Multi-Modal Medical Image Fusion Based on Improved Parameter Adaptive PCNN and Latent Low-Rank Representation

Multimodal medical image fusion can help physicians provide more accurate treatment plans for patients,as unimodal images provide limited valid information.To address the insufficient ability of traditional medical image fusion solutions to protect image details and significant information,a new multimodality medical image fusion method(NSST-PAPCNNLatLRR)is proposed in this paper.Firstly,the high and low-frequency sub-band coefficients are obtained by decomposing the source image using NSST.Then,the latent low-rank representation algorithm is used to process the low-frequency sub-band coefficients;An improved PAPCNN algorithm is also proposed for the fusion of high-frequency sub-band coefficients.The improved PAPCNN model was based on the automatic setting of the parameters,and the optimal method was configured for the time decay factor ae.The experimental results show that,in comparison with the five mainstream fusion algorithms,the new algorithm has significantly improved the visual effect over the comparison algorithm,enhanced the ability to characterize important information in images,and further improved the ability to protect the detailed information;the new algorithm has achieved at least four firsts in sixobjectiveindexes.

Multimodal Medical Image Fusion Based on Parameter Adaptive PCNN and Latent Low-rank Representation

Medical image fusion has been developed as an efficient assistive technology in various clinical applications such as medical diagnosis and treatment planning.Aiming at the problem of insufficient protection of image contour and detail information by traditional image fusion methods,a new multimodal medical image fusion method is proposed.This method first uses non-subsampled shearlet transform to decompose the source image to obtain high and low frequency subband coefficients,then uses the latent low rank representation algorithm to fuse the low frequency subband coefficients,and applies the improved PAPCNN algorithm to fuse the high frequency subband coefficients.Finally,based on the automatic setting of parameters,the optimization method configuration of the time decay factorαe is carried out.The experimental results show that the proposed method solves the problems of difficult parameter setting and insufficient detail protection ability in traditional PCNN algorithm fusion images,and at the same time,it has achieved great improvement in visual quality and objective evaluation indicators.

Research on infrared dim and small target detection algorithm based on low-rank tensor recovery

In order to rapidly and accurately detect infrared small and dim targets in the infrared image of complex scene collected by virtual prototyping of space-based downward-looking multiband detection,an improved detection algorithm of infrared small and dim target is proposed in this paper.Firstly,the original infrared images are changed into a new infrared patch tensor mode through data reconstruction.Then,the infrared small and dim target detection problems are converted to low-rank tensor recovery problems based on tensor nuclear norm in accordance with patch tensor characteristics,and inverse variance weighted entropy is defined for self-adaptive adjustment of sparseness.Finally,the low-rank tensor recovery problem with noise is solved by alternating the direction method to obtain the sparse target image,and the final small target is worked out by a simple partitioning algorithm.The test results in various spacebased downward-looking complex scenes show that such method can restrain complex background well by virtue of rapid arithmetic speed with high detection probability and low false alarm rate.It is a kind of infrared small and dim target detection method with good performance.

A malware propagation prediction model based on representation learning and graph convolutional networks

The traditional malware research is mainly based on its recognition and detection as a breakthrough point,without focusing on its propagation trends or predicting the subsequently infected nodes.The complexity of network structure,diversity of network nodes,and sparsity of data all pose difficulties in predicting propagation.This paper proposes a malware propagation prediction model based on representation learning and Graph Convolutional Networks(GCN)to address the aforementioned problems.First,to solve the problem of the inaccuracy of infection intensity calculation caused by the sparsity of node interaction behavior data in the malware propagation network,a mechanism based on a tensor to mine the infection intensity among nodes is proposed to retain the network structure information.The influence of the relationship between nodes on the infection intensity is also analyzed.Second,given the diversity and complexity of the content and structure of infected and normal nodes in the network,considering the advantages of representation learning in data feature extraction,the corresponding representation learning method is adopted for the characteristics of infection intensity among nodes.This can efficiently calculate the relationship between entities and relationships in low dimensional space to achieve the goal of low dimensional,dense,and real-valued representation learning for the characteristics of propagation spatial data.We also design a new method,Tensor2vec,to learn the potential structural features of malware propagation.Finally,considering the convolution ability of GCN for non-Euclidean data,we propose a dynamic prediction model of malware propagation based on representation learning and GCN to solve the time effectiveness problem of the malware propagation carrier.The experimental results show that the proposed model can effectively predict the behaviors of the nodes in the network and discover the influence of different characteristics of nodes on the malware propagation situation.

