PET Image Reconstruction with Kernel and Kernel Space Composite Regularizer

<div>Represented by the kernelized expectation maximization (KEM), the kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of non-kernelized MLEM methods in potentially large reconstruction variance and high sensitivity to iteration number. Also, it is generally difficult to simultaneously reduce image variance and preserve image details using kernels. To solve these problems, this paper presents a novel regularized KEM (RKEM) method with a kernel space composite regularizer for PET image reconstruction. The composite regularizer consists of a convex kernel space graph regularizer that smoothes the kernel coefficients, a non-convex kernel space energy regularizer that enhances the coefficients’ energy, and a composition constant that guarantees the convexity of composite regularizer. These kernel space regularizers are based on the theory of data manifold and graph regularization and can be constructed from different prior image data for simultaneous image variance reduction and image detail preservation. Using this kernel space composite regularizer and the technique of optimization transfer, a globally convergent iterative algorithm is derived for RKEM reconstruction. Tests and comparisons on the simulated and in vivo data are presented to validate and evaluate the proposed algorithm, and demonstrate its better performance and advantages over KEM and other conventional methods.</div>

PET Image Reconstruction with Kernel and Kernel Space Composite Regularizer

<div>Represented by the kernelized expectation maximization (KEM), the kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of non-kernelized MLEM methods in potentially large reconstruction variance and high sensitivity to iteration number. Also, it is generally difficult to simultaneously reduce image variance and preserve image details using kernels. To solve these problems, this paper presents a novel regularized KEM (RKEM) method with a kernel space composite regularizer for PET image reconstruction. The composite regularizer consists of a convex kernel space graph regularizer that smoothes the kernel coefficients, a non-convex kernel space energy regularizer that enhances the coefficients’ energy, and a composition constant that guarantees the convexity of composite regularizer. These kernel space regularizers are based on the theory of data manifold and graph regularization and can be constructed from different prior image data for simultaneous image variance reduction and image detail preservation. Using this kernel space composite regularizer and the technique of optimization transfer, a globally convergent iterative algorithm is derived for RKEM reconstruction. Tests and comparisons on the simulated and in vivo data are presented to validate and evaluate the proposed algorithm, and demonstrate its better performance and advantages over KEM and other conventional methods.</div>

Hyper-Laplacian regularized multi-view subspace clustering with jointing representation learning and weighted tensor nuclear norm constraint

In recent years, tensor-Singular Value Decomposition (t-SVD) based tensor nuclear norm has achieved remarkable progress in multi-view subspace clustering. However, most existing clustering methods still have the following shortcomings: (a) It has no meaning in practical applications for singular values to be treated equally. (b) They often ignore that data samples in the real world usually exist in multiple nonlinear subspaces. In order to solve the above shortcomings, we propose a hyper-Laplacian regularized multi-view subspace clustering model that joints representation learning and weighted tensor nuclear norm constraint, namely JWHMSC. Specifically, in the JWHMSC model, firstly, in order to capture the global structure between different views, the subspace representation matrices of all views are stacked into a low-rank constrained tensor. Secondly, hyper-Laplace graph regularization is adopted to preserve the local geometric structure embedded in the high-dimensional ambient space. Thirdly, considering the prior information of singular values, the weighted tensor nuclear norm (WTNN) based on t-SVD is introduced to treat singular values differently, which makes the JWHMSC more accurately obtain the sample distribution of classification information. Finally, representation learning, WTNN constraint and hyper-Laplacian graph regularization constraint are integrated into a framework to obtain the overall optimal solution of the algorithm. Compared with the state-of-the-art method, the experimental results on eight benchmark datasets show the good performance of the proposed method JWHMSC in multi-view clustering.

Graph Regularized Deep Sparse Representation for Unsupervised Anomaly Detection

Anomaly detection (AD) aims to distinguish the data points that are inconsistent with the overall pattern of the data. Recently, unsupervised anomaly detection methods have aroused huge attention. Among these methods, feature representation (FR) plays an important role, which can directly affect the performance of anomaly detection. Sparse representation (SR) can be regarded as one of matrix factorization (MF) methods, which is a powerful tool for FR. However, there are some limitations in the original SR. On the one hand, it just learns the shallow feature representations, which leads to the poor performance for anomaly detection. On the other hand, the local geometry structure information of data is ignored. To address these shortcomings, a graph regularized deep sparse representation (GRDSR) approach is proposed for unsupervised anomaly detection in this work. In GRDSR, a deep representation framework is first designed by extending the single layer MF to a multilayer MF for extracting hierarchical structure from the original data. Next, a graph regularization term is introduced to capture the intrinsic local geometric structure information of the original data during the process of FR, making the deep features preserve the neighborhood relationship well. Then, a L1-norm-based sparsity constraint is added to enhance the discriminant ability of the deep features. Finally, a reconstruction error is applied to distinguish anomalies. In order to demonstrate the effectiveness of the proposed approach, we conduct extensive experiments on ten datasets. Compared with the state-of-the-art methods, the proposed approach can achieve the best performance.

Non-negative sparse Laplacian regularized latent multi-view subspace clustering

Recently, in the area of artificial intelligence and machine learning, subspace clustering of multi-view data is a research hotspot. The goal is to divide data samples from different sources into different groups. We proposed a new subspace clustering method for multi-view data which termed as Non-negative Sparse Laplacian regularized Latent Multi-view Subspace Clustering (NSL2MSC) in this paper. The method proposed in this paper learns the latent space representation of multi view data samples, and performs the data reconstruction on the latent space. The algorithm can cluster data in the latent representation space and use the relationship of different views. However, the traditional representation-based method does not consider the non-linear geometry inside the data, and may lose the local and similar information between the data in the learning process. By using the graph regularization method, we can not only capture the global low dimensional structural features of data, but also fully capture the nonlinear geometric structure information of data. The experimental results show that the proposed method is effective and its performance is better than most of the existing alternatives.