相关论文: Sparse Recovery from Extreme Eigenvalues Deviation…

We formulate a generalization of the Restricted Isometry Property (RIP) referred to as the Restricted Quasiconvexity Isometry Property (RQIP) for alpha stable random projections with $0<\alpha<1$. A lower bound on the number of rows for…

In this paper, we study the edge eigenvalues of random geometric graphs (RGGs) generated by multivariate Gaussian samples in the sparse regime under a broad class of distance metrics. Previous work on edge eigenvalues under related setups…

The recovery of sparsest overcomplete representation has recently attracted intensive research activities owe to its important potential in the many applied fields such as signal processing, medical imaging, communication, and so on. This…

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…

Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…

Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via multiplicative…

Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…

The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy…

Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…

We consider minimum variance estimation within the sparse linear Gaussian model (SLGM). A sparse vector is to be estimated from a linearly transformed version embedded in Gaussian noise. Our analysis is based on the theory of reproducing…

Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…

We develop a unified approach to bounding the largest and smallest singular values of an inhomogeneous random rectangular matrix, based on the non-backtracking operator and the Ihara-Bass formula for general random Hermitian matrices with a…

Motivated by the construction of tractable robust estimators via convex relaxations, we present conditions on the sample size which guarantee an augmented notion of Restricted Eigenvalue-type condition for Gaussian designs. Such a notion is…

We consider the problem of sparsity-constrained $M$-estimation when both explanatory and response variables have heavy tails (bounded 4-th moments), or a fraction of arbitrary corruptions. We focus on the $k$-sparse, high-dimensional regime…

In this paper, we discuss the statistical properties of the $\ell_q$ optimization methods $(0<q\leq 1)$, including the $\ell_q$ minimization method and the $\ell_q$ regularization method, for estimating a sparse parameter from noisy…

We prove that iid random vectors that satisfy a rather weak moment assumption can be used as measurement vectors in Compressed Sensing, and the number of measurements required for exact reconstruction is the same as the best possible…

In this paper we theoretically study exact recovery of sparse vectors from compressed measurements by minimizing a general nonconvex function that can be decomposed into the sum of single variable functions belonging to a class of smooth…

Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including $\ell_1$ and nuclear norm minimization as well as…

Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…