Related papers: Coherence-Based Performance Guarantees for Estimat…
We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…
We study the estimation of the covariance matrix $\Sigma$ of a $p$-dimensional normal random vector based on $n$ independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of…
Basis Pursuit (BP), Basis Pursuit DeNoising (BPDN), and LASSO are popular methods for identifying important predictors in the high-dimensional linear regression model, i.e. when the number of rows of the design matrix X is smaller than the…
We study sparse linear regression over a network of agents, modeled as an undirected graph and no server node. The estimation of the $s$-sparse parameter is formulated as a constrained LASSO problem wherein each agent owns a subset of the…
This paper describes computationally efficient approaches and associated theoretical performance guarantees for the detection of known targets and anomalies from few projection measurements of the underlying signals. The proposed approaches…
We consider a problem of recovering a high-dimensional vector $\mu$ observed in white noise, where the unknown vector $\mu$ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family…
The orthogonal matching pursuit (OMP) is one of the mainstream algorithms for sparse data reconstruction or approximation. It acts as a driving force for the development of several other greedy methods for sparse data reconstruction, and it…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…
We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…
We study the problem of detection of a high-dimensional signal function in the white Gaussian noise model. As well as a smoothness assumption on the signal function, we assume an additive sparse condition on the latter. The detection…
In the Multiple Measurements Vector (MMV) model, measurement vectors are connected to unknown, jointly sparse signal vectors through a linear regression model employing a single known measurement matrix (or dictionary). Typically, the…
We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative…
Compressed sensing is by now well-established as an effective tool for extracting sparsely distributed information, where sparsity is a discrete concept, referring to the number of dominant nonzero signal components in some basis for the…
We study the problem of recovering Gaussian data under adversarial corruptions when the noises are low-rank and the corruptions are on the coordinate level. Concretely, we assume that the Gaussian noises lie in an unknown $k$-dimensional…
In wireless communication systems, Orthogonal Frequency-Division Multiplexing (OFDM) includes variants using either a cyclic prefix (CP) or a zero padding (ZP) as the guard interval to avoid inter-symbol interference. OFDM is ideally suited…
In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and whose gradient estimates are inexact and possibly random. The noise is assumed to be bounded in…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
We propose robust sparse reduced rank regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained non-convex…
We propose a fast sequential algorithm for the fundamental problem of estimating frequencies and amplitudes of a noisy mixture of sinusoids. The algorithm is a natural generalization of Orthogonal Matching Pursuit (OMP) to the continuum…
In this paper, we consider the problem of collaboratively estimating the sparsity pattern of a sparse signal with multiple measurement data in distributed networks. We assume that each node makes Compressive Sensing (CS) based measurements…