ABSTRACT FROM AUTHOR]

Tensor compressed sensing (TCS) from binary measurements aims to recover a tensor with low-rankness from the binary quantization of its degraded linear measurements, which inherits the advantages of low equipment cost and high sampling efficiency of coarse quantization. Recently, numerous studies have demonstrated that incorporating the properties of low-rankness and local smoothness, which are commonly observed in practical tensor data, can significantly enhance conventional tensor recovery tasks. This motivates us to utilize the low-rank and smooth properties in solving TCS problems from binary measurements. Equipped with the recently proposed tensor correlated total variation (TCTV) that simultaneously regularizes low-rankness and smoothness, we present a regularized model for this problem in this paper. We rigorously prove the recovery guarantee for the proposed model and provide an explicit selection rule for the regularization parameter. Moreover, the theoretical results demonstrate the robustness of the proposed method against both bit flips and pre-quantization noises. An algorithm based on alternating direction multiplier method (ADMM) is presented for solving the proposed model, with its global convergence been proven. Finally, a series of experiments demonstrate the superior performance of our method compared to many other competing approaches. • A method for tensor recovery from binary measurements which codes both low-rankness and smoothness was proposed. • We prove a recovery guarantee for the method and provide an explicit selection rule for the regularization parameter. • The method is robust to bit flips and pre-quantization noises, two common noises in one-bit quantization. • The proposed model can be solved using the alternating direction multiplier method with global convergence. [ABSTRACT FROM AUTHOR]

Many recent studies have shown that the adaptive total variation regularization has the advantage of better preserving local features of images compared with the celebrated total variation regularization. On the other hand, the superpixel-based weighted nuclear norm can compensate for the shortcomings of the superpixel-based standard nuclear norm, assigning different weights to singular values and improving flexibility. Inspired by these two factors, we propose two new hyperspectral sparse fusion models related to the adaptive total variation regularization and superpixel-based weighted nuclear norm. Furthermore, we design the alternating direction method of multipliers (ADMM) to efficiently solve the proposed models, with complexity and convergence analyses. Experimental results demonstrate that the proposed methods outperform several state-of-the-art methods both numerically and visually. • We propose two new hyperspectral sparse fusion models, namely SATVNN and SATVWNN. • We design an efficient ADMM to solve the proposed models. • The analyses of convergence and complexity are discussed. • Experimental results show our approaches surpass several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The appearance of consumer depth cameras makes it easy to obtain depth maps of a scene. However, the quality of depth maps is low and cannot satisfy the practical application. This paper proposes a novel depth map super-resolution method, which combines the advantages of the learning-based method and the reconstruction-based method, and incorporates both the learned nonlocal self-similarity prior and enhanced local geometry prior. On one hand, the nonlocal self-similarity prior is learned from the external examples by the patch group-based Gaussian mixture model (PG-GMM) and then used to explore the nonlocal self-similarity of depth maps. On the other hand, the local geometry prior is explored in both the gradient and spatial domain. For the gradient domain, the hyper-Laplacian prior is introduced to model the gradient distribution. For the spatial domain, a structure similarity-based auto-regressive model is proposed to acquire local correlation in a small area of a depth map. Finally, the learned nonlocal and enhanced local prior are cast into a unified optimization framework to acquire an estimation of the high-resolution image. Compared with state-of-the-art methods, experimental results indicate that our method can achieve better reconstruction performance in terms of both quantitative and qualitative evaluations. • Learned nonlocal self-similarity prior and enhanced local geometry prior. • The learned nonlocal self-similarity prior is learned from the external examples. • The enhanced local geometry prior is explored in both gradient and spatial domains. [ABSTRACT FROM AUTHOR]

The method based on non-local self-similarity patches has been widely applied in image denoising. For a given image patch, there are similar image patches at neighbor windows in the image. Traditionally, similar patches are vectorized and then rearranged into a matrix, which should have a low rank. Hence the denoising problem can be reformulated into a low rank recovery problem. However, the vectorization process can disrupt the spatial relationships among the patches. To improve this drawback, we rearrange the similar patches into a tensor to keep the spatial relationships. When the higher-order singular value decomposition (HOSVD) is applied to this tensor, the resulting core tensor should be sparse. In this paper, the sparse property of the core tensor is utilized to characterize similar patches, and then an optimization model is derived. Since the commonly used l 0 norm regularization is NP-hard, we adopt the MCP function to constrain the sparse property of the core tensor. In addition, a total variation (TV) regularization term for the tensor is added to the model to preserve structural information in the image such as edges. Using the dual form to represent the total variation regularization and transforming the original problem into a saddle point problem, the primal–dual algorithm is applied to overcome the non-differentiability of the TV regularization. Finally, experimental results demonstrate that compared to existing denoising methods, the method proposed can better preserve details and structural information in the image. • Firstly, we use HOSVD on the tensor composed of similar blocks to obtain its core tensor. • We establish a hybrid model of tensor sparse representation and total variation regularization. • The primal-dual algorithm is taken to overcome the non-differentiability of the TV regularization. • Experimental results show that our method can better preserve details and structural information than existing methods. [ABSTRACT FROM AUTHOR]

Multi-view non-negative matrix factorization (NMF) provides a reliable method to analyze multiple views of data for low-dimensional representation. A variety of multi-view learning methods have been developed in recent years, demonstrating successful applications in clustering. However, existing methods in multi-view learning often tend to overlook the non-linear relationships among data and the significance of the similarity of internal views, both of which are essential in multi-view tasks. Meanwhile, the mapping between the obtained representation and the original data typically contains complex hidden information that deserves to be thoroughly explored. In this paper, a novel multi-view NMF is proposed that explores the local geometric structure among multi-dimensional data and learns the hidden representation of different attributes through centric graph regularization and pairwise co-regularization of the coefficient matrix. In addition, the proposed model is further sparsified with l 2 , l o g -(pseudo) norm to efficiently generate sparse solutions. As a result, the model obtains a better part-based representation, enhancing its robustness and applicability in complex noisy scenarios. An effective iterative update algorithm is designed to solve the proposed model, and the convergence of the algorithm is proven to be theoretically guaranteed. The effectiveness of the proposed method is verified by comparing it with nine state-of-the-art methods in clustering tasks of eight public datasets. • The proposed method can learn hidden representations within multi-view data. • The centric graph regularization captures more information to strengthen spatial structure. • The pairwise co-regularization preserves local geometry and inter-view information. • The introduced l 2 , l o g -(pseudo) norm obtains better parts-based representation with less redundancy. • Extensive experiments on eight multi-view datasets demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