Low-Rank and Sparse Representation with Adaptive Neighborhood Regularization for Hyperspectral Image Classification

Low-Rank and Sparse Representation(LRSR)method has gained popularity in Hyperspectral Image(HSI)processing.However,existing LRSR models rarely exploited spectral-spatial classification of HSI.In this paper,we proposed a novel Low-Rank and Sparse Representation with Adaptive Neighborhood Regularization(LRSR-ANR)method for HSI classification.In the proposed method,we first represent the hyperspectral data via LRSR since it combines both sparsity and low-rankness to maintain global and local data structures simultaneously.The LRSR is optimized by using a mixed Gauss-Seidel and Jacobian Alternating Direction Method of Multipliers(M-ADMM),which converges faster than ADMM.Then to incorporate the spatial information,an ANR scheme is designed by combining Euclidean and Cosine distance metrics to reduce the mixed pixels within a neighborhood.Lastly,the predicted labels are determined by jointly considering the homogeneous pixels in the classification rule of the minimum reconstruction error.Experimental results based on three popular hyperspectral images demonstrate that the proposed method outperforms other related methods in terms of classification accuracy and generalization performance.

An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series expansion.The proof is also extended to any finite-dimensional inner-product space.

CANONICAL REPRESENTATIONS AND DEGREE OF FREEDOM FORMULAE OF ORTHOGONAL TENSORS IN N-DIMENSIONAL EUCLIDEAN SPACE

In this paper, with the help of the eigenvalue properties of orthogonal tensors in n-dimensional Euclidean space and the representations of the orthogonal tensors in 2-dimensional space, the canonical representations of orthogonal tensors in n-dimensional Euclidean space are easily gotten. The paper also gives all the constraint relationships among the principal invariants of arbitrarily given orthogonal tensor by use of Cayley-Hamilton theorem; these results make it possible to solve all the eigenvalues of any orthogonal tensor based on a quite reduced equation of m-th order, where m is the integer part ofn \2. Finally, the formulae of the degree of freedom of orthogonal tensors are given.

Explicit Algebraic Stress Model for Three-Dimensional Turbulent Buoyant Flows Derived Using Tensor Representation

An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant flux tensor into a two-dimensional and a three-dimensional component. The five-term basis was formed with the two-dimensional component of the buoyant flux tensor. As such, the derived EASM is limited to two-dimensional flows only. In this paper, a more general approach using a seven-term representation without partitioning the buoyant flux tensor is used to derive an EASM valid for two- and three-dimensional turbulent buoyant flows. Consequently, the basis tensors are formed with the fully three-dimensional buoyant flux tensor. The derived EASM has the two-dimensional flow as a special case. The matrices and the representation coefficients are further simplified using a four-term representation. When this four-term representation model is applied to calculate two-dimensional homogeneous buoyant flows, the results are essentially identical with those obtained previously using the two-dimensional component of the buoyant flux tensor. Therefore, the present approach leads to a more general EASM formulation that is equally valid for two- and three-dimensional turbulent buoyant flows.

Tensor-Product Representation for Switched Linear Systems

This paper presents the method for the construction of tensor-product representation for multivariate switched linear systems, based on a suitable tensor-product representation of vectors and matrices. We obtain a representation theorem for multivariate switched linear systems. The stability properties of the tensor-product representation are investigated in depth, achieving the important result that any stable switched systems can be constructed a stable tensor-product representation of finite dimension. It is shown that the tensor-product representation provides a high level framework for describing the dynamic behavior. The interpretation of expressions within the tensor-product representation framework leads to enhanced conceptual and physical understanding of switched linear systems dynamic behavior.

Weighted Sparse Image Classification Based on Low Rank Representation

The conventional sparse representation-based image classification usually codes the samples independently,which will ignore the correlation information existed in the data.Hence,if we can explore the correlation information hidden in the data,the classification result will be improved significantly.To this end,in this paper,a novel weighted supervised spare coding method is proposed to address the image classification problem.The proposed method firstly explores the structural information sufficiently hidden in the data based on the low rank representation.And then,it introduced the extracted structural information to a novel weighted sparse representation model to code the samples in a supervised way.Experimental results show that the proposed method is superiority to many conventional image classification methods.

Recovery of Corrupted Low-Rank Tensors

This paper studies the problem of recovering low-rank tensors, and the tensors are corrupted by both impulse and Gaussian noise. The problem is well accomplished by integrating the tensor nuclear norm and the l1-norm in a unified convex relaxation framework. The nuclear norm is adopted to explore the low-rank components and the l1-norm is used to exploit the impulse noise. Then, this optimization problem is solved by some augmented-Lagrangian-based algorithms. Some preliminary numerical experiments verify that the proposed method can well recover the corrupted low-rank tensors.

Non-intrusive temperature rise fault-identification of distribution cabinet based on tensor block-matching

In this study,a novel non-intrusive temperature rise fault-identification method for a distribution cabinet based on tensor block-matching is proposed.Two-stage data repair is used to reconstruct the temperature-field information to support the demand for temperature rise fault-identification of non-intrusive distribution cabinets.In the coarse-repair stage,this method is based on the outside temperature information of the distribution cabinet,using tensor block-matching technology to search for an appropriate tensor block in the temperature-field tensor dictionary,filling the target space area from the outside to the inside,and realizing the reconstruction of the three-dimensional temperature field inside the distribution cabinet.In the fine-repair stage,tensor super-resolution technology is used to fill the temperature field obtained from coarse repair to realize the smoothing of the temperature-field information inside the distribution cabinet.Non-intrusive temperature rise fault-identification is realized by setting clustering rules and temperature thresholds to compare the location of the heat source with the location of the distribution cabinet components.The simulation results show that the temperature-field reconstruction error is reduced by 82.42%compared with the traditional technology,and the temperature rise fault-identification accuracy is greater than 86%,verifying the feasibility and effectiveness of the temperature-field reconstruction and temperature rise fault-identification.

