Related papers: Modewise Operators, the Tensor Restricted Isometry…
In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. It is by now well-known that Gaussian…
Tensor recovery has recently arisen in a lot of application fields, such as transportation, medical imaging and remote sensing. Under the assumption that signals possess sparse and/or low-rank structures, many tensor recovery methods have…
In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…
Our interest lies in the recoverability properties of compressed tensors under the \textit{canonical polyadic decomposition} (CPD) model. The considered problem is well-motivated in many applications, e.g., hyperspectral image and video…
One of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the…
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…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
We study the recovery of sparse vectors from subsampled random convolutions via $\ell_1$-minimization. We consider the setup in which both the subsampling locations as well as the generating vector are chosen at random. For a subgaussian…
Compressive sensing has been receiving a great deal of interest from researchers in many areas because of its ability in speeding up data acquisition. This framework allows fast signal acquisition and compression when signals are sparse in…
In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of…
In compressed sensing, it is often desirable to consider signals possessing additional structure beyond sparsity. One such structured signal model - which forms the focus of this paper - is the local sparsity in levels class. This class has…
We consider the problem of recovering a low-multilinear-rank tensor from a small amount of linear measurements. We show that the Riemannian gradient algorithm initialized by one step of iterative hard thresholding can reconstruct an…
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…
Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that…
We study lower bounds on adaptive sensing algorithms for recovering low rank matrices using linear measurements. Given an $n \times n$ matrix $A$, a general linear measurement $S(A)$, for an $n \times n$ matrix $S$, is just the inner…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
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…