• Weighted mean curvature (WMC) is a novel spatial prior for image processing. • WMC is sampling-, scale-, and contrast-invariant, and is sparse on natural images. • WMC can be efficiently computed by eight small convolution kernels. • A simple, fast, and numerically stable computation scheme is presented. • WMC is the gradient of area regularization, which can be superior to TV and MC. In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an efficient computation scheme for its discretization in practical image processing applications. We first demonstrate the favorable properties of WMC, such as sampling invariance, scale invariance, and contrast invariance with Gaussian noise model; and we show the relation of WMC to area regularization. We further propose an efficient computation scheme for discretized WMC, which is demonstrated herein to process over 33.2 giga-pixels/second on GPU. This scheme yields itself to a convolutional neural network representation. Finally, WMC is evaluated on synthetic and real images, showing its superiority quantitatively to total-variation and mean curvature. [ABSTRACT FROM AUTHOR]

• The novel nonconvex minimization approach is proposed to solve the tensor completion problem more effectively by adopting a nonconvex regularization of parameter-free to further approximate the tensor-rank. • Alternating direction method of multipliers (ADMM) and iteratively reweighted nuclear norm (IRNN) are adopted to solve the constructed nonconvex models efficiently, and the convergence can also be guaranteed. • The proposed nonconvex optimization methods are suitable for solving the general problems induced by any invertible linear transform. Extensive experiments on real images and videos validate the superiority of our approach over the state-of-the-art algorithms. In this paper, we consider the low-rank tensor completion which aims to exactly recover incomplete high-dimensional visual data. Existing studies utilize widely tensor nuclear norm minimization (TNNM), a convex relaxation to tensor-rank minimization (TRM), to solve tensor completion tasks. Nevertheless, TNNM ignores the difference between different tensor singular values induced by the tensor singular value decompositions (t-SVD) and then the obtained solution may be suboptimal. In this paper, we propose a nonconvex minimization approach to solve the tensor completion problem more effectively by adopting a nonconvex regularization to further approximate the tensor-rank. Moreover, alternating direction method of multipliers (ADMM) and iteratively reweighted nuclear norm (IRNN) are adopted to solve the constructed nonconvex models efficiently, and the convergence can also be guaranteed. Finally, we present that the proposed nonconvex optimization methods are suitable for solving other TRM problems induced by any invertible linear transform, such as subspace clustering based on low-rank representation. Extensive experiments on real images and videos validate the superiority of our approach over the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• A novel generalized adaptive robust distance metric is presented, called L δ (u). • The L δ (u) has some desirable salient properties, such as symmetry, boundedness, robustness, nonconvexity, and adaptivity, with both first-order and higher-order moments from samples. • The L δ (u) can pick different robust distance metrics for different learning tasks during the learning process by the adaptive parameter δ. • A smooth regularized TELM learning framework for supervised and semi-supervised classification is proposed by introducing L δ (u) , regularization and smoothing techniques. • The fast Newton-Armijo algorithm and DC (difference of convex functions) programming algorithm (DCA) are used to solve the proposed methods. In this work, we propose a novel generalized adaptive robust distance metric called L δ (u). Compared with other distance metrics, L δ (u) has some desirable salient properties, such as symmetry, boundedness, robustness, nonconvexity, and adaptivity, with both first-order and higher-order moments from samples. On the other hand, L δ (u) can pick different robust distance metrics for different learning tasks during the learning process by the adaptive parameter δ. Furthermore, we apply L δ (u) to twin extreme learning machine (TELM) and develop an smooth regularized TELM learning framework for supervised and semi-supervised classification. By introducing the structural risk minimization (SRM) principle and smoothing techniques, the learning framework perfectly overcomes the computational burden associated with the matrix inversion operation required during TELM solving, while also significantly improving performance. More importantly, the proposed learning framework not only improves the robustness of TELM, but also can effectively use the geometric information of the marginal distribution embedded in the unlabeled samples to construct a more reasonable classifier. Finally, the globally convergent and quadratic convergent fast Newton-Armijo algorithm and DC (difference of convex functions) programming algorithm (DCA) are designed to solve the proposed methods. Experimental results demonstrate the effectiveness and robustness of our methods. [ABSTRACT FROM AUTHOR]

• The combined regularization parameter for normalized least-mean-square (CRP-NLMS) algorithm is proposed, in which the mixing parameter is derived by minimizing the energy of noise-free a posteriori error. • A novel reset method is designed to improve the tracking capability of the proposed algorithm. We also illustrate that the proposed algorithm is available for the nonstationary system modeled by a random walk process. • The theoretical analyses including the transient and steady-state mean-square error (MSE) are performed in a stationary system. This paper presents a combined regularization parameter for normalized least-mean-square (CRP-NLMS) algorithm. The proposed algorithm adaptively combines two different regularization parameters by employing a time-varying mixing parameter that is derived by minimizing the energy of noise-free a posteriori error. To avoid large fluctuations, the mixing parameter is updated in a moving-average method. A novel reset method is designed to improve the tracking capability when the unknown system encounters a sudden change. We illustrate that the proposed mixing parameter is also available for the nonstationary system modeled by a random walk process. In particular, the theoretical analyses including the transient and steady-state mean-square error (MSE) are performed. Simulations for system identification scenarios demonstrate the merits of Kour finding and support the theoretical analysis. [ABSTRACT FROM AUTHOR]

