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Recently, mapping a signal/image into a low rank Hankel/Toeplitz matrix has become an emerging alternative to the traditional sparse regularization, due to its ability to alleviate the basis mismatch between the true support in the…

In dynamic magnetic resonance (MR) imaging, low-rank plus sparse (L+S) decomposition, or robust principal component analysis (PCA), has achieved stunning performance. However, the selection of the parameters of L+S is empirical, and the…

Tensor completion is a challenging problem with various applications. Many related models based on the low-rank prior of the tensor have been proposed. However, the low-rank prior may not be enough to recover the original tensor from the…

Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…

As a real scenes sensing approach, depth information obtains the widespread applications. However, resulting from the restriction of depth sensing technology, the depth map captured in practice usually suffers terrible noise and missing…

Recent work in the matrix completion literature has shown that prior knowledge of a matrix's row and column spaces can be successfully incorporated into reconstruction programs to substantially benefit matrix recovery. This paper proposes a…

For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…

Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…

As a new color image representation tool, quaternion has achieved excellent results in color image processing problems. In this paper, we propose a novel low-rank quaternion matrix completion algorithm to recover missing data of color…

We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among…

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

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…

On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…

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…

Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…

This article investigates the problem of noisy low-rank matrix completion with a shared factor structure, leveraging the auxiliary information from the missing indicator matrix to enhance prediction accuracy. Despite decades of development…

Existing low-rank tensor completion (LRTC) approaches aim at restoring a partially observed tensor by imposing a global low-rank constraint on the underlying completed tensor. However, such a global rank assumption suffers the trade-off…

In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…

The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…