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Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires…

Recently, the \textit{Tensor Nuclear Norm~(TNN)} regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks. However, these models usually require smooth change of data along the third dimension to…

In this paper, a new definition of tensor p-shrinkage nuclear norm (p-TNN) is proposed based on tensor singular value decomposition (t-SVD). In particular, it can be proved that p-TNN is a better approximation of the tensor average rank…

Hyperspectral imaging, providing abundant spatial and spectral information simultaneously, has attracted a lot of interest in recent years. Unfortunately, due to the hardware limitations, the hyperspectral image (HSI) is vulnerable to…

The low rank tensor completion (LRTC) problem has attracted great attention in computer vision and signal processing. How to acquire high quality image recovery effect is still an urgent task to be solved at present. This paper proposes a…

Radio Frequency Neural Networks (RFNNs) have demonstrated advantages in realizing intelligent applications across various domains. However, as the model size of deep neural networks rapidly increases, implementing large-scale RFNN in…

In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding scheme. To overcome this drawback, a…

Hyperspectral image super-resolution addresses the problem of fusing a low-resolution hyperspectral image (LR-HSI) and a high-resolution multispectral image (HR-MSI) to produce a high-resolution hyperspectral image (HR-HSI). Tensor analysis…

Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by…

Low-rank matrix approximation, which aims to construct a low-rank matrix from an observation, has received much attention recently. An efficient method to solve this problem is to convert the problem of rank minimization into a nuclear norm…

Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for…

Non-local low-rank tensor approximation has been developed as a state-of-the-art method for hyperspectral image (HSI) denoising. Unfortunately, with more spectral bands for HSI, while the running time of these methods significantly…

Diffusion tensor imaging (DTI) holds significant importance in clinical diagnosis and neuroscience research. However, conventional model-based fitting methods often suffer from sensitivity to noise, leading to decreased accuracy in…

Most of the existing denoising algorithms are developed for grayscale images, while it is not a trivial work to extend them for color image denoising because the noise statistics in R, G, B channels can be very different for real noisy…

Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…

In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

The nuclear norm minimization (NNM) is commonly used to approximate the matrix rank by shrinking all singular values equally. However, the singular values have clear physical meanings in many practical problems, and NNM may not be able to…

Spectral variations pose a common challenge in analyzing hyperspectral images (HSI). To address this, low-rank tensor representation has emerged as a robust strategy, leveraging inherent correlations within HSI data. However, the spatial…

Recent findings indicate that over-parametrization, while crucial for successfully training deep neural networks, also introduces large amounts of redundancy. Tensor methods have the potential to efficiently parametrize over-complete…