• We propose a novel plug-and-play regularization (PPR) model that can exploit denoisers based on sparse representation. • We propose a flexible plug-and-play nonlinear imaging framework by using the proposed PPR model. • We propose an effective coded diffraction imaging algorithm. • Under the single and undersampled observation, experiments show that the proposed imaging algorithm can achieve better reconstructions, compared with the previous imaging algorithms. The problem of recovering an image of interest from nonlinear measured data is challenging. To address this nonlinear imaging inverse problem, we propose a novel Plug-and-Play Regularization (PPR) approach that can exploit multiple priors. The underlying image and its filtered image by a denoiser should have similar structures. To exploit this similarity, we enforce the similarity of their sparse coefficients with respect to a tight frame. We formulate a PPR-based nonlinear imaging optimization problem and solve it by using the alternating optimization strategy that consists of filtering step, sparse coding step and image updating step. To avoid the finely-tuned regularization parameter, the epigraph concept is employed in the image updating step. Multiple priors, including the priors employed by the denoiser and the sparsity in the sparsifying transform domain, can be utilized in the proposed PPR model. Under the coded diffraction imaging scenario, we show that the proposed algorithm of exploiting a deep denoiser can achieve higher quality images, compared to the previous imaging algorithms. [ABSTRACT FROM AUTHOR]

• A novel approach (DINPSVM) combining the discrimination metric and spatial distance measure is proposed. • DINPSVM considers both the tightness between the similar patterns and the discrepancy between the dissimilar pairs. • DINPSVM presents two novel discriminative regularization terms for each hyperplane by combining the discrimination metric and the spatial distance measure together. • Experimental results illustrate the validity and advantage of our approach. Twin support vector machine (TSVM), as a typical nonparallel support vector machine, has been demonstrated to be effective in terms of classification performance. However, the existing TSVM does not take the within-class and between-class constraint projections into account. Inspired by modified pairwise constraint trick, we propose a novel classifier termed discriminative information-based nonparallel support vector machine (DINPSVM) to improve the performance of TSVM by introducing two novel regularization terms for each hyperplane, which takes the tightness between the similar patterns and discrepancy between the dissimilar pairs into consideration. The new classifier can not only learn the prior discriminative information about each constrained pair, but also combine the discrimination metric and spatial distance measure together. Experimental results on an artificial and twenty-three UCI datasets verify the efficiency and advantage of the proposed DINPSVM. [ABSTRACT FROM AUTHOR]

Highlights • We introduce the manifold regularization (MR) to retinal image registration. • The MR can capture the intrinsic geometry of feature points in retinal images. • We devise a new formulation based on Gaussian field and MR for mismatch removal. • We use non-rigid transformation model to addressing non-linear registration problems. • We adopt a sparse approximation, which can achieve low computational complexity. Abstract Retinal image registration, which combines the information of retinal images from different modalities, viewpoints or times, plays an important role in diagnosing and treating many eye diseases. In this work, we propose an efficient algorithm called Gaussian field estimator with manifold regularization to address this requirement. We formulate the registration problem as a probabilistic model, that is, a Gaussian field estimator, to achieve a robust estimation, associated with a prior involving manifold regularization to preserve the intrinsic geometry of input data. A non-rigid transformation is specified in a reproducing kernel Hilbert space. Moreover, a sparse approximation is applied to the non-rigid transformation for a fast implementation. Extensive experiments on retinal images show the effectiveness of our approach, which can yield superior results compared with other state-of-the-art methods, especially in the case of severely degraded data. [ABSTRACT FROM AUTHOR]

Highlights • The proposed automatic tridiagonal loading (ATL) beamformer is parameter-free. • Computational cost of ATL is almost the same as the standard Capon beamformer. • ATL outperforms other robust beamformers in terms of robustness and sample size. Abstract Various uncertainties exist in real sensor arrays, which can significantly deteriorate the performance of adaptive beamformers. In this communication, we propose a simple tridiagonal loading method, called automatic tridiagonal loading (ATL), to enhance the robustness of adaptive beamformers. The ATL uses a symmetric tridiagonal matrix to regularize the sample covariance matrix, which approximately imposes a smooth constraint on the weight vector of beamformer. We also present a parameter-free method to determine the loading level based on the output power of a low sidelobe beam in the presumed direction of the desired signal. Thus, ATL does not require user-defined parameters. Moreover, simulation experiments show that ATL has better robust performance than other widely used robust techniques, although the computational cost of ATL is almost the same as the standard Capon beamformer. [ABSTRACT FROM AUTHOR]

Highlights • We propose a weighted–method-noise regularization model for image deblurring. • One advantages of our model is that the method-noise is better in removing noise in smooth areas. • Another advantage is that the incorporated gradient-based weight enables it better preserve image edges. • Experimental results show our method can obtain better results than other method-noise based regularization methods. Abstract Various image prior based regularization techniques have been proposed for image deblurring. By utilizing existing image smoothing operators, the method-noise provides a new way to formulate image regularizers. The method noise is defined as the difference of an image and its smoothed version, obtained by an image smoothing operator such as the non-local means(NLM). Therefore, the method noise mainly contains edges, small scaled details and noise (if exists). The l 2 -NLM method noise regularization has been successfully used in image denoising. However, the restored image exists over-smoothed edges and noise in smooth areas cannot be perfectly removed. In this work, we propose a weighted- l 1 -method-noise regularization model for image deblurring. We analyze the advantages of the proposed model in terms of variational form and its solution. Specifically, the l 1 penalty of the method noise is better than the l 2 penalty in removing noise in smooth areas. The incorporated gradient based weight can better preserve image edges. Experimental results show that the proposed method can obtain better results than other method noise based regularization methods. [ABSTRACT FROM AUTHOR]

