Tensor Completion via Nonlocal Low-Rank Regularization

Multichannel Image Completion With Mixture Noise: Adaptive Sparse Low-Rank Tensor Subspace Meets Nonlocal Self-Similarity

Multichannel image completion with mixture noise is a common but complex problem in the fields of machine learning, image processing, and computer vision. Most existing algorithms devote to explore global low-rank information and fail to optimize local and joint-mode structures, which may lead to oversmooth restoration results or lower quality restoration details. In this study, we propose a novel model to deal with multichannel image completion with mixture noise based on adaptive sparse low-rank tensor subspace and nonlocal self-similarity (ASLTS-NS). In the proposed model, a nonlocal similar patch matching framework cooperating with Tucker decomposition is used to explore information of global and joint modes and optimize the local structure for improving restoration quality. In order to enhance the robustness of low-rank decomposition to data missing and mixture noise, we present an adaptive sparse low-rank regularization to construct robust tensor subspace for self-weighing importance of different modes and capturing a stable inherent structure. In addition, joint tensor Frobenius and l1 regularizations are exploited to control two different types of noise. Based on alternating directions method of multipliers (ADMM), a convergent learning algorithm is designed to solve this model. Experimental results on three different types of multichannel image sets demonstrate the advantages of ASLTS-NS under five complex scenarios.

A Kalman-Filter-Incorporated Latent Factor Analysis Model for Temporally Dynamic Sparse Data

With the rapid development of services computing in the past decade, Quality-of-Service (QoS)-aware selection of Web services has become a hot yet thorny issue. Conducting warming-up tests on a large set of candidate services for QoS evaluation is time consuming and expensive, making it vital to implement accurate QoS-estimators. Existing QoS-estimators barely consider the temporal patterns hidden in QoS data. However, such data are naturally time dependent. For addressing this critical issue, this study presents a Kalman-filter-incorporated latent factor analysis (KLFA)-based QoS-estimator for accurate representation to temporally dynamic QoS data. Its main idea is to make the user latent features (LFs) time dependent, while the service ones time consistent. A novel iterative training scheme is designed, where the user LFs are learned through a Kalman filter for precisely modeling the temporal patterns, and the service ones are alternatively trained via an alternating least squares algorithm for precisely representing the historical QoS data. Empirical studies on large-scale and real Web service QoS datasets demonstrate that the proposed KLFA model significantly outperforms state-of-the-art QoS-estimators in estimation accuracy for dynamic QoS data.

Tensor Cascaded-Rank Minimization in Subspace: A Unified Regime for Hyperspectral Image Low-Level Vision

Low-rank tensor representation philosophy has enjoyed a reputation in many hyperspectral image (HSI) low-level vision applications, but previous studies often failed to comprehensively exploit the low-rank nature of HSI along different modes in low-dimensional subspace, and unsurprisingly handled only one specific task. To address these challenges, in this paper, we figured out that in addition to the spatial correlation, the spectral dependency of HSI also implicitly exists in the coefficient tensor of its subspace, this crucial dependency that was not fully utilized by previous studies yet can be effectively exploited in a cascaded manner. This led us to propose a unified subspace low-rank learning regime with a new tensor cascaded rank minimization, named STCR, to fully couple the low-rankness of HSI in different domains for various low-level vision tasks. Technically, the high-dimensional HSI was first projected into a low-dimensional tensor subspace, then a novel tensor low-cascaded-rank decomposition was designed to collapse the constructed tensor into three core tensors in succession to more thoroughly exploit the correlations in spatial, nonlocal, and spectral modes of the coefficient tensor. Next, difference continuity-regularization was introduced to learn a basis that more closely approximates the HSI's endmembers. The proposed regime realizes a comprehensive delineation of the self-portrait of HSI tensor. Extensive evaluations conducted with dozens of state-of-the-art (SOTA) baselines on eight datasets verified that the proposed regime is highly effective and robust to typical HSI low-level vision tasks, including denoising, compressive sensing reconstruction, inpainting, and destriping. The source code of our method is released at https://github.com/CX-He/STCR.git.

