Related papers: A Survey on Compressive Sensing: Classical Results…
Sparse approximation is important in many applications because of concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is…
A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…
We consider compressed sampling over finite fields and investigate the number of compressed measurements needed for successful L0 recovery. Our results are obtained while the sparseness of the sensing matrices as well as the size of the…
This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering…
As a paradigm to recover the sparse signal from a small set of linear measurements, compressed sensing (CS) has stimulated a great deal of interest in recent years. In order to apply the CS techniques to wireless communication systems,…
One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while…
Compressive Sensing (CS) stipulates that a sparse signal can be recovered from a small number of linear measurements, and that this recovery can be performed efficiently in polynomial time. The framework of model-based compressive sensing…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
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,…
Sparse linear regression is a vast field and there are many different algorithms available to build models. Two new papers published in Statistical Science study the comparative performance of several sparse regression methodologies,…
Compressed sensing (CS) is an innovative technique allowing to represent signals through a small number of their linear projections. Hence, CS can be thought of as a natural candidate for acquisition of multidimensional signals, as the…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
Greedy Pursuits are very popular in Compressed Sensing for sparse signal recovery. Though many of the Greedy Pursuits possess elegant theoretical guarantees for performance, it is well known that their performance depends on the statistical…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…
Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…
Compressive Learning is an emerging topic that combines signal acquisition via compressive sensing and machine learning to perform inference tasks directly on a small number of measurements. Many data modalities naturally have a…