Highlights • A general framework for learning discriminant representations of samples is proposed to better solve the classification of image sets. • Under the low-rank and the Grassmann assumptions, a latent space is obtained to capture the lowest-rank representations of samples. • An alternating direction algorithm based on ISTA is proposed to better ensure the convergence of the proposed model. Abstract Although image set classification has attracted great attention in computer vision and pattern recognition communities, however, learning a compact and discriminative representation is still a challenge. In this paper, we present a novel tensor discriminant representation learning method to better solve the image classification task. Specifically, we first exploit the advantages of Grassmann manifold and tensor to model image sets as a high-order tensor. We then propose a transductive low-rank regularized tensor discriminant representation algorithm referred as LRRTDR to learn more intrinsic representations for image sets. Our proposed LRRTDR mainly contains two components: low-rank tensor embedding and discriminant graph embedding. The low-rank tensor embedding is to learn the lowest-rank representation from a low-dimensional subspace, which is spanned by a set of latent basis matrices. The discriminant graph embedding is to further enhance the discriminant ability of the learned representations under the graph embedding framework. To solve the optimization problem of LRRTDR, we develop an alternating direction scheme based on Iterative Shrinkage Thresholding Algorithm (ISTA). Experimental results on five publicly available datasets demonstrate that our proposed algorithm not only converges with few iterations, but also achieves better accuracy compared with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Highlights • We propose a binary level set variational model involving L 1 data term for noisy image segmentation. • We design a three-step time-splitting scheme to numerically solve our model. • The proposed model is robust to impulse noise (i.e., salt & pepper and random-valued) and effective for some real images. Abstract In this paper, we propose a variational model in binary level set framework for segmenting two-phase images with impulse noise. In this model, the contour is implicitly represented by the discontinuity of a binary level set function instead of the zero-level set. The energy functional consists of three terms, i.e., the data term that is defined by L 1-norm metric, the regularization term that is defined by Dirichlet energy of level set function, and the penalty term that punishes the deviation of level set function from binary function. We design a three-step time-splitting scheme to solve the gradient descent flow of the proposed model efficiently, in which the flow equation is divided into three differential equations that are solved sequentially and alternatively until convergence. We present some experimental results that are performed on simulated and real images, which demonstrate that our model is very robust to impulse noise and has the best performance compared with five relevant models. [ABSTRACT FROM AUTHOR]

This work analyzes the effects on support recovery for different choices of the hyper- or regularization parameter in LASSO-like sparse and group-sparse regression problems. The hyperparameter implicitly selects the model order of the solution, and is typically set using cross-validation (CV). This may be computationally prohibitive for large-scale problems, and also often overestimates the model order, as CV optimizes for prediction error rather than support recovery. In this work, we propose a probabilistic approach to select the hyperparameter, by quantifying the type I error (false positive rate) using extreme value analysis. From Monte Carlo simulations, one may draw inference on the upper tail of the distribution of the spurious parameter estimates, and the regularization level may be selected for a specified false positive rate. By solving the e group-LASSO problem, the choice of hyperparameter becomes independent of the noise variance. Furthermore, the effects on the false positive rate caused by collinearity in the dictionary is discussed, including ways of circumventing them. The proposed method is compared to other hyperparameter-selection methods in terms of support recovery, false positive rate, false negative rate, and computational complexity. Simulated data illustrate how the proposed method outperforms CV and comparable methods in both computational complexity and support recovery. [ABSTRACT FROM AUTHOR]

Sparse methods have been recently introduced in Direction-Of-Arrival (DOA) estimation as an alternative to subspace-based methods and Maximum Likelihood (ML) techniques. This paper proposes a low complexity sparse L0-regularized method for DOA estimation of coherent signals in multipath environment, a scenario in which subspace-based methods fail. The first eigenvector of the covariance matrix is used as an observation and its statistics in the presence of modeling errors are derived. Thanks to those statistics, we present a theoretical statistical analysis of an interval in which the regularization parameter, usually empirically tuned, should stand. For a regularization parameter in this interval, the global solution of the L0-regularized problem coincides with the solution of the deterministic ML. An off-line selection of the regularization parameter is therefore proposed. Simulations confirm the relevance of this interval and of the proposed method. [ABSTRACT FROM AUTHOR]

Single image super-resolution (SR) aims at generating a plausible and visually pleasing high-resolution (HR) image from a low-resolution (LR) input. In this paper, we propose an effective single image SR algorithm by using collaborative representation and exploiting non-local self-similarity of natural images. In particular, the collaborative-representation-based method is applied to build the so-called self-projection matrices from a training set of HR images. Then the learned self-projection matrices are used to establish the collaborative-representation-based regularization (CRR), which is responsible for introducing the external HR information. Furthermore, to guarantee a reliable estimation of the HR image, the non-local low-rank regularization (NLR) which exploits internal prior of images is also taken into consideration. Since the CRR term and NLR term are complementary, they are assembled together to form a new reconstruction-based framework for SR recovery. Finally, to implement the proposed framework, an iterative algorithm is designed to gradually improve the quality of the SR results. Extensive experimental results indicate that the proposed approach is capable of delivering higher quality of SR results than several state-of-the-art SR methods. [ABSTRACT FROM AUTHOR]

Active contour models have been widely used for image segmentation purposes. However, they may fail to delineate objects of interest depicted on images with intensity inhomogeneity. To resolve this issue, a novel image feature, termed as local edge entropy, is proposed in this study to reduce the negative impact of inhomogeneity on image segmentation. An active contour model is developed on the basis of this feature, where an edge entropy fitting (EEF) energy is defined with the combination of a redesigned regularization term. Minimizing the energy in a variational level set formulation can successfully drive the motion of an initial contour curve towards optimal object boundaries. Experiments on a number of test images demonstrate that the proposed model has the capability of handling intensity inhomogeneity with reasonable segmentation accuracy. [ABSTRACT FROM AUTHOR]

In this paper, motivated by approximating the Euler-Lagrange equation of the p th-order regularization for 0 <  p  ≤ 1, we propose a new regularization model with adaptive diffusivity for variational image denoising. The model is equipped with a regularization controller which is introduced to adaptively adjust the diffusivity from pixel to pixel according to the magnitude of image gradient. The associated energy functional is convex and thus the minimization problem can be efficiently solved using a modified split Bregman iterative scheme. A convergence analysis of the iterative scheme is established. Numerical experiments are performed to demonstrate the good performance of the proposed model. Comparisons with some other image denoising models are also made. [ABSTRACT FROM AUTHOR]

