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

The recently proposed tensor robust principal component analysis (TRPCA) methods based on tensor singular value decomposition (t-SVD) have achieved numerous successes in many fields. However, most of these methods are only applicable to…

Matrix completion focuses on recovering a matrix from a small subset of its observed elements, and has already gained cumulative attention in computer vision. Many previous approaches formulate this issue as a low-rank matrix approximation…

Robust tensor completion (RTC) aims to recover a low-rank tensor from its incomplete observation with outlier corruption. The recently proposed tensor ring (TR) model has demonstrated superiority in solving the RTC problem. However, the…

Compressed sensing (CS) methods in magnetic resonance imaging (MRI) offer rapid acquisition and improved image quality but require iterative reconstruction schemes with regularization to enforce sparsity. Regardless of the difficulty in…

The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high…

In this paper, we propose a new approach to solve low-rank tensor completion and robust tensor PCA. Our approach is based on some novel notion of (even-order) tensor ranks, to be called the M-rank, the symmetric M-rank, and the strongly…

Total variation (TV) regularization has proven effective for a range of computer vision tasks through its preferential weighting of sharp image edges. Existing TV-based methods, however, often suffer from the over-smoothing issue and…

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks…

In recent years, quaternion matrix completion (QMC) based on low-rank regularization has been gradually used in image de-noising and de-blurring.Unlike low-rank matrix completion (LRMC) which handles RGB images by recovering each color…

This paper studies the Tensor Robust Principal Component (TRPCA) problem which extends the known Robust PCA (Candes et al. 2011) to the tensor case. Our model is based on a new tensor Singular Value Decomposition (t-SVD) (Kilmer and Martin…

In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this…

Frequency modulated continuous wave (FMCW) radar is widely used in autonomous driving and industrial inspection due to its high-resolution target location and velocity estimation capability. However, the plethora of connected devices in…

For image denoising problems, the structure tensor total variation (STV)-based models show good performances when compared with other competing regularization approaches. However, the STV regularizer does not couple the local information of…

Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have…

This work studies the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is motivated by the recently proposed linear transforms based…

In this paper, we propose a regularization technique for noisy-image super-resolution and image denoising. Total variation (TV) regularization is adopted in many image processing applications to preserve the local smoothness. However, TV…

Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the…

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

Total variation (TV) regularization is popular in image restoration and reconstruction due to its ability to preserve image edges. To date, most research activities on TV models concentrate on image restoration from blurry and noisy…

Despite the popularity and practical success of total variation (TV) regularization for function estimation, surprisingly little is known about its theoretical performance in a statistical setting. While TV regularization has been known for…