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Video has become one of the main ways of information transmission with the development of the Internet. Video copyright protection becomes an urgent task. Video watermark technology embeds copyright into the redundant information of the carrier, and video copyright protection is achieved. However, most video watermark algorithms do not use the correlation and redundancy among adjacent frames of a video and are weak to resist frame attacks. In order to make up this shortage and improve robustness, a video watermark algorithm based on a tensor feature map is proposed. A grayscale video segment with the same scene is selected and represented as a 3-order tensor, a high-order singular value decomposition is performed on the video tensor to obtain a stable core tensor and three factor matrices. A feature tensor is obtained by the mode-3 product of the video tensor with the transpose of the factor matrix that contains a time axis. It is called a tensor feature map. Since the tensor feature map contains the main information of each frame of a video, the watermark is distributed in each frame of a video by embedding the watermark into the tensor feature map. The first-order discrete wavelet transform and discrete cosine transform are used to embed the watermark into the tensor feature map. The experimental results show that the proposed watermark algorithm based on the tensor feature map has better transparency and is robust to common video attacks.

As a kind of transportation in a smart city, urban public bicycles have been adopted by major cities and bear the heavy responsibility of the “last mile” of urban public transportation. At present, the main problem of the urban public bicycle system is that it is difficult for users to rent a bike during peak h, and real-time monitoring cannot be solved adequately. Therefore, predicting the demand for bicycles in a certain period and performing redistribution in advance is of great significance for solving the lag of bicycle system scheduling with the help of IoT. Based on the HOSVD-LSTM prediction model, a prediction model of urban public bicycles based on the hybrid model is proposed by transforming the source data (multiple time series) into a high-order tensor time series. Furthermore, it uses the tensor decomposition technology (HOSVD decomposition) to extract new features (kernel tenor) from higher-order tensors. At the same time, these kernel tenors are directly used to train tensor LSTM models to obtain new kernel tenors. The inverse tensor decomposition and high-dimensional, multidimensional, and tensor dimensionality reduction were introduced. The new kernel tenor obtains the predicted value of the source sequence. Then the bicycle rental amount is predicted.

Ultrasonic welding has been used for joining lithium-ion battery cells in electric vehicle manufacturing. The geometric profile change of tool shape significantly affects the weld quality and should be monitored during production. In this paper, a high-order decomposition method is suggested for tool wear monitoring. In the proposed monitoring scheme, a low dimensional set of monitoring features is extracted from the high dimensional tool profile measurement data for detecting tool wear at an early stage. Furthermore, the proposed method can be effectively used to analyze the data cross-correlation structure in order to help identify the unusual wear pattern and find the associated assignable cause. The effectiveness of the proposed monitoring method was demonstrated using a simulation and a real-world case study.

Prior to the estimation process of channelized reservoirs, in the context of any Assisted History Matching method, the parameterization of facies field is a necessary task. The parameterization of the facies field consists of defining a numerical field (parameter field) on the reservoir domain so that, using a projection function, we are able to recover the facies field from the values of parameter field. One of the most important issues encountered is the loss of the multipoint geostatistical properties in the updates (channel continuity). In this study, we start from an initial (global) parameterization of the channelized field and infer from it a low-dimensional parameterization obtained after a high-order singular value decomposition of a tensor built with the parameter fields. We decompose the parameter field as a linear combination of some basis functions with coefficients. The decomposition is followed by a truncation so that we keep the relevant information from the channel continuity perspective, but with a small number of coefficients. The coefficients will represent the low-dimensional parameterization and are further introduced in the estimation process of facies field, using the Ensemble Smoother with Multiple Data Assimilations (ES-MDA). For a fair assessment of the parameterization, we perform a comparison of the results with those obtained by applying the traditional truncated singular value decomposition and the global parameterization. In addition, we compare the parameterization with a low-dimensional parameterization defined with the PCA decomposition. The comparison is done from the perspective of multipoint geostatistical characteristics of the updates and predictions. We show that the new parameterization is able to better keep the multipoint geostatistical structure in the updates than the other parameterizations, while the prediction capabilities are the same.

Recently, machine learning methods have gained lots of attention from researchers seeking to analyze brain images such as Resting-State Functional Magnetic Resonance Imaging (rs-fMRI) to obtain a deeper understanding of the brain and such related diseases, for example, Alzheimer's disease. Finding the common patterns caused by a brain disorder through analysis of the functional connectivity (FC) network along with discriminating brain diseases from normal controls have long been the two principal goals in studying rs-fMRI data. The majority of FC extraction methods calculate the FC matrix for each subject and then use simple techniques to combine them and obtain a general FC matrix. In addition, the state-of-the-art classification techniques for finding subjects with brain disorders also rely on calculating an FC for each subject, vectorizing, and feeding them to the classifier. Considering these problems and based on multi-dimensional nature of the data, we have come up with a novel tensor framework in which a general FC matrix is obtained without the need to construct an FC matrix for each sample. This framework also allows us to reduce the dimensionality and create a novel discriminant function that rather than using FCs works directly with each sample, avoids vectorization in any step, and uses the test data in the training process without forcing any prior knowledge of its label into the classifier. Extensive experiments using the ADNI dataset demonstrate that our proposed framework effectively boosts the fMRI classification performance and reveals novel connectivity patterns in Alzheimer's disease at its early stages.

