Related papers: Low rank matrix recovery from Clifford orbits
A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…
The problem of recovering a matrix of low rank from an incomplete and possibly noisy set of linear measurements arises in a number of areas. In order to derive rigorous recovery results, the measurement map is usually modeled…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
Statistical inference and information processing of high-dimensional data often require efficient and accurate estimation of their second-order statistics. With rapidly changing data, limited processing power and storage at the acquisition…
We prove new results about the robustness of well-known convex noise-blind optimization formulations for the reconstruction of low-rank matrices from underdetermined linear measurements. Our results are applicable for symmetric rank-one…
Low-rank matrix recovery problems are inverse problems which naturally arise in various fields like signal processing, imaging and machine learning. They are non-convex and NP-hard in full generality. It is therefore a delicate problem to…
We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…
Existing results for low-rank matrix recovery largely focus on quadratic loss, which enjoys favorable properties such as restricted strong convexity/smoothness (RSC/RSM) and well conditioning over all low rank matrices. However, many…
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that properly constrained nuclear-norm…
Subspace recovery from corrupted and missing data is crucial for various applications in signal processing and information theory. To complete missing values and detect column corruptions, existing robust Matrix Completion (MC) methods…
Low-rank matrix recovery addresses the problem of recovering an unknown low-rank matrix from few linear measurements. Nuclear-norm minimization is a tractible approach with a recent surge of strong theoretical backing. Analagous to the…
We introduce a novel framework for an approxi- mate recovery of data matrices which are low-rank on graphs, from sampled measurements. The rows and columns of such matrices belong to the span of the first few eigenvectors of the graphs…
Consider the task of recovering an unknown $n$-vector from phaseless linear measurements. This task is the phase retrieval problem. Through the technique of lifting, this nonconvex problem may be convexified into a semidefinite rank-one…
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…
Common clustering methods, such as $k$-means and convex clustering, group similar vector-valued observations into clusters. However, with the increasing prevalence of matrix-valued observations, which often exhibit low rank characteristics,…
As a generalization of the standard phase retrieval problem, we seek to reconstruct symmetric rank-1 matrices from inner products with subclasses of positive semidefinite matrices. For such subclasses, we introduce random cubatures for…
Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets…
We study the Low Rank Phase Retrieval (LRPR) problem defined as follows: recover an $n \times q$ matrix $X^*$ of rank $r$ from a different and independent set of $m$ phaseless (magnitude-only) linear projections of each of its columns. To…
This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…
Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by…