张量学习诱导的多视图谱聚类

现有的方法将通过张量奇异值分解(t-SVD)正则化的低秩表示应用到多视图子空间聚类中,取得了令人印象深刻的聚类性能.然而,它们都具有以下两个共同的缺点:(1)他们专注于探索样本之间的关系以构建表征,然后将其堆叠为张量,其计算复杂度至少为O(n2logn);(2)他们总是直接在整合的表征上运行标准的谱聚类算法,而忽略了不同表征对最终聚类结果的先验知识.为了解决这些问题,本文提出了一种新颖的张量学习诱导的多视图谱聚类(TLIMSC)方法,其中同时探索了空间聚类结构和互补信息.具体来说,该方法将关联样本和簇关系的多视图谱嵌入表示堆叠成张量,计算复杂度最终变为O(n logn).然后,将学习到的带有不同自适应置信度的表征与最终的一致聚类结果联系起来.在五个数据集上的广泛实验证明了TLIMSC所具有的有效性和高效性.

四元数矩阵方程(A_(1)XB_(1),…,A_(k)XB_(k))=(C_(1),…,C_(k))的极小范数最小二乘Toeplitz解

基于四元数矩阵实表示,结合矩阵H-表示和矩阵半张量积提出一种求解四元数矩阵方程(A_(1)XB_(1),…,A_(k)XB_(k))=(C_(1),…,C_(k))的极小范数最小二乘Toeplitz解的有效方法,给出该四元数矩阵方程存在Toeplitz解的充要条件及通解表达式.给出数值算法并通过算例分别从误差与计算时间两个方面验证该方法的有效性.

基于张量Tucker分解的高光谱图像异常目标识别

高光谱图像每个像素点的光谱信息包含数百甚至数千个波段,使得高光谱图像在维度上具有高度的复杂性,且由于光谱波段众多,其中存在大量的冗余信息,加大了异常目标识别计算的负担。为此,文中提出基于张量Tucker分解的高光谱图像异常目标识别方法。通过张量Tucker分解压缩高光谱图像后,采用依据高光谱图像数据样本学习的构造方法,构建压缩后高光谱图像的字典,获取高光谱图像数据的稀疏表示形式后,通过RX异常检测方法检测出高光谱图像中的异常目标。实验结果表明:所提方法张量分解重构高光谱图像后,可以缩短压缩时间,减少算法复杂度;重构后的高光谱图像清晰度高,且高光谱图像异常目标检测虚警率低。

基于张量分解嵌入的时序知识图谱推理

针对现有时序知识图谱推理中外推方法没有充分利用时间信息的问题,受张量分解模型的启发,提出将关系嵌入分为静态和动态(时序)2个部分,并通过头实体嵌入、关系嵌入和所有实体嵌入之间的双线性评分函数,计算得到对象实体的概率,从而预测对象实体。最后,在3个数据集上的实验结果验证了该方法的有效性。

An irreducible polynomial functional basis of two-dimensional Eshelby tensors

The two-dimensional (2D) Eshelby tensors are discussed. Based upon the complex variable method, an integrity basis of ten isotropic invariants of the 2D Eshelby tensors is obtained. Since an integrity basis is always a polynomial functional basis, these ten isotropic invariants are further proven to form an irreducible polynomial functional basis of the 2D Eshelby tensors.

FIfth-ORDER ISOTROPIC DESCARTES TENSOR

Fifth-order isotropic descartes tensor and its existence theorem and representation problems are researched, then a general representation formula of fifth-order isotropic descartes tensor is got.

PRINCIPAL AXIS INTRINSIC METHOD AND THE HIGH DIMENSIONAL TENSOR EQUATION AX－XA＝C

The present paper spreads the principal axis intrinsic method to the highdimensional case and discusses the solution of the tensor equation AX --XA = C

Parallel Active Subspace Decomposition for Tensor Robust Principal Component Analysis

Tensor robust principal component analysis has received a substantial amount of attention in various fields.Most existing methods,normally relying on tensor nuclear norm minimization,need to pay an expensive computational cost due to multiple singular value decompositions at each iteration.To overcome the drawback,we propose a scalable and efficient method,named parallel active subspace decomposition,which divides the unfolding along each mode of the tensor into a columnwise orthonormal matrix(active subspace)and another small-size matrix in parallel.Such a transformation leads to a nonconvex optimization problem in which the scale of nuclear norm minimization is generally much smaller than that in the original problem.We solve the optimization problem by an alternating direction method of multipliers and show that the iterates can be convergent within the given stopping criterion and the convergent solution is close to the global optimum solution within the prescribed bound.Experimental results are given to demonstrate that the performance of the proposed model is better than the state-of-the-art methods.