相关论文: An RIP-based approach to $\Sigma\Delta$ quantizati…
We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at…
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representations. When such a signal is acquired according to the principles of CS, the measurements still…
The many variants of the restricted isometry property (RIP) have proven to be crucial theoretical tools in the fields of compressed sensing and matrix completion. The study of extending compressed sensing to accommodate phaseless…
Compressed sensing is the art of reconstructing a sparse vector from its inner products with respect to a small set of randomly chosen measurement vectors. It is usually assumed that the ensemble of measurement vectors is in isotropic…
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…
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representations. This is achieved by collecting linear, non-adaptive measurements of a signal, which can be…
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…
The Restricted Isometry Property (RIP) introduced by Cand\'es and Tao is a fundamental property in compressed sensing theory. It says that if a sampling matrix satisfies the RIP of certain order proportional to the sparsity of the signal,…
The restricted isometry property (RIP) has become well-known in the compressed sensing community. Recently, a weaken version of RIP was proposed for exact sparse recovery under weak moment assumptions. In this note, we prove that the weaken…
The purpose of this paper is twofold. The first is to point out that the Restricted Isometry Property (RIP) does not hold in many applications where compressed sensing is successfully used. This includes fields like Magnetic Resonance…
Quantized compressive sensing (QCS) deals with the problem of representing compressive signal measurements with finite precision representation, i.e., a mandatory process in any practical sensor design. To characterize the signal…
In this paper we study the quantization stage that is implicit in any compressed sensing signal acquisition paradigm. We propose using Sigma-Delta quantization and a subsequent reconstruction scheme based on convex optimization. We prove…
Restricted Isometry Property (RIP) is of fundamental importance in the theory of compressed sensing and forms the base of many exact and robust recovery guarantees in this field. A quantitative description of RIP involves bounding the…
The expicit restricted isometry property (RIP) measurement matrices are needed in practical application of compressed sensing in signal processing. RIP matrices from Reed-Solomon codes, BCH codes, orthogonal codes, expander graphs have been…
Restricted isometry property (RIP), essentially stating that the linear measurements are approximately norm-preserving, plays a crucial role in studying low-rank matrix recovery problem. However, RIP fails in the robust setting, when a…
Quantized compressive sensing (QCS) deals with the problem of coding compressive measurements of low-complexity signals with quantized, finite precision representations, i.e., a mandatory process involved in any practical sensing model.…
We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the…
Suppose that the collection $\{e_i\}_{i=1}^m$ forms a frame for $\R^k$, where each entry of the vector $e_i$ is a sub-Gaussian random variable. We consider expansions in such a frame, which are then quantized using a Sigma-Delta scheme. We…
Iterative hard thresholding (IHT) and compressive sampling matching pursuit (CoSaMP) are two types of mainstream compressed sensing algorithms using hard thresholding operators for signal recovery and approximation. The guaranteed…
Compressed sensing was proposed by E. J. Cand\'es, J. Romberg, T. Tao, and D. Donoho for efficient sampling of sparse signals in 2006 and has vast applications in signal processing. The expicit restricted isometry property (RIP) measurement…