相关论文: Harmonic Retrieval with $L_1$-Tucker Tensor Decomp…

This paper proposes a super-resolution harmonic retrieval method for uncorrelated strictly non-circular signals, whose covariance and pseudo-covariance present Toeplitz and Hankel structures, respectively. Accordingly, the augmented…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…

The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…

We consider the problem of learning mixtures of generalized linear models (GLM) which arise in classification and regression problems. Typical learning approaches such as expectation maximization (EM) or variational Bayes can get stuck in…

Recovering intrinsic data structure from corrupted observations plays an important role in various tasks in the communities of machine learning and signal processing. In this paper, we propose a novel model, named log-sum heuristic recovery…

We derive a CUR-type factorization for tensors in the Tucker format based on interpolatory decomposition, which we will denote as Higher Order Interpolatory Decomposition (HOID). Given a tensor $\mathcal{X}$, the algorithm provides a set of…

We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is $O(d\log d)$ for $d$-th…

Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in…

Suppose we are given an $n$-dimensional order-3 symmetric tensor $T \in (\mathbb{R}^n)^{\otimes 3}$ that is the sum of $r$ random rank-1 terms. The problem of recovering the rank-1 components is possible in principle when $r \lesssim n^2$…

The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required…

Tensor recovery has recently arisen in a lot of application fields, such as transportation, medical imaging and remote sensing. Under the assumption that signals possess sparse and/or low-rank structures, many tensor recovery methods have…

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…

This work revisits coupled tensor decomposition (CTD)-based hyperspectral super-resolution (HSR). HSR aims at fusing a pair of hyperspectral and multispectral images to recover a super-resolution image (SRI). The vast majority of the HSR…

This paper presents a canonical polyadic (CP) tensor decomposition that addresses unaligned observations. The mode with unaligned observations is represented using functions in a reproducing kernel Hilbert space (RKHS). We introduce a…

We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…

We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…

The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…