Multiscale Feature Tensor Train Rank Minimization for Multidimensional Image Recovery

The general tensor-based methods can recover missing values of multidimensional images by exploiting the low-rankness on the pixel level. However, especially when considerable pixels of an image are missing, the low-rankness is not reliable on the pixel level, resulting in some details losing in their results, which hinders the performance of subsequent image applications (e.g., image recognition and segmentation). In this article, we suggest a novel multiscale feature (MSF) tensorization by exploiting the MSFs of multidimensional images, which not only helps to recover the missing values on a higher level, that is, the feature level but also benefits subsequent image applications. By exploiting the low-rankness of the resulting MSF tensor constructed by the new tensorization, we propose the convex and nonconvex MSF tensor train rank minimization (MSF-TT) to conjointly recover the MSF tensor and the corresponding original tensor in a unified framework. We develop the alternating directional method of multipliers (ADMMs) to solve the convex MSF-TT and the proximal alternating minimization (PAM) to solve the nonconvex MSF-TT. Moreover, we establish the theoretical guarantee of convergence for the PAM algorithm. Numerical examples of real-world multidimensional images show that the proposed MSF-TT outperforms other compared approaches in image recovery and the recovered MSF tensor can benefit the subsequent image recognition.

Nonconvex Structural Sparsity Residual Constraint for Image Restoration

This article proposes a novel nonconvex structural sparsity residual constraint (NSSRC) model for image restoration, which integrates structural sparse representation (SSR) with nonconvex sparsity residual constraint (NC-SRC). Although SSR itself is powerful for image restoration by combining the local sparsity and nonlocal self-similarity in natural images, in this work, we explicitly incorporate the novel NC-SRC prior into SSR. Our proposed approach provides more effective sparse modeling for natural images by applying a more flexible sparse representation scheme, leading to high-quality restored images. Moreover, an alternating minimizing framework is developed to solve the proposed NSSRC-based image restoration problems. Extensive experimental results on image denoising and image deblocking validate that the proposed NSSRC achieves better results than many popular or state-of-the-art methods over several publicly available datasets.

Adaptive Rank and Structured Sparsity Corrections for Hyperspectral Image Restoration

Hyperspectral images (HSIs) are inevitably contaminated by the mixed noise (such as Gaussian noise, impulse noise, deadlines, and stripes), which could influence the subsequent processing accuracy. Generally, HSI restoration can be transformed into the low-rank matrix recovery (LRMR). In the LRMR, the nuclear norm is widely used to substitute the matrix rank, but its effectiveness is still worth improving. Besides, the l₀ -norm cannot capture the sparse noise's structured sparsity property. To handle these issues, the adaptive rank and structured sparsity corrections (ARSSC) are presented for HSI restoration. The ARSSC introduces two convex regularizers, that is: 1) the rank correction (RC) and 2) the structured sparsity correction (SSC), to, respectively, approximate the matrix rank and the l_2,0 -norm. The RC and the SSC can adaptively offset the penalization of large entries from the nuclear norm and the l_2,1 -norm, respectively, where the larger the entry, the greater its offset. Therefore, the proposed ARSSC achieves a tighter approximation of the noise-free HSI low-rank structure and promotes the structured sparsity of sparse noise. An efficient alternative direction method of multipliers (ADMM) algorithm is applied to solve the resulting convex optimization problem. The superiority of the ARSSC in terms of the mixed noise removal and spatial-spectral structure information preserving, is demonstrated by several experimental results both on simulated and real datasets, compared with other state-of-the-art HSI restoration approaches.

A Nonlocal Self-Similarity-Based Weighted Tensor Low-Rank Decomposition for Multichannel Image Completion With Mixture Noise

Multichannel image completion with mixture noise is a challenging problem in the fields of machine learning, computer vision, image processing, and data mining. Traditional image completion models are not appropriate to deal with this problem directly since their reconstruction priors may mismatch corruption priors. To address this issue, we propose a novel nonlocal self-similarity-based weighted tensor low-rank decomposition (NSWTLD) model that can achieve global optimization and local enhancement. In the proposed model, based on the corruption priors and the reconstruction priors, a pixel weighting strategy is given to characterize the joint effects of missing data, the Gaussian noise, and the impulse noise. To discover and utilize the accurate nonlocal self-similarity information to enhance the restoration quality of the details, the traditional nonlocal learning framework is optimized by employing improved index determination of patch group and handling strip noise caused by patch overlapping. In addition, an efficient and convergent algorithm is presented to solve the NSWTLD model. Comprehensive experiments are conducted on four types of multichannel images under various corruption scenarios. The results demonstrate the efficiency and effectiveness of the proposed model.

