Related papers: Reconstruction Guarantee Analysis of Binary Measur…
In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…
Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…
Deterministic constructions of measurement matrices in compressed sensing (CS) are considered in this paper. The constructions are inspired by the recent discovery of Dimakis, Smarandache and Vontobel which says that parity-check matrices…
We consider the problem of recovering sparse vectors from underdetermined linear measurements via $\ell_p$-constrained basis pursuit. Previous analyses of this problem based on generalized restricted isometry properties have suggested that…
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…
Sparse binary matrices are of great interest in the field of sparse recovery, nonnegative compressed sensing, statistics in networks, and theoretical computer science. This class of matrices makes it possible to perform signal recovery with…
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…
The null space property (NSP) and the restricted isometry property (RIP) are two properties which have received considerable attention in the compressed sensing literature. As the name suggests, NSP is a property that depends solely on the…
This work focuses on the reconstruction of sparse signals from their 1-bit measurements. The context is the one of 1-bit compressive sensing where the measurements amount to quantizing (dithered) random projections. Our main contribution…
The restricted isometry property (RIP) is essential for the linear map to guarantee the successful recovery of low-rank matrices. The existing works show that the linear map generated by the measurement matrices with independent and…
The Compressive Sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. Practical ADCs not only sample but also quantize each…
In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. It is by now well-known that Gaussian…
Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…
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…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…
We introduce a general framework to deterministically construct binary measurement matrices for compressed sensing. The proposed matrices are composed of (circulant) permutation submatrix blocks and zero submatrix blocks, thus making their…
We investigate recovery of nonnegative vectors from non-adaptive compressive measurements in the presence of noise of unknown power. In the absence of noise, existing results in the literature identify properties of the measurement that…
Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…
Consider the compressed sensing setup where the support $s^*$ of an $m$-sparse $d$-dimensional signal $x$ is to be recovered from $n$ linear measurements with a given algorithm. Suppose that the measurements are such that the algorithm does…
In this paper we study the reconstruction of binary sparse signals from partial random circulant measurements. We show that the reconstruction via the least-squares algorithm is as good as the reconstruction via the usually used program…