Related papers: H2TF for Hyperspectral Image Denoising: Where Hier…
The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…
Cross-spectral image guided denoising has shown its great potential in recovering clean images with rich details, such as using the near-infrared image to guide the denoising process of the visible one. To obtain such image pairs, a…
Second-order Latent Factor (SLF) model, a class of low-rank representation learning methods, has proven effective at extracting node-to-node interaction patterns from High-dimensional and Incomplete (HDI) data. However, its optimization is…
The higher-order tensor renormalization group (HOTRG) is a fundamental method to calculate the physical quantities by using a tensor network representation. This method is based on the singular value decomposition (SVD) to take the…
The higher order singular value decomposition (HOSVD) of tensors is a generalization of matrix SVD. The perturbation analysis of HOSVD under random noise is more delicate than its matrix counterpart. Recently, polynomial time algorithms…
We present a new formulation of the hyperbolic singular value decomposition (HSVD) for an arbitrary complex (or real) matrix without hyperexchange matrices and redundant invariant parameters. In our formulation, we use only the concept of…
Non-negative matrix factorization (NMF) is an important tool in signal processing and widely used to separate mixed sources into their components. Algorithms for NMF require that the user choose the number of components in advance, and if…
Hyperspectral image has become increasingly crucial due to its abundant spectral information. However, It has poor spatial resolution with the limitation of the current imaging mechanism. Nowadays, many convolutional neural networks have…
Learning neural fields has been an active topic in deep learning research, focusing, among other issues, on finding more compact and easy-to-fit representations. In this paper, we introduce a novel low-rank representation termed Tensor…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
Non-local low-rank tensor approximation has been developed as a state-of-the-art method for hyperspectral image (HSI) restoration, which includes the tasks of denoising, compressed HSI reconstruction and inpainting. Unfortunately, while its…
This paper studies the data sparsity problem in multi-view learning. To solve data sparsity problem in multiview ratings, we propose a generic architecture of deep transfer tensor factorization (DTTF) by integrating deep learning and…
We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the…
The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential…
Single Image Reflection Removal (SIRR) technique plays a crucial role in image processing by eliminating unwanted reflections from the background. These reflections, often caused by photographs taken through glass surfaces, can…
The t-SVD based Tensor Robust Principal Component Analysis (TRPCA) decomposes low rank multi-linear signal corrupted by gross errors into low multi-rank and sparse component by simultaneously minimizing tensor nuclear norm and l 1 norm. But…
This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost…
Table structure recognition (TSR) aims to convert tabular images into a machine-readable format, where a visual encoder extracts image features and a textual decoder generates table-representing tokens. Existing approaches use classic…
Image denoising is a typical ill-posed problem due to complex degradation. Leading methods based on normalizing flows have tried to solve this problem with an invertible transformation instead of a deterministic mapping. However, the…
Recent advancements in computer vision have highlighted the scalability of Vision Transformers (ViTs) across various tasks, yet challenges remain in balancing adaptability, computational efficiency, and the ability to model higher-order…