Non-Local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration

Non-local low-rank tensor approximation has been developed as a state-of-the-art method for hyperspectral image (HSI) restoration, which includes the tasks of denoising, compressed HSI reconstruction and inpainting. Unfortunately, while its restoration performance benefits from more spectral bands, its runtime also substantially increases. In this paper, we claim that the HSI lies in a global spectral low-rank subspace, and the spectral subspaces of each full band patch group should lie in this global low-rank subspace. This motivates us to propose a unified paradigm combining the spatial and spectral properties for HSI restoration. The proposed paradigm enjoys performance superiority from the non-local spatial denoising and light computation complexity from the low-rank orthogonal basis exploration. An efficient alternating minimization algorithm with rank adaptation is developed. It is done by first solving a fidelity term-related problem for the update of a latent input image, and then learning a low-dimensional orthogonal basis and the related reduced image from the latent input image. Subsequently, non-local low-rank denoising is developed to refine the reduced image and orthogonal basis iteratively. Finally, the experiments on HSI denoising, compressed reconstruction, and inpainting tasks, with both simulated and real datasets, demonstrate its superiority with respect to state-of-the-art HSI restoration methods.

Prior-Based Tensor Approximation for Anomaly Detection in Hyperspectral Imagery

The key to hyperspectral anomaly detection is to effectively distinguish anomalies from the background, especially in the case that background is complex and anomalies are weak. Hyperspectral imagery (HSI) as an image-spectrum merging cube data can be intrinsically represented as a third-order tensor that integrates spectral information and spatial information. In this article, a prior-based tensor approximation (PTA) is proposed for hyperspectral anomaly detection, in which HSI is decomposed into a background tensor and an anomaly tensor. In the background tensor, a low-rank prior is incorporated into spectral dimension by truncated nuclear norm regularization, and a piecewise-smooth prior on spatial dimension can be embedded by a linear total variation-norm regularization. For anomaly tensor, it is unfolded along spectral dimension coupled with spatial group sparse prior that can be represented by the l_2,1 -norm regularization. In the designed method, all the priors are integrated into a unified convex framework, and the anomalies can be finally determined by the anomaly tensor. Experimental results validated on several real hyperspectral data sets demonstrate that the proposed algorithm outperforms some state-of-the-art anomaly detection methods.

Tensor Completion via Complementary Global, Local, and Nonlocal Priors

Completing missing entries in multidimensional visual data is a typical ill-posed problem that requires appropriate exploitation of prior information of the underlying data. Commonly used priors can be roughly categorized into three classes: global tensor low-rankness, local properties, and nonlocal self-similarity (NSS); most existing works utilize one or two of them to implement completion. Naturally, there arises an interesting question: can one concurrently make use of multiple priors in a unified way, such that they can collaborate with each other to achieve better performance? This work gives a positive answer by formulating a novel tensor completion framework which can simultaneously take advantage of the global-local-nonlocal priors. In the proposed framework, the tensor train (TT) rank is adopted to characterize the global correlation; meanwhile, two Plug-and-Play (PnP) denoisers, including a convolutional neural network (CNN) denoiser and the color block-matching and 3 D filtering (CBM3D) denoiser, are incorporated to preserve local details and exploit NSS, respectively. Then, we design a proximal alternating minimization algorithm to efficiently solve this model under the PnP framework. Under mild conditions, we establish the convergence guarantee of the proposed algorithm. Extensive experiments show that these priors organically benefit from each other to achieve state-of-the-art performance both quantitatively and qualitatively.

Scheduling-Guided Automatic Processing of Massive Hyperspectral Image Classification on Cloud Computing Architectures

The large data volume and high algorithm complexity of hyperspectral image (HSI) problems have posed big challenges for efficient classification of massive HSI data repositories. Recently, cloud computing architectures have become more relevant to address the big computational challenges introduced in the HSI field. This article proposes an acceleration method for HSI classification that relies on scheduling metaheuristics to automatically and optimally distribute the workload of HSI applications across multiple computing resources on a cloud platform. By analyzing the procedure of a representative classification method, we first develop its distributed and parallel implementation based on the MapReduce mechanism on Apache Spark. The subtasks of the processing flow that can be processed in a distributed way are identified as divisible tasks. The optimal execution of this application on Spark is further formulated as a divisible scheduling framework that takes into account both task execution precedences and task divisibility when allocating the divisible and indivisible subtasks onto computing nodes. The formulated scheduling framework is an optimization procedure that searches for optimized task assignments and partition counts for divisible tasks. Two metaheuristic algorithms are developed to solve this divisible scheduling problem. The scheduling results provide an optimized solution to the automatic processing of HSI big data on clouds, improving the computational efficiency of HSI classification by exploring the parallelism during the parallel processing flow. Experimental results demonstrate that our scheduling-guided approach achieves remarkable speedups by facilitating the automatic processing of HSI classification on Spark, and is scalable to the increasing HSI data volume.

