Nonlocal Low-Rank Tensor Completion for Visual Data Zhang, Lefei; Song, Liangchen; Du, Bo ...
IEEE transactions on cybernetics,
2021-Feb., 2021-Feb, 2021-2-00, 20210201, Letnik:
51, Številka:
2
Journal Article
Recenzirano
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.
Hyperspectral anomaly detection (HAD) is regarded as an indispensable, pivotal technology in remote sensing and Earth science domains. Nevertheless, most existing detection approaches for anomaly ...targets flatten 3-D hyperspectral images (HSIs) with spatial and spectral information into 2-D spectral vector data, which virtually breaks up the internal spatial structure in HSIs and degenerates the detection performance. To this end, we directly consider the HSI data cube as a 3-D tensor and develop a novel tensor low-rank approximation (TLRA) detection algorithm to separate the sparse anomalous component from the background with low-rank characteristics. Then, in light of the multisubspace structure in heterogeneous backgrounds, we utilize multiple subspace learning (MSL) theory to encode the background tensor with a coefficient tensor and corresponding dictionary tensor. In addition, considering that different singular values indicate different information quantities and should be penalized to different extents, we introduce a tighter tensor rank surrogate named the <inline-formula> <tex-math notation="LaTeX">\epsilon </tex-math></inline-formula>-shrinkage tensor nuclear norm (<inline-formula> <tex-math notation="LaTeX">\epsilon </tex-math></inline-formula>-TNN) to recover the low-rank component more accurately. Meanwhile, concerning the sparse anomaly target, the <inline-formula> <tex-math notation="LaTeX">{l_{2,1}} </tex-math></inline-formula> constraint is incorporated to represent the group sparsity of the abnormal component. Finally, an effective iterative optimization algorithm based on the alternating direction method of multipliers (ADMM) is devised to solve the proposed TLRA-MSL model. We conduct extensive experiments on six hyperspectral datasets to prove the effectiveness and robustness of our method. The experimental results illustrate that better detection performance is obtained using the proposed model compared with other state-of-the-art algorithms.
•A low-rank tensor completion framework is developed for spatiotemporal traffic.•We use a truncated nuclear norm (TNN) in tensor rank approximation.•The TNN-based model shows superior performance on ...various traffic data sets.
Sparsity and missing data problems are very common in spatiotemporal traffic data collected from various sensing systems. Making accurate imputation is critical to many applications in intelligent transportation systems. In this paper, we formulate the missing data imputation problem in spatiotemporal traffic data in a low-rank tensor completion (LRTC) framework and define a novel truncated nuclear norm (TNN) on traffic tensors of location × day × time of day. In particular, we introduce an universal rate parameter to control the degree of truncation on all tensor modes in the proposed LRTC-TNN model, and this allows us to better characterize the hidden patterns in spatiotemporal traffic data. Based on the framework of the Alternating Direction Method of Multipliers (ADMM), we present an efficient algorithm to obtain the optimal solution for each variable. We conduct numerical experiments on four spatiotemporal traffic data sets, and our results show that the proposed LRTC-TNN model outperforms many state-of-the-art imputation models with missing rates/patterns. Moreover, the proposed model also outperforms other baseline models in extreme missing scenarios.
In this paper, we investigate tensor recovery problems within the tensor singular value decomposition (t-SVD) framework. We propose the partial sum of the tubal nuclear norm (PSTNN) of a tensor. The ...PSTNN is a surrogate of the tensor tubal multi-rank. We build two PSTNN-based minimization models for two typical tensor recovery problems, i.e., the tensor completion and the tensor principal component analysis. We give two algorithms based on the alternating direction method of multipliers (ADMM) to solve proposed PSTNN-based tensor recovery models. Experimental results on the synthetic data and real-world data reveal the superior of the proposed PSTNN.
•We propose the partial sum of the tubal nuclear norm (PSTNN) for tensor recovery.•The partial singular value thresholding (PSVT) is extended for complex matrices.•Two PSTNN minimization models are developed for TC and TRPCA problems.•Two efficient ADMM algorithms have been designed to solve the proposed models.•Extensive experiments are conducted on simulated and real-world data.
