Related papers: Robust Low-Rank Tensor Completion based on M-produ…

Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…

Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally…

Total Variation (TV) and related extensions have been popular in image restoration due to their robust performance and wide applicability. While the original formulation is still relevant after two decades of extensive research, its…

The nuclear norm and Schatten-$p$ quasi-norm are popular rank proxies in low-rank matrix recovery. However, computing the nuclear norm or Schatten-$p$ quasi-norm of a tensor is hard in both theory and practice, hindering their application…

We propose a new tensor completion method based on tensor trains. The to-be-completed tensor is modeled as a low-rank tensor train, where we use the known tensor entries and their coordinates to update the tensor train. A novel tensor train…

Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of…

Various problems in data analysis and statistical genetics call for recovery of a column-sparse, low-rank matrix from noisy observations. We propose ReFACTor, a simple variation of the classical Truncated Singular Value Decomposition (TSVD)…

Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…

We study a noisy tensor completion problem of broad practical interest, namely, the reconstruction of a low-rank tensor from highly incomplete and randomly corrupted observations of its entries. While a variety of prior work has been…

Robust tensor principal component analysis (RTPCA) can separate the low-rank component and sparse component from multidimensional data, which has been used successfully in several image applications. Its performance varies with different…

The tensor data recovery task has thus attracted much research attention in recent years. Solving such an ill-posed problem generally requires to explore intrinsic prior structures underlying tensor data, and formulate them as certain forms…

Supervised learning has been widely used for attack categorization, requiring high-quality data and labels. However, the data is often imbalanced and it is difficult to obtain sufficient annotations. Moreover, supervised models are subject…

In this paper a new Riemannian rank adaptive method (RRAM) is proposed for the low-rank tensor completion problem (LRTCP) formulated as a least-squares optimization problem on the algebraic variety of tensors of bounded tensor-train (TT)…

The fully-connected tensor network (FCTN) decomposition has gained prominence in the field of tensor completion owing to its powerful capacity to capture the low-rank characteristics of tensors. Nevertheless, the recovery of local details…

The modern convolutional neural networks although achieve great results in solving complex computer vision tasks still cannot be effectively used in mobile and embedded devices due to the strict requirements for computational complexity,…

In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…

In this paper, we propose a novel approach to hyperspectral image super-resolution by modeling the global spatial-and-spectral correlation and local smoothness properties over hyperspectral images. Specifically, we utilize the tensor…

Vector valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns.…

In this paper we propose efficient randomized fixed-precision techniques for low tubal rank approximation of tensors. The proposed methods are faster and more efficient than the existing fixed-precision algorithms for approximating the…

In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…