This article provides an overview of tensors, their properties, and their applications in
statistics. Tensors, also known as multidimensional arrays, are generalizations of matrices to …

Abstract The problem of Knowledge Base Completion can be framed as a 3rd-order binary
tensor completion problem. In this light, the Canonical Tensor Decomposition (CP) seems …

Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise
during the acquisition process, eg, Gaussian noise, impulse noise, dead lines, stripes, etc …

Tensor completion is a problem of filling the missing or unobserved entries of partially
observed tensors. Due to the multidimensional character of tensors in describing complex …

In recent years, low-rank based tensor completion, which is a higher order extension of
matrix completion, has received considerable attention. However, the low-rank assumption …

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 …

Infrared small target detection is an important fundamental task in the infrared system.
Therefore, many infrared small target detection methods have been proposed, in which the …

We study a completion problem of broad practical interest: the reconstruction of a low-rank
symmetric tensor from highly incomplete and randomly corrupted observations of its entries …

Moment and polynomial optimization has received high attention in recent decades. It has
beautiful theory and efficient methods, as well as broad applications for various …

In the noisy tensor completion problem we observe m entries (whose location is chosen
uniformly at random) from an unknown n_1\times n_2\times n_3 tensor T. We assume that T …