Related papers: On the exact recovery of sparse signals via conic …
We discuss two new methods of recovery of sparse signals from noisy observation based on $\ell_1$- minimization. They are closely related to the well-known techniques such as Lasso and Dantzig Selector. However, these estimators come with…
Compressed sensing provides an efficient framework for reconstructing wave signals from reduced measurements. For multi-channel buoy data, the three displacement components exhibit intrinsic correlations, as wave motion contributes…
The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in…
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…
Sparse principal component analysis (SPCA) is widely used for dimensionality reduction and feature extraction in high-dimensional data analysis. Despite many methodological and theoretical developments in the past two decades, the…
The angular synchronization problem of estimating a set of unknown angles from their known noisy pairwise differences arises in various applications. It can be reformulated as a optimization problem on graphs involving the graph Laplacian…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
We present a new approach for computing approximate global minimizers to a large class of non-local pairwise interaction problems defined over probability distributions. The approach predicts candidate global minimizers, with a recovery…
A sparse regression approach for the computation of high-dimensional optimal feedback laws arising in deterministic nonlinear control is proposed. The approach exploits the control-theoretical link between Hamilton-Jacobi-Bellman PDEs…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
This paper considers a quadratically-constrained cardinality minimization problem with applications to digital filter design, subset selection for linear regression, and portfolio selection. Two relaxations are investigated: the continuous…
In this paper a new result of recovery of sparse vectors from deterministic and noisy measurements by l1 minimization is given. The sparse vector is randomly chosen and follows a generic p-sparse model introduced by Candes and al. The main…
We investigate the recovery of signals exhibiting a sparse representation in a general (i.e., possibly redundant or incomplete) dictionary that are corrupted by additive noise admitting a sparse representation in another general dictionary.…
The recently proposed modified-compressive sensing (modified-CS), which utilizes the partially known support as prior knowledge, significantly improves the performance of recovering sparse signals. However, modified-CS depends heavily on…
We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of {\em subset selection}…
We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…