Related papers: Hankel Matrix Nuclear Norm Regularized Tensor Comp…
In this paper, we investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. We show that a gradient descent algorithm with initial value obtained from a spectral method can,…
We study the recovery of multiple high-dimensional signals from two noisy, correlated modalities: a spiked matrix and a spiked tensor sharing a common low-rank structure. This setting generalizes classical spiked matrix and tensor models,…
We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the…
Tensors serve as a crucial tool in the representation and analysis of complex, multi-dimensional data. As data volumes continue to expand, there is an increasing demand for developing optimization algorithms that can directly operate on…
This work considers a super-resolution framework for overcomplete tensor decomposition. Specifically, we view tensor decomposition as a super-resolution problem of recovering a sum of Dirac measures on the sphere and solve it by minimizing…
This work investigates the geometry of a nonconvex reformulation of minimizing a general convex loss function $f(X)$ regularized by the matrix nuclear norm $\|X\|_*$. Nuclear-norm regularized matrix inverse problems are at the heart of many…
Anisotropic two-dimensional diffraction signals encode additional structural information, including atom-pair angular distributions, beyond conventional isotropic scattering. However, experimental constraints such as beam stops result in…
We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
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…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
The recently established Convolution Nuclear Norm Minimization (CNNM) addresses the problem of \textit{tensor completion with arbitrary sampling} (TCAS), which involves restoring a tensor from a subset of its entries sampled in an arbitrary…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…
We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of completing or denoising low-rank matrices that are structured, e.g., that possess a Hankel, Toeplitz or block-Hankel/Toeplitz structure. The algorithm…
We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The law of large numbers and the central limit theorem suggest…
The $k$-tensor Ising model is an exponential family on a $p$-dimensional binary hypercube for modeling dependent binary data, where the sufficient statistic consists of all $k$-fold products of the observations, and the parameter is an…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
Recently, the \textit{Tensor Nuclear Norm~(TNN)} regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks. However, these models usually require smooth change of data along the third dimension to…