Related papers: Optimal Spectral Initialization for Signal Recover…

Latent class models are widely used for identifying unobserved subgroups from multivariate categorical data in social sciences, with binary data as a particularly popular example. However, accurately recovering individual latent class…

We study the problem of approximately recovering signals on a manifold from one-bit linear measurements drawn from either a Gaussian ensemble, partial circulant ensemble, or bounded orthonormal ensemble and quantized using Sigma-Delta or…

Our ability to structure materials at the nanoscale has, and continues to, enable key advances in optical control. In pursuit of optimal photonic designs, substantial progress has been made on two complementary fronts: bottom-up structural…

Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…

In this paper, we analyze the non-convex framework of Wirtinger Flow (WF) for phase retrieval and identify a novel sufficient condition for universal exact recovery through the lens of low rank matrix recovery theory. Via a perspective in…

We study the problem of exact community recovery in general, two-community block models, in the presence of node-attributed $side$ $information$. We allow for a very general side information channel for node attributes, and for pairwise…

We address the problem of reconstructing a multi-band signal from its sub-Nyquist point-wise samples. To date, all reconstruction methods proposed for this class of signals assumed knowledge of the band locations. In this paper, we develop…

In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, including…

Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…

In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted…

We discuss an approach to signal recovery in Generalized Linear Models (GLM) in which the signal estimation problem is reduced to the problem of solving a stochastic monotone variational inequality (VI). The solution to the stochastic VI…

We consider the problem of recovering elements of a low-dimensional model from under-determined linear measurements. To perform recovery, we consider the minimization of a convex regularizer subject to a data fit constraint. Given a model,…

The recovery of unknown signals from quadratic measurements finds extensive applications in fields such as phase retrieval, power system state estimation, and unlabeled distance geometry. This paper investigates the finite sample properties…

Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…

We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…

Recent efforts to accelerate first-order methods have focused on convex optimization problems that satisfy a geometric property known as error-bound condition, which covers a broad class of problems, including piece-wise linear programs and…

We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions, a simple subgradient method converges linearly when initialized within a constant relative distance of an…

Spectral estimation plays a fundamental role in frequency-domain identification and related signal processing problems. This paper revisits a 2-D spectral estimation problem formulated in terms of convex optimization. More precisely, we…

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…

Band selection has a great impact on the spectral recovery quality. To solve this ill-posed inverse problem, most band selection methods adopt hand-crafted priors or exploit clustering or sparse regularization constraints to find most…