Related papers: A Sublinear Algorithm for Sparse Reconstruction wi…
In the context of compressed sensing (CS), both Subspace Pursuit (SP) and Compressive Sampling Matching Pursuit (CoSaMP) are very important iterative greedy recovery algorithms which could reduce the recovery complexity greatly comparing…
Compressive sensing (CS) has recently emerged as a powerful framework for acquiring sparse signals. The bulk of the CS literature has focused on the case where the acquired signal has a sparse or compressible representation in an…
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…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…
We introduce a new class of measurement matrices for compressed sensing, using low order summaries over binary sequences of a given length. We prove recovery guarantees for three reconstruction algorithms using the proposed measurements,…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
Signal reconstruction in compressive sensing involves finding a sparse solution that satisfies a set of linear constraints. Several approaches to this problem have been considered in existing reconstruction algorithms. They each provide a…
Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance…
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…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…
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…
We consider the problem of recovering a signal $\mathbf{x}^* \in \mathbf{R}^n$, from magnitude-only measurements $y_i = |\left\langle\mathbf{a}_i,\mathbf{x}^*\right\rangle|$ for $i=[m]$. Also called the phase retrieval, this is a…
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…
Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a…
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…
Compressed sensing is a new scheme which shows the ability to recover sparse signal from fewer measurements, using $l_1$ minimization. Recently, Chartrand and Staneva shown in \cite{CS1} that the $l_p$ minimization with $0<p<1$ recovers…
We present a novel sparse signal reconstruction method "ISD", aiming to achieve fast reconstruction and a reduced requirement on the number of measurements compared to the classical l_1 minimization approach. ISD addresses failed…
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,…