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The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$-norm minimization - a sparse quaternion signal from a limited number of its linear measurements,…

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,…

This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this…

The goal of compressed sensing is to learn a structured signal $x$ from a limited number of noisy linear measurements $y \approx Ax$. In traditional compressed sensing, "structure" is represented by sparsity in some known basis. Inspired by…

We provide a scheme for exploring the reconstruction limit of compressed sensing by minimizing the general cost function under the random measurement constraints for generic correlated signal sources. Our scheme is based on the statistical…

An appealing requirement from the well-known diffraction tomography (DT) exists for success reconstruction from few-view and limited-angle data. Inspired by the well-known compressive sensing (CS), the accurate super-resolution…

This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the…

Compressive sensing (CS) is a technique for estimating a sparse signal from the random measurements and the measurement matrix. Traditional sparse signal recovery methods have seriously degeneration with the measurement matrix uncertainty…

Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using…

We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…

A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…

Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…

The concept of compressive sensing was recently proposed to significantly reduce the electron dose in scanning transmission electron microscopy (STEM) while still maintaining the main features in the image. Here, an experimental setup based…

Compressed sensing seeks to recover a sparse vector from a small number of linear and non-adaptive measurements. While most work so far focuses on Gaussian or Bernoulli random measurements we investigate the use of partial random circulant…

This paper presents a tutorial for CS applications in communications networks. The Shannon's sampling theorem states that to recover a signal, the sampling rate must be as least the Nyquist rate. Compressed sensing (CS) is based on the…

Compressed sensing (CS) theory assures us that we can accurately reconstruct magnetic resonance images using fewer k-space measurements than the Nyquist sampling rate requires. In traditional CS-MRI inversion methods, the fact that the…

Compressed sensing takes advantage of low-dimensional signal structure to reduce sampling requirements far below the Nyquist rate. In magnetic resonance imaging (MRI), this often takes the form of sparsity through wavelet transform, finite…

Compressed sensing (CS) with prior information concerns the problem of reconstructing a sparse signal with the aid of a similar signal which is known beforehand. We consider a new approach to integrate the prior information into CS via…

Electron tomography has achieved higher resolution and quality at reduced doses with recent advances in compressed sensing. Compressed sensing (CS) theory exploits the inherent sparse signal structure to efficiently reconstruct…

We consider the problem of recovering a single or multiple frequency-sparse signals, which share the same frequency components, from a subset of regularly spaced samples. The problem is referred to as continuous compressed sensing (CCS) in…