Related papers: Recovery from Linear Measurements with Complexity-…
In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy…
In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing (DCS) extends this framework by defining ensemble sparsity models,…
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…
We introduce a new class of measurement matrices for compressed sensing, using low order summaries over binary sequences of a given length. We prove recovery guarantees for three reconstruction algorithms using the proposed measurements,…
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…
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…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary.…
Compressed Sensing (CS) seeks to recover an unknown vector with $N$ entries by making far fewer than $N$ measurements; it posits that the number of compressed sensing measurements should be comparable to the information content of the…
Exploiting intrinsic structures in sparse signals underpins the recent progress in compressive sensing (CS). The key for exploiting such structures is to achieve two desirable properties: generality (\ie, the ability to fit a wide range of…
Recent breakthrough results in compressive sensing (CS) have established that many high dimensional signals can be accurately recovered from a relatively small number of non-adaptive linear observations, provided that the signals possess a…
Parallel acquisition systems arise in various applications in order to moderate problems caused by insufficient measurements in single-sensor systems. These systems allow simultaneous data acquisition in multiple sensors, thus alleviating…
Measurement samples are often taken in various monitoring applications. To reduce the sensing cost, it is desirable to achieve better sensing quality while using fewer samples. Compressive Sensing (CS) technique finds its role when the…
We demonstrate that a sparse signal can be estimated from the phase of complex random measurements, in a "phase-only compressive sensing" (PO-CS) scenario. With high probability and up to a global unknown amplitude, we can perfectly recover…
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…
Most of compressed sensing (CS) theory to date is focused on incoherent sensing, that is, columns from the sensing matrix are highly uncorrelated. However, sensing systems with naturally occurring correlations arise in many applications,…
We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…
We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…
We address the problem of compressed sensing with multiple measurement vectors associated with prior information in order to better reconstruct an original sparse matrix signal. $\ell_{2,1}-\ell_{2,1}$ minimization is used to emphasize…
Support recovery of sparse signals from compressed linear measurements is a fundamental problem in compressed sensing (CS). In this paper, we study the orthogonal matching pursuit (OMP) algorithm for the recovery of support under noise. We…