相关论文: Sharp thresholds for high-dimensional and noisy re…

We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…

Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…

We introduce a \emph{batch} version of sparse recovery, where the goal is to report a sequence of vectors $A_1',\ldots,A_m' \in \mathbb{R}^n$ that estimate unknown signals $A_1,\ldots,A_m \in \mathbb{R}^n$ using a few linear measurements,…

In this paper, we introduce a sparse approximation property of order $s$ for a measurement matrix ${\bf A}$: $$\|{\bf x}_s\|_2\le D \|{\bf A}{\bf x}\|_2+ \beta \frac{\sigma_s({\bf x})}{\sqrt{s}} \quad {\rm for\ all} \ {\bf x},$$ where ${\bf…

Solving under-determined systems of linear equations with sparse solutions attracted enormous amount of attention in recent years, above all, due to work of \cite{CRT,CanRomTao06,DonohoPol}. In \cite{CRT,CanRomTao06,DonohoPol} it was…

We propose a new iterative greedy algorithm for reconstructions of sparse signals with or without noisy perturbations in compressed sensing. The proposed algorithm, called \emph{subspace thresholding pursuit} (STP) in this paper, is a…

We study the problem of exact support recovery based on noisy observations and present Refined Least Squares (RLS). Given a set of noisy measurement $$ \myvec{y} = \myvec{X}\myvec{\theta}^* + \myvec{\omega},$$ and $\myvec{X} \in…

In signal processing and data recovery, reconstructing a signal from quadratic measurements poses a significant challenge, particularly in high-dimensional settings where measurements $m$ is far less than the signal dimension $n$ (i.e., $m…

Mixture models are widely used to fit complex and multimodal datasets. In this paper we study mixtures with high dimensional sparse latent parameter vectors and consider the problem of support recovery of those vectors. While parameter…

The observations in many applications consist of counts of discrete events, such as photons hitting a dector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model.…

We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…

The recovery of signals that are sparse not in a basis, but rather sparse with respect to an over-complete dictionary is one of the most flexible settings in the field of compressed sensing with numerous applications. As in the standard…

We study the fundamental limits for reconstruction in weighted graph (or matrix) database alignment. We consider a model of two graphs where $\pi^*$ is a planted uniform permutation and all pairs of edge weights $(A_{i,j},…

The constrained $\ell_p^p/\ell_q^p$ ratio model is scale invariant and is therefore attractive for sparse signal recovery. However, its nonconvex, nonsmooth, and fractional structure makes a unified theoretical and algorithmic analysis…

We study the problem of recovering an $s$-sparse signal $\mathbf{x}^{\star}\in\mathbb{C}^n$ from corrupted measurements $\mathbf{y} = \mathbf{A}\mathbf{x}^{\star}+\mathbf{z}^{\star}+\mathbf{w}$, where $\mathbf{z}^{\star}\in\mathbb{C}^m$ is…

In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…

We present a detailed analysis of the unconstrained $\ell_1$-weighted LASSO method for recovery of sparse data from its observation by randomly generated matrices, satisfying the Restricted Isometry Property (RIP) with constant $\delta<1$,…

Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…

This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…