相关论文: Permutation recovery of spikes in noisy high-dimen…

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…

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…

Consider a noisy linear observation model with an unknown permutation, based on observing $y = \Pi^* A x^* + w$, where $x^* \in \mathbb{R}^d$ is an unknown vector, $\Pi^*$ is an unknown $n \times n$ permutation matrix, and $w \in…

We propose Selective Multiple Power Iterations (SMPI), a new algorithm to address the important Tensor PCA problem that consists in recovering a spike $\bf{v_0}^{\otimes k}$ corrupted by a Gaussian noise tensor $\bf{Z} \in…

In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…

We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…

We study asymmetric rank-one spiked tensor models in the high-dimensional regime, where the noise entries are independent and identically distributed with zero mean, unit variance, and finite fourth moment. This extends the classical…

This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our approach generates a high-dimensional and sparse generalized polynomial-chaos expansion that provides useful statistical information. The result…

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…

This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative…

We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new…

We formulate and solve a generalized inverse Navier-Stokes problem for the joint velocity field reconstruction and boundary segmentation of noisy flow velocity images. To regularize the problem we use a Bayesian framework with Gaussian…

In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…

We use tools from random matrix theory to study the multi-spiked tensor model, i.e., a rank-$r$ deformation of a symmetric random Gaussian tensor. In particular, thanks to the nature of local optimization methods used to find the maximum…

We introduce the spiked mixture model (SMM) to address the problem of estimating a set of signals from many randomly scaled and noisy observations. Subsequently, we design a novel expectation-maximization (EM) algorithm to recover all…

The problem of consistently estimating the sparsity pattern of a vector $\betastar \in \real^\mdim$ based on observations contaminated by noise arises in various contexts, including subset selection in regression, structure estimation in…

While normalizing flows for continuous data have been extensively researched, flows for discrete data have only recently been explored. These prior models, however, suffer from limitations that are distinct from those of continuous flows.…

One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while…

Recovering the support of sparse vectors in underdetermined linear regression models, \textit{aka}, compressive sensing is important in many signal processing applications. High SNR consistency (HSC), i.e., the ability of a support recovery…

Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from…