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Compressive Sensing (CS) is a new technique for the efficient acquisition of signals, images, and other data that have a sparse representation in some basis, frame, or dictionary. By sparse we mean that the N-dimensional basis…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…
Compressed sensing (CS) techniques demand significant storage and computational resources, when recovering high-dimensional sparse signals. Block CS (BCS), a special class of CS, addresses both the storage and complexity issues by…
Compressive sensing (CS) is a signal processing technique that enables sub-Nyquist sampling and near lossless reconstruction of a sparse signal. The technique is particularly appealing for neural signal processing since it avoids the issues…
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,…
The theory of compressive sensing (CS) asserts that an unknown signal $\mathbf{x} \in \mathbb{C}^N$ can be accurately recovered from $m$ measurements with $m\ll N$ provided that $\mathbf{x}$ is sparse. Most of the recovery algorithms need…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
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…
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) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS…
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…
This paper addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse…
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…
The application of Compressive sensing approach to the speech and musical signals is considered in this paper. Compressive sensing (CS) is a new approach to the signal sampling that allows signal reconstruction from a small set of randomly…
Compressed sensing (CS) is a valuable technique for reconstructing measurements in numerous domains. CS has not yet gained widespread adoption in scanning tunneling microscopy (STM), despite potentially offering the advantages of lower…
This work treats the recovery of sparse, binary signals through box-constrained basis pursuit using biased measurement matrices. Using a probabilistic model, we provide conditions under which the recovery of both sparse and saturated binary…
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…
Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…
Compressive Sensing (CS) theory asserts that sparse signal reconstruction is possible from a small number of linear measurements. Although CS enables low-cost linear sampling, it requires non-linear and costly reconstruction. Recent…
The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in…