Related papers: Compressed Sensing for Finite-Valued Signals
Recovery of sparse signals from compressed measurements constitutes an l0 norm minimization problem, which is unpractical to solve. A number of sparse recovery approaches have appeared in the literature, including l1 minimization…
Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…
Sparse Bayesian learning (SBL) is a popular approach to sparse signal recovery in compressed sensing (CS). In SBL, the signal sparsity information is exploited by assuming a sparsity-inducing prior for the signal that is then estimated…
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…
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…
In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative…
We propose a new method, {\it binary fused compressive sensing} (BFCS), to recover sparse piece-wise smooth signals from 1-bit compressive measurements. The proposed algorithm is a modification of the previous {\it binary iterative hard…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable…
This paper studies the problem of reconstructing sparse or compressible signals from compressed sensing measurements that have undergone nonuniform quantization. Previous approaches to this Quantized Compressed Sensing (QCS) problem based…
This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
Based on $\alpha$-stable random projections with small $\alpha$, we develop a simple algorithm for compressed sensing (sparse signal recovery) by utilizing only the signs (i.e., 1-bit) of the measurements. Using only 1-bit information of…
This paper concerns the problem of 1-bit compressed sensing, where the goal is to estimate a sparse signal from a few of its binary measurements. We study a non-convex sparsity-constrained program and present a novel and concise analysis…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…