Nonlocal Low-Rank Tensor Completion for Visual Data

In this paper, we propose a novel nonlocal patch tensor-based visual data completion algorithm and analyze its potential problems. Our algorithm consists of two steps: the first step is initializing the image with triangulation-based linear interpolation and the second step is grouping similar nonlocal patches as a tensor then applying the proposed tensor completion technique. Specifically, with treating a group of patch matrices as a tensor, we impose the low-rank constraint on the tensor through the recently proposed tensor nuclear norm. Moreover, we observe that after the first interpolation step, the image gets blurred and, thus, the similar patches we have found may not exactly match the reference. We name the problem "Patch Mismatch," and then in order to avoid the error caused by it, we further decompose the patch tensor into a low-rank tensor and a sparse tensor, which means the accepted horizontal strips in mismatched patches. Furthermore, our theoretical analysis shows that the error caused by Patch Mismatch can be decomposed into two components, one of which can be bounded by a reasonable assumption named local patch similarity, and the other part is lower than that using matrix completion. Extensive experimental results on real-world datasets verify our method's superiority to the state-of-the-art tensor-based image inpainting methods.

Temporal Pattern-Aware QoS Prediction via Biased Non-Negative Latent Factorization of Tensors

Quality-of-service (QoS) data vary over time, making it vital to capture the temporal patterns hidden in such dynamic data for predicting missing ones with high accuracy. However, currently latent factor (LF) analysis-based QoS-predictors are mostly defined on static QoS data without the consideration of such temporal dynamics. To address this issue, this paper presents a biased non-negative latent factorization of tensors (BNLFTs) model for temporal pattern-aware QoS prediction. Its main idea is fourfold: 1) incorporating linear biases into the model for describing QoS fluctuations; 2) constraining the model to be non-negative for describing QoS non-negativity; 3) deducing a single LF-dependent, non-negative, and multiplicative update scheme for training the model; and 4) incorporating an alternating direction method into the model for faster convergence. The empirical studies on two dynamic QoS datasets from real applications show that compared with the state-of-the-art QoS-predictors, BNLFT represents temporal patterns more precisely with high computational efficiency, thereby achieving the most accurate predictions for missing QoS data.

Learning a Low Tensor-Train Rank Representation for Hyperspectral Image Super-Resolution

Hyperspectral images (HSIs) with high spectral resolution only have the low spatial resolution. On the contrary, multispectral images (MSIs) with much lower spectral resolution can be obtained with higher spatial resolution. Therefore, fusing the high-spatial-resolution MSI (HR-MSI) with low-spatial-resolution HSI of the same scene has become the very popular HSI super-resolution scheme. In this paper, a novel low tensor-train (TT) rank (LTTR)-based HSI super-resolution method is proposed, where an LTTR prior is designed to learn the correlations among the spatial, spectral, and nonlocal modes of the nonlocal similar high-spatial-resolution HSI (HR-HSI) cubes. First, we cluster the HR-MSI cubes as many groups based on their similarities, and the HR-HSI cubes are also clustered according to the learned cluster structure in the HR-MSI cubes. The HR-HSI cubes in each group are much similar to each other and can constitute a 4-D tensor, whose four modes are highly correlated. Therefore, we impose the LTTR constraint on these 4-D tensors, which can effectively learn the correlations among the spatial, spectral, and nonlocal modes because of the well-balanced matricization scheme of TT rank. We formulate the super-resolution problem as TT rank regularized optimization problem, which is solved via the scheme of alternating direction method of multipliers. Experiments on HSI data sets indicate the effectiveness of the LTTR-based method.

Hyperspectral Images Denoising via Nonconvex Regularized Low-Rank and Sparse Matrix Decomposition

Hyperspectral images (HSIs) are often degraded by a mixture of various types of noise during the imaging process, including Gaussian noise, impulse noise, and stripes. Such complex noise could plague the subsequent HSIs processing. Generally, most HSI denoising methods formulate sparsity optimization problems with convex norm constraints, which over-penalize large entries of vectors, and may result in a biased solution. In this paper, a nonconvex regularized low-rank and sparse matrix decomposition (NonRLRS) method is proposed for HSI denoising, which can simultaneously remove the Gaussian noise, impulse noise, dead lines, and stripes. The NonRLRS aims to decompose the degraded HSI, expressed in a matrix form, into low-rank and sparse components with a robust formulation. To enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions, a novel nonconvex regularizer named as normalized ε -penalty, is presented, which can adaptively shrink each entry. In addition, an effective algorithm based on the majorization minimization (MM) is developed to solve the resulting nonconvex optimization problem. Specifically, the MM algorithm first substitutes the nonconvex objective function with the surrogate upper-bound in each iteration, and then minimizes the constructed surrogate function, which enables the nonconvex problem to be solved in the framework of reweighted technique. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed method.