相关论文: The geometry of off-the-grid compressed sensing

In this short article we present the theory of sparse representations recovery in convex regularized optimization problems introduced in (Carioni and Del Grande, arXiv:2311.08072, 2023). We focus on the scenario where the unknowns belong to…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…

We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…

This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…

In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…

We consider the problem of detecting the locations of targets in the far field by sending probing signals from an antenna array and recording the reflected echoes. Drawing on key concepts from the area of compressive sensing, we use an…

We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. We introduce an $\ell_2$ regularized formulation of CS which we…

Regularization of the inverse problem is a complex issue when using Near-field Acoustic Holography (NAH) techniques to identify the vibrating sources. This paper shows that, for convex homogeneous plates with arbitrary boundary conditions,…

A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in 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 application that motivates this paper is molecular imaging at the atomic level. When discretized at sub-atomic distances, the volume is inherently sparse. Noiseless measurements from an imaging technology can be modeled by convolution…

We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…

Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…

There are two main algorithmic approaches to sparse signal recovery: geometric and combinatorial. The geometric approach starts with a geometric constraint on the measurement matrix and then uses linear programming to decode information…

In this paper, we introduce a sparse approximation property of order $s$ for a measurement matrix ${\bf A}$: $$\|{\bf x}_s\|_2\le D \|{\bf A}{\bf x}\|_2+ \beta \frac{\sigma_s({\bf x})}{\sqrt{s}} \quad {\rm for\ all} \ {\bf x},$$ where ${\bf…

Performance of regularized least-squares estimation in noisy compressed sensing is analyzed in the limit when the dimensions of the measurement matrix grow large. The sensing matrix is considered to be from a class of random ensembles that…

We present GLIMPSE - Gravitational Lensing Inversion and MaPping with Sparse Estimators - a new algorithm to generate density reconstructions in three dimensions from photometric weak lensing measurements. This is an extension of earlier…

Inspired by significant real-life applications, in particular, sparse phase retrieval and sparse pulsation frequency detection in Asteroseismology, we investigate a general framework for compressed sensing, where the measurements are…

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Numerous renowned algorithms for tackling the compressed sensing problem…