相关论文: Sparse Recovery from Extreme Eigenvalues Deviation…
This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…
We study a class of real robust phase retrieval problems under a Gaussian assumption on the coding matrix when the received signal is sparsely corrupted by noise. The goal is to establish conditions on the sparsity under which the input…
In this paper, {the goal is to design deterministic sampling patterns on the sphere and the rotation group} and, thereby, construct sensing matrices for sparse recovery of band-limited functions. It is first shown that random sensing…
In this paper, we present several estimators of the diagonal elements of the inverse of the covariance matrix, called precision matrix, of a sample of iid random vectors. The focus is on high dimensional vectors having a sparse precision…
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 $\delta<1$,…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
A noisy underdetermined system of linear equations is considered in which a sparse vector (a vector with a few nonzero elements) is subject to measurement. The measurement matrix elements are drawn from a Gaussian distribution. We study the…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…
The restricted isometry property (RIP) for design matrices gives guarantees for optimal recovery in sparse linear models. It is of high interest in compressed sensing and statistical learning. This property is particularly important for…
In this paper we look at isometry properties of random matrices. During the last decade these properties gained a lot attention in a field called compressed sensing in first place due to their initial use in \cite{CRT,CT}. Namely, in…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary $D$. This problem is now understood to be well-posed and…
Recovery of sparse vectors and low-rank matrices from a small number of linear measurements is well-known to be possible under various model assumptions on the measurements. The key requirement on the measurement matrices is typically the…
This note considers the unstructured sparse recovery problems in a general form. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. The main challenges are…
Many inverse problems in signal processing deal with the robust estimation of unknown data from underdetermined linear observations. Low dimensional models, when combined with appropriate regularizers, have been shown to be efficient at…
We study statistical restricted isometry, a property closely related to sparse signal recovery, of deterministic sensing matrices of size $m \times N$. A matrix is said to have a statistical restricted isometry property (StRIP) of order $k$…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…
Dantzig selector (DS) and LASSO problems have attracted plenty of attention in statistical learning, sparse data recovery and mathematical optimization. In this paper, we provide a theoretical analysis of the sparse recovery stability of…
The columnwise Khatri-Rao product of two matrices is an important matrix type, reprising its role as a structured sensing matrix in many fundamental linear inverse problems. Robust signal recovery in such inverse problems is often…