The fusion of multiple features is important for achieving state-of-the-art face recognition results. This has been proven in both traditional and deep learning approaches. Existing feature fusion methods either reduce the dimensionality of each feature first and then concatenate all low-dimensional feature vectors, named as DR-Cat, or the vice versa, named as Cat-DR. However, DR-Cat ignores the correlation information between different features which is useful for classification. In Cat-DR, on the other hand, the correlation information estimated from the training data may not be reliable especially when the number of training samples is limited. We propose a covariance matrix regularization (CMR) technique to solve problems of DR-Cat and Cat-DR. It works by assigning weights to cross-feature covariances in the covariance matrix of training data. Thus the feature correlation estimated from training data is regularized before being used to train the feature fusion model. The proposed CMR is applied to 4 feature fusion schemes: fusion of pixel values from 3 color channels, fusion of LBP features from 3 color channels, fusion of pixel values and LBP features from a single color channel, and fusion of CNN features extracted by 2 deep models. Extensive experiments of face recognition and verification are conducted on databases including MultiPIE, Georgia Tech, AR and LFW. Results show that the proposed CMR technique significantly and consistently outperforms the best single feature, DR-Cat and Cat-DR. [ABSTRACT FROM AUTHOR]

Appropriate user and item representation learning is critical to a successful recommender system. A set of models from natural language processing domain, namely neural language models, have recently been utilized to user and item representation learning in standard recommendation tasks. This paper proposes to exploit neural language models in the social recommendation task. Unlike previous studies that focus on modeling the user-item interaction matrix and only consider the item-level context, this paper models user social relationship information and adds an additional layer to incorporate user-level context. The derived representation is very like the social regularization imposed in matrix factorization-based recommendation, but with more flexible context. Experiments on a Douban movie dataset validate the advantage of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonconvex and nonsmooth total generalized variation (TGV) model for image restoration, which can provide an even sparser representation of the variation of the image function than the traditional TGV model that uses convex l 1 norm to measure the variation. New model combines the advantages of nonconvex regularization and TGV regularization, and can preserve image edges well and simultaneously alleviate the staircase effects often arising in the total variation based models. Two different iteratively reweighed algorithms are introduced to numerically solve the proposed nonconvex and nonsmooth TGV model. Numerical results show that the proposed model is effective in edge-preserving and staircase-reduction in image restoration. In addition, compared with several state-of-the-art variational models, the proposed model has the best performance in terms of PSNR and MSSIM values. [ABSTRACT FROM AUTHOR]

In this paper, we propose a semi-supervised graph-based retargeted least squares regression model (SSGReLSR) for multicategory classification. The main motivation behind SSGReLSR is to utilize a graph regularization to restrict the regression labels of ReLSR, such that similar samples should have similar regression labels. However, in SSGReLSR, constructing the graph structure and learning the regression matrix are two independent processes, which can’t guarantee an overall optimum. To overcome this shortage of SSGReLSR, we also propose a semi-supervised graph learning retargeted least squares regression model (SSGLReLSR), where linear squares regression and graph construction are unified into a same framework to achieve an overall optimum. To optimize our proposed SSGLReLSR, an efficient iteration algorithm is proposed. Extensive experiments results confirm the effectiveness of our proposed methods. [ABSTRACT FROM AUTHOR]

Due to the environmental and instrumental factors, the hyperspectral image (HSI) is corrupted by various noise, which inevitably affects the subsequent HSI-based applications. Several band by band Total Variation(TV)-regularized low rank based models have been proposed for HSI mixed denoising. However, these methods only utilize the spatial smooth constraint in a separated way, but ignore the local spectral smooth property, which may cause the undesirable jagged spectral distortion. To cope with this problem, we propose a novel low rank constraint and spatial spectral total variation regularization model. First, we adopt the weighted nuclear norm to restore the clean HSI from the mixed noise based on the low rank property. Then, the spatial spectral total variation is modeled as a special regularization to further remove the Gaussian noise and enhance the local spatial and spectral smoothness. Finally, an iterative strategy based on the Alternating Direction Method of Multipliers is designed to solve the derived optimization problem. Extensive experiments demonstrate the superiority of the proposed model in terms of mean PSNR, mean SSIM, mean spectral angle distance and visual quality. Especially, the proposed model is very effective for suppressing the jagged spectral distortion while removing the noise. [ABSTRACT FROM AUTHOR]

The method described here performs blind deconvolution of the beamforming output in the frequency domain. To provide accurate blind deconvolution, sparsity priors are introduced with a smoothed ℓ 1 / ℓ 2 regularization term. As the mean of the noise in the power spectrum domain depends on its variance in the time domain, the proposed method includes a variance estimation step, which allows more robust blind deconvolution. Validation of the method on both simulated and real data, and of its performance, are compared with two well-known methods from the literature: the deconvolution approach for the mapping of acoustic sources, and sound density modeling. [ABSTRACT FROM AUTHOR]

This paper analyzes the statistical properties of the signal-to-noise ratio (SNR) at the output of the Capon's minimum variance distortionless response (MVDR) beamformers when operating over impulsive noises. Particularly, we consider the supervised case in which the receiver employs the regularized Tyler estimator in order to estimate the covariance matrix of the interference-plus-noise process using n observations of size N × 1 . The choice for the regularized Tyler estimator (RTE) is motivated by its resilience to the presence of outliers and its regularization parameter that guarantees a good conditioning of the covariance estimate. Of particular interest in this paper is the derivation of the second order statistics of the SINR. To achieve this goal, we consider two different approaches. The first one is based on considering the classical regime, referred to as the n -large regime, in which N is assumed to be fixed while n grows to infinity. The second approach is built upon recent results developed within the framework of random matrix theory and assumes that N and n grow large together. Numerical results are provided in order to compare between the accuracies of each regime under different settings. [ABSTRACT FROM AUTHOR]

