Related papers: Compressed Sensing with Cross Validation
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
The multi-user linearly-separable distributed computing problem is considered here, in which $N$ servers help to compute the real-valued functions requested by $K$ users, where each function can be written as a linear combination of up to…
As an alternative to the traditional sampling theory, compressed sensing allows acquiring much smaller amount of data, still estimating the spectra of frequency-sparse signals accurately. However, compressed sensing usually requires random…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they…
The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…
In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which…
Expander graphs have been recently proposed to construct efficient compressed sensing algorithms. In particular, it has been shown that any $n$-dimensional vector that is $k$-sparse (with $k\ll n$) can be fully recovered using…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy this…
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…
Compressed sensing proposes to reconstruct more degrees of freedom in a signal than the number of values actually measured. Compressed sensing therefore risks introducing errors -- inserting spurious artifacts or masking the abnormalities…
In the compressive phase retrieval problem, or phaseless compressed sensing, or compressed sensing from intensity only measurements, the goal is to reconstruct a sparse or approximately $k$-sparse vector $x \in \mathbb{R}^n$ given access to…
In a distributed information application an encoder compresses an arbitrary vector while a similar reference vector is available to the decoder as side information. For the Hamming-distance similarity measure, and when guaranteed perfect…
The practice of compressed sensing suffers importantly in terms of the efficiency/accuracy trade-off when acquiring noisy signals prior to measurement. It is rather common to find results treating the noise affecting the measurements,…
In this paper we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. We present a new class of convex optimization programs, or decoders, coined Basis Pursuit DeQuantizer of moment $p$…
Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable…
Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is…
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 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.,…