Related papers: One-bit compressed sensing with non-Gaussian measu…
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
This work theoretically studies the problem of estimating a structured high-dimensional signal $x_0 \in \mathbb{R}^n$ from noisy $1$-bit Gaussian measurements. Our recovery approach is based on a simple convex program which uses the hinge…
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…
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…
The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l0-norm among all signals…
We investigate the sign-linear embeddings of 1-bit compressed sensing given by Gaussian measurements. One can give short arguments concerning a Restricted Isometry Property of such maps using Vapnik-Chervonenkis dimension of sparse…
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 1-bit compressed sensing, the aim is to estimate a $k$-sparse unit vector $x\in S^{n-1}$ within an $\epsilon$ error (in $\ell_2$) from minimal number of linear measurements that are quantized to just their signs, i.e., from measurements…
We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may…
This chapter gives an overview over recovery guarantees for total variation minimization in compressed sensing for different measurement scenarios. In addition to summarizing the results in the area, we illustrate why an approach that is…
Compressed sensing is a recent set of mathematical results showing that sparse signals can be exactly reconstructed from a small number of linear measurements. Interestingly, for ideal sparse signals with no measurement noise, random…
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…
Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…
A different compressive sensing framework, convolution with white noise waveform followed by subsampling at fixed (not randomly selected) locations, is studied in this paper. We show that its recoverability for sparse signals depends on the…
We consider faithfully combining phase retrieval with classical compressed sensing. Inspired by the recent novel formulation for phase retrieval called PhaseMax, we present and analyze SparsePhaseMax, a linear program for phaseless…
In this letter, the problem of sparse signal reconstruction from one bit compressed sensing measurements is investigated. To solve the problem, a variational Bayes framework with a new statistical multivariate model is used. The dependency…
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…
For wideband spectrum sensing, compressive sensing has been proposed as a solution to speed up the high dimensional signals sensing and reduce the computational complexity. Compressive sensing consists of acquiring the essential information…
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
Compressed sensing (sparse signal recovery) has been a popular and important research topic in recent years. By observing that natural signals are often nonnegative, we propose a new framework for nonnegative signal recovery using…