In recent years, block-based compressive sensing (BCS) has been extensively studied because it can reduce computational complexity and data storage by dividing the image into smaller patches, but the performance of the reconstruction algorithm is not satisfactory. In this paper, a new reconstruction model for image and video is proposed. The model makes full use of spatio-temporal correlation and utilizes low-rank tensor approximation to improve the quality of the reconstructed image and video. For image recovery, the proposed model obtains a low-rank approximation of a tensor formed by non-local similar patches, and improves the reconstruction quality from a spatial perspective by combining non-local similarity and low-rank property. For video recovery, the reconstruction process is divided into two phases. In the first phase, each frame of the video sequence is regarded as an independent image to be reconstructed by taking advantage of spatial property. The second phase performs tensor approximation through searching similar patches within frames near the target frame, to achieve reconstruction by putting the spatio-temporal correlation into full play. The resulting model is solved by an efficient Alternating Direction Method of Multipliers (ADMM) algorithm. A series of experiments show that the quality of the proposed model is comparable to the current state-of-the-art recovery methods.

In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named sparse tensor alternating thresholding for singular value decomposition (STAT-SVD) is proposed. The proposed procedure features a novel double projection & thresholding scheme, which provides a sharp criterion for thresholding in each iteration. Compared with regular tensor SVD model, STAT-SVD permits more robust estimation under weaker assumptions. Both the upper and lower bounds for estimation accuracy are developed. The proposed procedure is shown to be minimax rate-optimal in a general class of situations. Simulation studies show that STAT-SVD performs well under a variety of configurations. We also illustrate the merits of the proposed procedure on a longitudinal tensor dataset on European country mortality rates. Supplementary materials for this article are available online.

An ultrasonic reverse time migration imaging method, based on high-order singular value decomposition, is proposed in the study to solve the problems of low signal-to-noise ratio (SNR) and excessive artifacts in defect ultrasonic detection imaging results of materials with high noise levels. In this method, based on the 3D structural properties of the ultrasonic full-matrix capture data, higher-order singular value decomposition is directly performed with the 3D data. The method overcomes the difficulty in selecting the number of singular values in the original singular value decomposition noise-reduction algorithm and realizes the one-step noise reduction processing of all the signals. Subsequently, the reverse time migration imaging is performed in the frequency domain, and high-quality acoustic images are obtained. The effects of the number of array elements, the center frequency of the excitation signal, and the number of defects on the denoising effect of the algorithm are investigated. It was experimentally demonstrated that the method could suppress the interference of noise signals and significantly improve the imaging SNR compared with total focusing method and the reverse time migration.

Purpose Compressed Sensing Magnetic Resonance Imaging (CS-MRI) is a promising technique to accelerate dynamic cardiac MR imaging (DCMRI). For DCMRI, the CS-MRI usually exploits image signal sparsity and low-rank property to reconstruct dynamic images from the undersampled k-space data. In this paper, a novel CS algorithm is investigated to improve dynamic cardiac MR image reconstruction quality under the condition of minimizing the k-space recording. Methods The sparse representation of 3D cardiac magnetic resonance data is implemented by synergistically integrating 3D total generalized variation (3D-TGV) algorithm and high order singular value decomposition (HOSVD) based Tensor Decomposition, termed k-t TGV-TD method. In the proposed method, the low rank structure of the 3D dynamic cardiac MR data is performed with the HOSVD method, and the localized image sparsity is achieved by the 3D-TGV method. Moreover, the Fast Composite Splitting Algorithm (FCSA) method, combining the variable splitting with operator splitting techniques, is employed to solve the low-rank and sparse problem. Two different cardiac MR datasets (cardiac perfusion and cine MR datasets) are used to evaluate the performance of the proposed method. Results Compared with the state-of-art methods, such as k-t SLR, 3D-TGV, HOSVD based tensor decomposition and low-rank plus sparse method, the proposed k-t TGV-TD method can offer improved reconstruction accuracy in terms of higher peak SNR (PSNR) and structural similarity index (SSIM). The proposed k-t TGV-TD method can achieve significantly better and stable reconstruction results than state-of-the-art methods in terms of both PSNR and SSIM, especially for cardiac perfusion MR dataset. Conclusions This work proved that the k-t TGV-TD method was an effective sparse representation way for DCMRI, which was capable of significantly improving the reconstruction accuracy with different acceleration factors.