The Twist Tensor Nuclear Norm for Video Completion Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng ...
IEEE transaction on neural networks and learning systems,
12/2017, Letnik:
28, Številka:
12
Journal Article
In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to ...laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.
•Our model captures local and global structural information of the samples.•Data derive from linear or nonlinear subspaces can be accurately clustered.•Robust affinity matrices and weighted tensor ...nuclear norm are used to handle noise.•Experimental performance outperforms several state-of-the-art counter-parts.
Multi-view subspace clustering achieves impressive performance for high-dimensional data. However, many of these models do not sufficiently mine the intrinsic information among samples and consider the robustness problem of the affinity matrices, resulting in the degradation of clustering performance. To address these problems, we propose a novel high-order manifold regularized multi-view subspace clustering with robust affinity matrices and a weighted tensor nuclear norm (TNN) model (termed HMRMSC) to characterize real-world data. Specifically, all the similarity matrices of different views are first stacked into a third-order tensor. However, the constructed tensor may contain an additional inter-class representation since the data are usually noisy. Then, we use a technique similar to tensor principal component analysis (TPCA) to obtain a more robust similarity tensor, which is constrained by the so-called weighted TNN since the original TNN treats each singular value equally and usually considers no prior information of singular values. In addition, a high-order manifold regularized term is also added to utilize the manifold information of data. Finally, all the steps are unified into a framework, which is resolved by the augmented Lagrange multiplier (ALM) method. Experimental results on six representative datasets show that our model outperforms several state-of-the-art counterparts.
Multidimensional (M-D) seismic data denoising is cast as an underdetermined inverse problem whose solution hinges on effective image priors extracted from machine learning knowledge. However, ...modeling seismic image priors is challenging due to the M-D nature of seismic images. Among the most promising prevailing image prior techniques is learning prior knowledge of the underlying structure by various 2-D or 3-D deep learning (DL)-based methods. However, for higher dimensional seismic data such as 4-D prestack data, these DL denoising schemes undoubtedly fail to capture the complete image structure in the absence of the flattening operation. To address this challenge, we present a framelet-based order-<inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> tensor neural network (dubbed the FPTNN) model to implicitly learn the priors reflecting the typical behavior of clear M-D seismic images in a data-driven manner. First, motivated by the supremacy of the framelet transform over the Fourier transform, replacing the Fourier transform with the framelet gives a new definition with respect to the order-<inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> tensor-tensor product (t-product). Then, through the redefined order-<inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> t-product, the order-<inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> tNN framework is a straightforward extension of the tNN with a standard t-product for M-D seismic denoising. By exploiting the fact that the order-<inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> t-product can be computed through matrix multiplication in the framelet domain, we can readily reach the optimal weighted parameters in FPTNN via DL on a set of transformed matrix frontal slices. The experiments on both the synthetic and real field seismic datasets comprehensively demonstrate the advantages of our method against other state-of-the-art (SOTA) methods.
As a challenging problem, incomplete multi-view clustering (MVC) has drawn much attention in recent years. Most of the existing methods contain the feature recovering step inevitably to obtain the ...clustering result of incomplete multi-view datasets. The extra target of recovering the missing feature in the original data space or common subspace is difficult for unsupervised clustering tasks and could accumulate mistakes during the optimization. Moreover, the biased error is not taken into consideration in the previous graph-based methods. The biased error represents the unexpected change of incomplete graph structure, such as the increase in the intra-class relation density and the missing local graph structure of boundary instances. It would mislead those graph-based methods and degrade their final performance. In order to overcome these drawbacks, we propose a new graph-based method named Graph Structure Refining for Incomplete MVC (GSRIMC). GSRIMC avoids recovering feature steps and just fully explores the existing subgraphs of each view to produce superior clustering results. To handle the biased error, the biased error separation is the core step of GSRIMC. In detail, GSRIMC first extracts basic information from the precomputed subgraph of each view and then separates refined graph structure from biased error with the help of tensor nuclear norm. Besides, cross-view graph learning is proposed to capture the missing local graph structure and complete the refined graph structure based on the complementary principle. Extensive experiments show that our method achieves better performance than other state-of-the-art baselines.
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