Related papers: The Restricted Isometry Property for Measurements …
A matrix is said to possess the Restricted Isometry Property (RIP) if it acts as an approximate isometry when restricted to sparse vectors. Previous work has shown it to be NP-hard to determine whether a matrix possess this property, but…
Restricted Isometry Constants (RICs) provide a measure of how far from an isometry a matrix can be when acting on sparse vectors. This, and related quantities, provide a mechanism by which standard eigen-analysis can be applied to topics…
The restricted isometry property (RIP) is an integral tool in the analysis of various inverse problems with sparsity models. Motivated by the applications of compressed sensing and dimensionality reduction of low-rank tensors, we propose…
The paper introduces a framework for the recoverability analysis in compressive sensing for imaging applications such as CI cameras, rapid MRI and coded apertures. This is done using the fact that the Spherical Section Property (SSP) of a…
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…
We analyze a multiple-input multiple-output (MIMO) radar model and provide recovery results for a compressed sensing (CS) approach. In MIMO radar different pulses are emitted by several transmitters and the echoes are recorded at several…
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…
We study verifiable sufficient conditions and computable performance bounds for sparse recovery algorithms such as the Basis Pursuit, the Dantzig selector and the Lasso estimator, in terms of a newly defined family of quality measures for…
The most frequently used condition for sampling matrices employed in compressive sampling is the restricted isometry (RIP) property of the matrix when restricted to sparse signals. At the same time, imposing this condition makes it…
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…
We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance structure. This class of matrices arises from random sampling of…
The performance of estimating the common support for jointly sparse signals based on their projections onto lower-dimensional space is analyzed. Support recovery is formulated as a multiple-hypothesis testing problem. Both upper and lower…
Inspired by significant real-life applications, in particular, sparse phase retrieval and sparse pulsation frequency detection in Asteroseismology, we investigate a general framework for compressed sensing, where the measurements are…
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…
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…
Compressed sensing (CS) theory considers the restricted isometry property (RIP) as a sufficient condition for measurement matrix which guarantees the recovery of any sparse signal from its compressed measurements. The RIP condition also…
In previous work, theoretical analysis based on the tensor Restricted Isometry Property (t-RIP) established the robust recovery guarantees of a low-tubal-rank tensor. The obtained sufficient conditions depend strongly on the assumption that…
Compressive sensing (CS) allows for acquisition of sparse signals at sampling rates significantly lower than the Nyquist rate required for bandlimited signals. Recovery guarantees for CS are generally derived based on the assumption that…
We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an $s$-sparse signal from linear measurements…
In this paper, we study the restricted isometry property of partial random circulant matrices. For a bounded subgaussian generator with independent entries, we prove that the partial random circulant matrices satisfy $s$-order RIP with high…