Related papers: Compressed sensing with l0-norm: statistical physi…
Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become…
The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l0-norm among all signals…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
In this paper, we bring together two trends that have recently emerged in sparse signal recovery: the problem of sparse signals that stem from finite alphabets and the techniques that introduce concave penalties. Specifically, we show that…
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy…
Compressed sensing (sparse signal recovery) has been a popular and important research topic in recent years. By observing that natural signals are often nonnegative, we propose a new framework for nonnegative signal recovery using…
Compressed sensing is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…
Goal: This paper deals with the problems that some EEG signals have no good sparse representation and single channel processing is not computationally efficient in compressed sensing of multi-channel EEG signals. Methods: An optimization…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and…
The traditional compressed sensing approach is naturally offline, in that it amounts to sparsely sampling and reconstructing a given dataset. Recently, an online algorithm for performing compressed sensing on streaming data was proposed:…
We present reconstruction algorithms for smooth signals with block sparsity from their compressed measurements. We tackle the issue of varying group size via group-sparse least absolute shrinkage selection operator (LASSO) as well as via…
We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…
Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm…
This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly…
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.…