Related papers: An ideal-sparse generalized moment problem reformu…

Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize…

Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…

Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We…

We present an algorithm for low rank decomposition of tensors of any symmetry type, from fully asymmetric to fully symmetric. It recovers the decomposition one summand at a time via the higher-order power method. This approach is known to…

Modern neural networks have revolutionized the fields of computer vision (CV) and Natural Language Processing (NLP). They are widely used for solving complex CV tasks and NLP tasks such as image classification, image generation, and machine…

The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…

Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is…

In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…

Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…

In this paper, we study the problem of a batch of linearly correlated image alignment, where the observed images are deformed by some unknown domain transformations, and corrupted by additive Gaussian noise and sparse noise simultaneously.…

This article addresses the image denoising problem in the situations of strong noise. We propose a dual sparse decomposition method. This method makes a sub-dictionary decomposition on the over-complete dictionary in the sparse…

We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…

We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the…

A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step.…

In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the…

Sparse codes in neuroscience have been suggested to offer certain computational advantages over other neural representations of sensory data. To explore this viewpoint, a sparse code is used to represent natural images in an optimal control…

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to…

In this paper, we propose a new unified optimization algorithm for general tensor decomposition which is formulated as an inverse problem for low-rank tensors in the general linear observation models. The proposed algorithm supports three…

This paper addresses an ill-posed problem of recovering a color image from its compressively sensed measurement data. Differently from the typical 1D vector-based approach of the state-of-the-art methods, we exploit the nonlocal…

In numerous applications, binary reactions or event counts are observed and stored within high-order tensors. Tensor decompositions (TDs) serve as a powerful tool to handle such high-dimensional and sparse data. However, many traditional…