相关论文: Phase Transitions in Phase-Only Compressed Sensing

Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…

A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is…

We study the recovery conditions of weighted $\ell_1$ minimization for real-valued signal reconstruction from phaseless compressive sensing measurements when partial support information is available. A strong restricted isometry property…

Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data popularized as Robust PCA (Candes et al., 2011; Chandrasekaran et al., 2009). Compressed sensing,…

To strike a balance between energy efficiency and data quality control, this paper proposes a sensor censoring scheme for distributed sparse signal recovery via compressive-sensing based wireless sensor networks. In the proposed approach,…

In engineered quantum systems, the Hamiltonian is often not completely known and needs to be determined experimentally with accuracy and efficiency. We show that this may be done at temperatures that are greater than the characteristic…

Many applications have benefited remarkably from low-dimensional models in the recent decade. The fact that many signals, though high dimensional, are intrinsically low dimensional has given the possibility to recover them stably from a…

We study the support recovery problem for compressed sensing, where the goal is to reconstruct the a high-dimensional $K$-sparse signal $\mathbf{x}\in\mathbb{R}^N$, from low-dimensional linear measurements with and without noise. Our key…

The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…

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…

Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix $A$ and a recovery algorithm, such…

This short note studies a variation of the Compressed Sensing paradigm introduced recently by Vaswani et al., i.e. the recovery of sparse signals from a certain number of linear measurements when the signal support is partially known. The…

In this paper, we present a novel yet simple homotopy proximal mapping algorithm for compressive sensing. The algorithm adopts a simple proximal mapping of the $\ell_1$ norm at each iteration and gradually reduces the regularization…

This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this…

We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number 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…

Compressed sensing is now established as an effective method for dimension reduction when the underlying signals are sparse or compressible with respect to some suitable basis or frame. One important, yet under-addressed problem regarding…

We study the problem of estimating a function of many parameters acquired by sensors that are distributed in space, e.g., the spatial gradient of a field. We restrict ourselves to a setting where the distributed sensors are probed with…

Compressed sensing is a processing method that significantly reduces the number of measurements needed to accurately resolve signals in many fields of science and engineering. We develop a two-dimensional (2D) variant of compressed sensing…

We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of…