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Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery…
We introduce a \emph{batch} version of sparse recovery, where the goal is to report a sequence of vectors $A_1',\ldots,A_m' \in \mathbb{R}^n$ that estimate unknown signals $A_1,\ldots,A_m \in \mathbb{R}^n$ using a few linear measurements,…
We consider the problem of estimating the frequency components of a mixture of s complex sinusoids from a random subset of n regularly spaced samples. Unlike previous work in compressed sensing, the frequencies are not assumed to lie on a…
In homogenization theory and multiscale modeling, typical functions satisfy the scaling law $f^{\epsilon}(x) = f(x,x/\epsilon)$, where $f$ is periodic in the second variable and $\epsilon$ is the smallest relevant wavelength,…
Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…
We introduce Lipschitz continuous and $C^{1,1}$ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in $\mathbb{R}^n$ by using…
Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable…
We study the recovery of sparse vectors from subsampled random convolutions via $\ell_1$-minimization. We consider the setup in which both the subsampling locations as well as the generating vector are chosen at random. For a subgaussian…
Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…
We consider the problem of reconstructing an unknown function $u\in L^2(D,\mu)$ from its evaluations at given sampling points $x^1,\dots,x^m\in D$, where $D\subset \mathbb R^d$ is a general domain and $\mu$ a probability measure. The…
We propose interpretable graph neural networks for sampling and recovery of graph signals, respectively. To take informative measurements, we propose a new graph neural sampling module, which aims to select those vertices that maximally…
The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…
We consider a polynomial reconstruction of smooth functions from their noisy values at discrete nodes on the unit sphere by a variant of the regularized least-squares method of An et al., SIAM J. Numer. Anal. 50 (2012), 1513--1534. As nodes…
In this paper, we consider the problem of estimating the underlying graph associated with an Ising model given a number of independent and identically distributed samples. We adopt an \emph{approximate recovery} criterion that allows for a…
This work introduces and analyzes B-spline approximation spaces defined on general geometric domains obtained through a mapping from a parameter domain. These spaces are constructed as sparse-grid tensor products of univariate spaces in the…
We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…
In this paper, we consider the problem of sparse recovery from nonlinear measurements, which has applications in state estimation and bad data detection for power networks. An iterative mixed $\ell_1$ and $\ell_2$ convex program is used to…
The problem of recovering a structured signal $\mathbf{x} \in \mathbb{C}^p$ from a set of dimensionality-reduced linear measurements $\mathbf{b} = \mathbf {A}\mathbf {x}$ arises in a variety of applications, such as medical imaging,…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…
We study the problem of recovering an $s$-sparse signal $\mathbf{x}^{\star}\in\mathbb{C}^n$ from corrupted measurements $\mathbf{y} = \mathbf{A}\mathbf{x}^{\star}+\mathbf{z}^{\star}+\mathbf{w}$, where $\mathbf{z}^{\star}\in\mathbb{C}^m$ is…