Related papers: Exact 3D seismic data reconstruction using Tubal-A…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…
The recent proposed Tensor Nuclear Norm (TNN) [Lu et al., 2016; 2018a] is an interesting convex penalty induced by the tensor SVD [Kilmer and Martin, 2011]. It plays a similar role as the matrix nuclear norm which is the convex surrogate of…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
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…
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…
A crucial step in seismic data processing consists in reconstructing the wavefields at spatial locations where faulty or absent sources and/or receivers result in missing data. Several developments in seismic acquisition and interpolation…
Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…
In this paper, we study multi-dimensional image recovery. Recently, transform-based tensor nuclear norm minimization methods are considered to capture low-rank tensor structures to recover third-order tensors in multi-dimensional image…
Recently, low-rank tensor completion has become increasingly attractive in recovering incomplete visual data. Considering a color image or video as a three-dimensional (3D) tensor, existing studies have put forward several definitions of…
Non-random missing data is a ubiquitous yet undertreated flaw in multidimensional time series, fundamentally threatening the reliability of data-driven analysis and decision-making. Pure low-rank tensor completion, as a classical data…
In this paper we develop two new Tensor Alternating Steepest Descent algorithms for tensor completion in the low-rank $\star_{M}$-product format, whereby we aim to reconstruct an entire low-rank tensor from a small number of measurements…
Sparsity-based tensor recovery methods have shown great potential in suppressing seismic data noise. These methods exploit tensor sparsity measures capturing the low-dimensional structures inherent in seismic data tensors to remove noise by…
Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor…
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…
Reconstruction of seismic data with missing traces is a long-standing issue in seismic data processing. In recent years, rank reduction operations are being commonly utilized to overcome this problem, which require the rank of seismic data…
The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low-tubal-rank was shown to give a valuable characterization…
Low-rank tensor completion (LRTC) aims to recover a complete low-rank tensor from incomplete observed tensor, attracting extensive attention in various practical applications such as image processing and computer vision. However, current…
Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of nuclear norms of matricizations of a tensor has been shown to be very efficient in…