The smoothed ℓ ° norm (SL0) algorithm as one of the fastest implementations of sparse signal recovery suffers from significant performance degradation in noisy environments due to the inaccurate equality constraint involved in the optimization problem. Based on the regularized SL0 (ReSL0) algorithm adopting the regularization term to tolerate error, we propose an improved algorithm termed “adaptive regularized SL0 (AReSL0) algorithm” for making the sparse solution more robust against noise. The AReSL0 algorithm adaptively generates the efficient and reliable regularization parameter to balance the fit of the sparsity and residual error in the ReSL0-based objective function during the iteration process, and then exhibits higher immunity to noise than both the SL0 and ReSL0 algorithms. In an attempt to accelerate the AReSL0 algorithm, the SVD-based approach is employed for fast computing the inverse of the successive updated large matrices, thus increasing the execution speed of AReSL0 without loss of accuracy. Simulation results are presented to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Ultrasonography is widely used in clinical diagnosis and therapeutic procedures, but speckle noise often obscures important features and complicates interpretation and analysis of ultrasound images. In this regard, speckle reduction is a crucial prerequisite of many computer aided ultrasound diagnosis and treatment systems However, removing speckle noise while simultaneously preserving features in ultrasound images is a challenging task. We propose a novel optimization framework for speckle reduction by leveraging the concept of phase congruency and incorporating a feature asymmetry metric into the regularization term of the objective function to effectively distinguish the features and speckle noise. The feature asymmetry metric can productively separate features from speckle noise by analyzing the local frequency information. Compared with traditional methods employing intensity gradients as regularization terms, our framework is invariant to the intensity amplitude of features so that low contrast features are almost equally protected as high contrast features. In addition, rather than adopting the gradient descent, we propose a novel solver by decomposing the original non-convex optimization into solving several linear systems, leading to an efficient solution of the optimization. Owing to different penalties on speckle noise and features, our method can efficiently remove speckle noise and preserve features at the same time. Experiments on simulated and real ultrasound images demonstrate our method can better maintain features with speckle removal than state-of-the-art methods, especially for the low contrast features. [ABSTRACT FROM AUTHOR]

A novel communication efficient scheme for reconstructing a field sensed by spatially scattered sensors is proposed. The field is formed by multiple sources, while a fusion center gathers the sensor measurements. The goal is to reconstruct the field at the fusion center using only the measurements of a small number of sensors. The framework entails learning the correlation structure of the field by determining clusters of correlated sensors observing the same set of sources. Combining moving-average filtering along with principal component analysis applied in the sensor data covariance the number of sources can be determined, while norm-one regularized canonical correlations are utilized to determine the different correlated clusters. A novel iterative interplay of regularized canonical correlations with principal component analysis is designed that determines correctly the correlated clusters as the number of training data goes to infinity. From each cluster only a head sensor transmits data to the fusion center, while the measurements of the remaining sensors are reconstructed using proper linear filters that learn the correlation pattern within a cluster via normalized least mean squares. The novel approach substantially reduces the communication cost. Extensive numerical tests demonstrate the effectiveness of the proposed scheme in field recovery. [ABSTRACT FROM AUTHOR]

This paper addresses the structurally constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal regularization term is designed and used together with the standard ℓ 1 regularization term to enforce a sparse decomposition preserving the spatio-temporal structure of the signal. Secondly, an optimization algorithm based on the split Bregman approach is proposed to handle the associated optimization problem, and its convergence is analyzed. Our well-founded approach yields same accuracy as the other algorithms at the state of the art, with significant gains in terms of convergence speed. Thirdly, the empirical validation of the approach on artificial and real-world problems demonstrates the generality and effectiveness of the method. On artificial problems, the proposed regularization subsumes the Total Variation minimization and recovers the expected decomposition. On the real-world problem of electro-encephalography brainwave decomposition, the approach outperforms similar approaches in terms of P300 evoked potentials detection, using structured spatial priors to guide the decomposition. [ABSTRACT FROM AUTHOR]

We treat the estimation of a sparse set of sources emitting plane waves observed by a sensor array as a complex-valued LASSO (c–LASSO) problem where the usual ℓ 1 -norm constraint is replaced by the ℓ 1 -norm of a matrix D times the solution vector. When the sparsity order is given, algorithmically selecting a suitable value for the c–LASSO regularization parameter remains a challenging task. The corresponding dual problem is formulated and it is shown that the dual solution is useful for selecting the regularization parameter of the c-LASSO. The solution path of the c-LASSO is analyzed and this motivates an order-recursive algorithm for the selection of the regularization parameter and a faster iterative algorithm that is based on a further approximation. This greatly facilitates computation of the c-LASSO-path as we can predict the changes in the active indices as the regularization parameter is reduced. Using this regularization parameter, the directions of arrival for all sources are estimated. [ABSTRACT FROM AUTHOR]

• A new non-convex regularization is utilized to attain robustness and sparseness, and its proximity operator is derived, which makes the corresponding optimization problem solvable in an efficient manner. • We theoretically analyze that any limit point of the iterates is a critical point of the objective function. • There are no tunable parameters other than the termination conditions in the proposed algorithm and experiments demonstrate that our method exhibits better restoration results, compared with the competing approaches. In this paper, we propose a new non-convex regularization term named half-quadratic function to achieve robustness and sparseness for robust principal component analysis, and derive its proximity operator, indicating that the resultant optimization problem can be solved in computationally attractive manner. In addition, the low-rank matrix component is expressed as the factorization form and proximal block coordinate descent is leveraged to seek its solution, whose convergence is rigorously analyzed. We prove that any limit point of the iterations is a critical point of the objective function. Furthermore, the parameter that controls the robustness and sparseness in our algorithm, is automatically adjusted according to the statistical residual error. Experimental results based on synthetic and real-world data demonstrate that the devised algorithm can effectively extract the low-rank and sparse components. MATLAB code is available at https://github.com/bestzywang. [ABSTRACT FROM AUTHOR]

