相关论文: Bilinear Compressed Sensing under known Signs via …

In this paper we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. We present a new class of convex optimization programs, or decoders, coined Basis Pursuit DeQuantizer of moment $p$…

Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed…

Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive, and sometimes even impossible to…

Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in…

We consider the problem of clustering a graph $G$ into two communities by observing a subset of the vertex correlations. Specifically, we consider the inverse problem with observed variables $Y=B_G x \oplus Z$, where $B_G$ is the incidence…

A sharp phase transition emerges in convex programs when solving the linear inverse problem, which aims to recover a structured signal from its linear measurements. This paper studies this phenomenon in theory under Gaussian random…

We study the recovery of sparse signals from underdetermined linear measurements when a potentially erroneous support estimate is available. Our results are twofold. First, we derive necessary and sufficient conditions for signal recovery…

This paper aims to develop new and fast algorithms for recovering a sparse vector from a small number of measurements, which is a fundamental problem in the field of compressive sensing (CS). Currently, CS favors incoherent systems, in…

We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An uncertainty relation for block-sparse signals is derived, based on a block-coherence measure, which we…

The recovery of structured signals from a few linear measurements is a central point in both compressed sensing (CS) and discrete tomography. In CS the signal structure is described by means of a low complexity model e.g. co-/sparsity. The…

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…

A simple hard-thresholding operation is shown to be able to recover $L$ signals $\mathbf{x}_1,...,\mathbf{x}_L \in \mathbb{R}^n$ that share a common support of size $s$ from $m = \mathcal{O}(s)$ one-bit measurements per signal if $L \ge…

Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…

Recently, several promising approximate message passing (AMP) based algorithms have been developed for bilinear recovery with model $\boldsymbol{Y}=\sum_{k=1}^K b_k \boldsymbol{A}_k \boldsymbol{C} +\boldsymbol{W} $, where $\{b_k\}$ and…

Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is…

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…

Block-sparse signal recovery without knowledge of block sizes and boundaries, such as those encountered in multi-antenna mmWave channel models, is a hard problem for compressed sensing (CS) algorithms. We propose a novel Sparse Bayesian…

In this paper, we study the issue of estimating a structured signal $x_0 \in \mathbb{R}^n$ from non-linear and noisy Gaussian observations. Supposing that $x_0$ is contained in a certain convex subset $K \subset \mathbb{R}^n$, we prove that…

We investigate the problem of reconstructing n-by-n structured matrix signal X via convex programming, where each column xj is a vector of s-sparsity and all columns have the same l1-norm. The regularizer in use is matrix norm…

This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform…