Related papers: Sparse Signal Recovery from Nonadaptive Linear Mea…
This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribution F; it includes all models - e.g.…
Many applications concern sparse signals, for example, detecting anomalies from the differences between consecutive images taken by surveillance cameras. This paper focuses on the problem of recovering a K-sparse signal x in N dimensions.…
This short note studies a variation of the Compressed Sensing paradigm introduced recently by Vaswani et al., i.e. the recovery of sparse signals from a certain number of linear measurements when the signal support is partially known. The…
The problem of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy is addressed. Basics of the sampling theory are outlined to show that the lower bound of signal sampling…
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…
In this paper, we study the recovery of a signal from a set of noisy linear projections (measurements), when such projections are unlabeled, that is, the correspondence between the measurements and the set of projection vectors (i.e., the…
The paper introduces a framework for the recoverability analysis in compressive sensing for imaging applications such as CI cameras, rapid MRI and coded apertures. This is done using the fact that the Spherical Section Property (SSP) of a…
The performance of estimating the common support for jointly sparse signals based on their projections onto lower-dimensional space is analyzed. Support recovery is formulated as a multiple-hypothesis testing problem. Both upper and lower…
We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
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…
Compressed sensing is an imaging paradigm that allows one to invert an underdetermined linear system by imposing the a priori knowledge that the sought after solution is sparse (i.e., mostly zeros). Previous works have shown that if one…
This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…
This paper considers efficient sampling of simultaneously sparse and correlated (S$\&$C) signals. Such signals arise in various applications in array processing. We propose an implementable sampling architecture for the acquisition of…
Recently, many practical algorithms have been proposed to recover the sparse signal from fewer measurements. Orthogonal matching pursuit (OMP) is one of the most effective algorithm. In this paper, we use the restricted isometry property to…
The theory of Compressed Sensing (CS) asserts that an unknown signal $x\in\mathbb{R}^p$ can be accurately recovered from an underdetermined set of $n$ linear measurements with $n\ll p$, provided that $x$ is sufficiently sparse. However, in…
Compressed Sensing (CS) seeks to recover an unknown vector with $N$ entries by making far fewer than $N$ measurements; it posits that the number of compressed sensing measurements should be comparable to the information content of the…
Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted…
We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…
Within the Compressive Sensing (CS) paradigm, sparse signals can be reconstructed based on a reduced set of measurements. Reliability of the solution is determined by the uniqueness condition. With its mathematically tractable and feasible…