This paper studies the intrinsic connection between a generalized LASSO and a basic LASSO formulation. The former is the extended version of the latter by introducing a regularization matrix to the coefficients. We show that when the regularization matrix is even- or under-determined with full rank conditions, the generalized LASSO can be transformed into the LASSO form via the Lagrangian framework. In addition, we show that some published results of LASSO can be extended to the generalized LASSO, and some variants of LASSO, e.g. , robust LASSO, can be rewritten into the generalized LASSO form and hence can be transformed into basic LASSO. Based on this connection, many existing results concerning LASSO, e.g. , efficient LASSO solvers, can be used for generalized LASSO. [ABSTRACT FROM AUTHOR]

This work treats multi-pitch estimation, and in particular the common misclassification issue wherein the pitch at half the true fundamental frequency, the sub-octave, is chosen instead of the true pitch. Extending on current group LASSO-based methods for pitch estimation, this work introduces an adaptive total variation penalty, which enforces both group- and block sparsity, as well as deals with errors due to sub-octaves. Also presented is a scheme for signal adaptive dictionary construction and automatic selection of the regularization parameters. Used together with this scheme, the proposed method is shown to yield accurate pitch estimates when evaluated on synthetic speech data. The method is shown to perform as good as, or better than, current state-of-the-art sparse methods while requiring fewer tuning parameters than these, as well as several conventional pitch estimation methods, even when these are given oracle model orders. When evaluated on a set of ten musical pieces, the method shows promising results for separating multi-pitch signals. [ABSTRACT FROM AUTHOR]

Image classification is an active research area in signal processing and pattern recognition, with extensively academic and industrial applications. Existing image classification methods usually assumes consistent image source for training and testing which, however, seldom holds for practical applications. We define the scenario of images being captured from diverse sources (e.g. Internet, surveillance cameras, and mobile phones) as heterogeneous sensor-cyber sources (HSCS). We indicate that, information fusion in HSCS is able to make full use of the diversity of images, and thus improves the generalization of classifier. A novel algorithm named Cross Domain Boosting (CD-Boost) is proposed to fuse information in HSCS. Our CD-Boost algorithm has two characteristics, weighted loss objective and manifold smoothness regularization. Concretely, the weighted boosting loss objective can fuse information by assigning different weights to each source sample, and the weights are determined by minimizing the difference between the data distribution in HSCS. Furthermore, when the images are scarce, a manifold smoothness regularization can prevent overfitting and further improve the accuracy. The experimental results on real data demonstrate that our algorithm outperforms existing methods. [ABSTRACT FROM AUTHOR]

Heterogeneous sensing systems, consisting of sensors with different sensing capabilities, offer flexibility and provide multiple views of the sensed field by acquiring different types of measurements. The acquired sensor measurements are affected by different and unknown in number phenomena/sources of interest. To this end, a novel canonical correlation analysis (CCA) framework equipped with norm-one and norm-two regularization terms is designed to cluster the sensor data based on their information content. Block coordinate descent (BCD) is combined with the alternating direction method of multipliers (ADMM) framework to derive a centralized algorithm tackling the novel regularized CCA framework. Further, splitting of the regularized CCA into localized minimization subtasks across sensors enables distributed clustering of heterogeneous data based on their information content. Numerical tests demonstrate that the novel framework can achieve higher probability of correct clustering than existing alternatives. [ABSTRACT FROM AUTHOR]

Non-negative matrix factorization (NMF) has been a powerful data representation tool which has been widely applied in pattern recognition and computer vision due to its simplicity and effectiveness. However, existing NMF methods suffer from one or both of the following deficiencies: (1) they cannot theoretically guarantee the decomposition results to be sparse, and (2) they completely neglect geometric structure of data, especially when some examples are heavily corrupted. In this paper, we propose a local coordinate based graph regularized NMF method (LCGNMF) to simultaneously overcome both deficiencies. In particular, LCGNMF enforces the learned coefficients to be sparse by incorporating the local coordinate constraint over both factors meanwhile preserving the geometric structure of the data by incorporating graph regularization. To enhance the robustness of NMF, LCGNMF removes the effect of the outliers via the maximum correntropy criterion (MCC). LCGNMF is difficult because the MCC induced objective function is neither quadratic nor convex. We therefore developed a multiplicative update rule to solve LCGNMF and theoretically proved its convergence. Experiments of image clustering on several popular image datasets verify the effectiveness of LCGNMF compared to the representative methods in quantities. [ABSTRACT FROM AUTHOR]

Visual tracking is a key technique used by video abstraction to achieve efficient post-analysis for big video surveillance. In order to tackle the problem of constantly changing scenarios during online tracking, additional factors such as motion can be incorporated by utilizing a fusion strategy to improve the final performance. Unfortunately, straightforward output fusion is difficult to be synchronized due to the diversity in model regression. Therefore, a widely cited problem for learning based fusion is to incorporate regularizers for label assignment of unlabeled samples, which is one of the major research focuses on semi-supervised learning. In this paper, a novel tracking strategy based on semi-supervised learning with high order regularization fusion has been proposed. It employs two different types of regularizers to achieve more accurate label assignment based on kernelized confidence prediction and graph-based bi-directional trace from motion. The computation of the proposed tracker takes advantage of the unique feature of circulant matrix in Fourier domain and integral patterns, and thus can be readily implemented for real-time processing, even without any code optimization. Via a dynamic budget maintenance for model updating, the proposed tracking method demonstrated to outperform most state-of-art trackers on challenging benchmark videos with a fixed parameter configuration. [ABSTRACT FROM AUTHOR]

Image-based human pose recovery is usually conducted by retrieving relevant poses with image features. However, semantic gap exists for current feature extractors, which limits recovery performance. In this paper, we propose a novel feature extractor with deep learning. It is based on denoising autoencoder and improves traditional methods by adopting locality preserved restriction. To impose this restriction, we introduce manifold regularization with hypergraph Laplacian. Hypergraph Laplacian matrix is constructed with patch alignment framework. In this way, an automatic feature extractor for silhouettes is achieved. Experimental results on two datasets show that the recovery error has been reduced by 10% to 20%, which demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

