Related papers: Cross: Efficient Low-rank Tensor Completion

Cross-correlation is a popular signal processing technique used in numerous location tracking systems for obtaining reliable range information. However, its efficient design and practical implementation has not yet been achieved on mote…

Let us consider a case where all of the elements in some continuous slices are missing in tensor data. In this case, the nuclear-norm and total variation regularization methods usually fail to recover the missing elements. The key problem…

The low-rank tensor completion (LRTC) problem aims to reconstruct a tensor from partial sample information, which has attracted significant interest in a wide range of practical applications such as image processing and computer vision.…

We introduce a Tucker tensor cross approximation method that constructs a low-rank representation of a $d$-dimensional tensor by sparsely sampling its fibers. These fibers are selected using the discrete empirical interpolation method…

In this paper, we present a method to certify the approximation quality of a low rank tensor to a given third order symmetric tensor. Under mild assumptions, best low rank approximation is attained if a control parameter is zero or…

We study the problem of low-rank tensor factorization in the presence of missing data. We ask the following question: how many sampled entries do we need, to efficiently and exactly reconstruct a tensor with a low-rank orthogonal…

Harmonic retrieval (HR) has a wide range of applications in the scenes where signals are modelled as a summation of sinusoids. Past works have developed a number of approaches to recover the original signals. Most of them rely on classical…

In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties -- the set of tensors with bounded Tucker…

Sparse and low rank tensor recovery has emerged as a significant area of research with applications in many fields such as computer vision. However, minimizing the $\ell_0$-norm of a vector or the rank of a matrix is NP-hard. Instead, their…

We propose an isogeometric solver for Poisson problems that combines i)low-rank tensor techniques to approximate the unknown solution and the system matrix, as a sum of a few terms having Kronecker product structure, ii) a Truncated…

Unlike matrix completion, tensor completion does not have an algorithm that is known to achieve the information-theoretic sample complexity rate. This paper develops a new algorithm for the special case of completion for nonnegative…

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…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

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…

Radio-frequency (RF) tomographic imaging is a promising technique for inferring multi-dimensional physical space by processing RF signals traversed across a region of interest. However, conventional RF tomography schemes are generally based…

In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…

This paper studies a recovery task of finding a low multilinear-rank tensor that fulfills some linear constraints in the general settings, which has many applications in computer vision and graphics. This problem is named as the low…

In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…

This paper is concerned with the problem of recovering third-order tensor data from limited samples. A recently proposed tensor decomposition (BMD) method has been shown to efficiently compress third-order spatiotemporal data. Using the…

Performance tuning, software/hardware co-design, and job scheduling are among the many tasks that rely on models to predict application performance. We propose and evaluate low-rank tensor decomposition for modeling application performance.…