One promising technique for single image super-resolution (SR) is reconstruction-based framework, where the key issue is to apply reasonable prior knowledge to well pose the solution to upsampled images. In this paper, we employ the non-local steering kernel regression (NLSKR) model to devise an effective regularization term for solving single image SR problem. The proposed regularization term is based on the complementary properties of local structural regularity and non-local self-similarity existing in natural images, aiming at preserving sharp edges and producing fine details in the resultant image. By integrating the regularization term into the standard back-projection framework, we solve a least squares minimization problem to seek the desired high-resolution (HR) image. Extensive experimental results on several public databases indicate that the proposed method produces promising results in terms of both objective and subjective quality assessments. [ABSTRACT FROM AUTHOR]

In this paper we take a novel approach to the regularization of underdetermined linear systems. Typically, a prior distribution is imposed on the unknown to hopefully force a sparse solution, which often relies on uniqueness of the regularized solution (something which is typically beyond our control) to work as desired. But here we take a direct approach, by imposing the requirement that the system takes on a unique solution. Then we seek a minimal residual for which this uniqueness requirement holds. When applied to systems with non-negativity constraints or forms of regularization for which sufficient sparsity is a requirement for uniqueness, this approach necessarily gives a sparse result. The approach is based on defining a metric of distance to uniqueness for the system, and optimizing an adjustment that drives this distance to zero. We demonstrate the performance of the approach with numerical experiments. [ABSTRACT FROM AUTHOR]

Sparse signal recovery is attractive in compressed sensing (CS). Based on the smoothed ℓ 0 norm (SL0) algorithm, we have developed an error-tolerant regularized SL0 (ReSL0) algorithm, which has the same computational advantages as the SL0 algorithm while having better immunity against inaccuracy caused by noise or model mismatch. The performance of the ReSL0 is evaluated with simulated data. In addition, we have extended the ReSL0 to the matrix form (MReSL0), which is more suitable for dealing with matrix form signals and also has good resilience against inaccuracy. Finally we apply the ReSL0 and MReSL0 to joint CS-based radar imaging and phase error correction. Experimental results from both simulated and real data demonstrate that the proposed algorithms provide remarkable performance improvements in inaccurate scenarios (such as noisy data and mismatched settings) compared with the SL0 algorithm. [ABSTRACT FROM AUTHOR]

Nowadays, listening to music has become a habit for almost everyone. Music recommendation helps the users discover the songs they like to listen. In this paper, we propose a music recommendation framework based on graph based quality model to make fine-grained music recommendation. We first discover the recommendation cues, which we called user׳s preference relations from the users’ ratings. Then we model them using the quality model and propose a regularization framework to calculate the recommendation probability of songs. Our experiments show that the proposed framework is superior to two traditional algorithms, especially in solving the cold start problem in recommendation. [ABSTRACT FROM AUTHOR]

Non-negative matrix factorization (NMF) is one of the most important models for learning compact representations of high-dimensional data. With the separability condition, separable NMF further enjoys a global optimal solution. However, separable NMF is unable to make use of data label information and thus unfavourable for supervised learning problems. In this paper, we propose discriminative separable NMF (DS-NMF), which extends separable NMF by encoding data label information into data representations. Assuming that each conical basis vector under the separability condition is only contributable to representing data from a few classes, DS-NMF exploits a structured sparse regularization to learning a sparse data representation and provides higher discrimination power than the standard separable NMF. Empirical evaluations on face recognition and scene classification problems confirm the effectiveness of DS-NMF and its superiority to separable NMF. [ABSTRACT FROM AUTHOR]

In this paper, a new adaptive active contour model is proposed for image segmentation, which is built based on fractional order differentiation, level set method and curve evolution. The energy functional for the proposed model consists of three terms: fitting term, regularization tern and penalty term. By incorporating the fractional order fitting term, the novel fitting term can describe the original image more accurately, and be robustness to noise. In order to ensure stable evolution of the level set function, a penalty tern is added into the proposed model. The results evolution of the level set function is the gradient flow that minimizes the overall energy functional. Experimental results for both synthetic and real image show desirable performance of our method. [ABSTRACT FROM AUTHOR]

Mixed noise removal is a challenging problem due to the complexity of statistical model of image noise. Additive white Gaussian noise (AWGN) combined with impulse noise (IN) is a representative among commonly encountered mixed noise. At present, nonlocal self-similarity (NSS) prior coupled with adaptive regularization have shown great potential in AWGN removal and led to satisfactory denoising performance. However, few studies unify these properties to remove mixture of AWGN and IN. In this paper, we propose a simple yet effective method, namely sparse nonlocal priors based two-phase approach (SNTP), for mixed noise removal. In SNTP, a median-type filter is used to detect outlier pixels which are likely to be corrupted by IN, and the remaining pixels are mainly corrupted by AWGN. We recover the image by encoding free-outlier pixels over a pre-learned dictionary to remove AWGN, and integrate the image sparse nonlocal priors as a regularization term. Meanwhile, adaptive regularization is used to further improve the denoising performance. Experimental results show that the proposed SNTP algorithm outperforms state-of-the-art mixed noise removal methods in terms of both quantitative measures and visual perception quality. [ABSTRACT FROM AUTHOR]

In recent years, deblurring image with Poisson noise has attracted more and more attention in many areas such as astronomy and biological imaging. This is an ill-posed problem and can be regularized to improve the quality of the solution. Fractional-order total variation regularization can eliminate the staircase effect caused by the total variation regularization and avoid over-smoothing at the edges caused by the high-order total variation regularization, but it cannot preserve textures well. Non-local regularization can preserve textures well but often causes extra artifacts especially in the non-texture regions. In this paper, we deal with the cartoon component and the texture component differently and propose a cartoon-texture composite regularization based non-blind deblurring method. We utilize fractional-order total variation regularization for the cartoon component to eliminate the staircase effect and avoid over-smoothing at the edges, and use the non-local total variation regularization for the texture component to preserve the details and eliminate the artifacts in the non-textured regions. We develop an alternating direction method of multipliers based algorithm to solve the proposed model. Experiments results show that our method can improve the result both visually and in terms of the peak signal to noise ratio and structural similarity index efficiently. [ABSTRACT FROM AUTHOR]