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We show the potential of greedy recovery strategies for the sparse approximation of multivariate functions from a small dataset of pointwise evaluations by considering an extension of the orthogonal matching pursuit to the setting of…

Numerical Analysis · Mathematics 2019-05-06 Ben Adcock , Simone Brugiapaglia

We demonstrate that the best $k$-sparse approximation of a length-$n$ vector can be recovered within a $(1+\epsilon)$-factor approximation in $O((k/\epsilon) \log n)$ time using a non-adaptive linear sketch with $O((k/\epsilon) \log n)$…

Data Structures and Algorithms · Computer Science 2025-10-24 Nick Fischer , Vasileios Nakos

We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…

Data Structures and Algorithms · Computer Science 2015-01-09 Aditya Bhaskara , Ananda Theertha Suresh , Morteza Zadimoghaddam

The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…

Signal Processing · Electrical Eng. & Systems 2018-01-16 Shaogang Wang , Vishal M. Patel , Athina Petropulu

This paper presents a new analysis for the orthogonal matching pursuit (OMP) algorithm. It is shown that if the restricted isometry property (RIP) is satisfied at sparsity level $O(\bar{k})$, then OMP can recover a $\bar{k}$-sparse signal…

Information Theory · Computer Science 2011-06-06 Tong Zhang

In this paper we continue the studies on the integer sparse recovery problem that was introduced in \cite{FKS} and studied in \cite{K},\cite{KS}. We provide an algorithm for the recovery of an unknown sparse integer vector for the…

Numerical Analysis · Mathematics 2019-05-08 K. S. Ryutin

We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our…

Numerical Analysis · Mathematics 2020-01-22 Nick Dexter , Hoang Tran , Clayton Webster

This work deals with directional of arrival (DOA) estimation with a large antenna array. We first develop a novel signal model with a sparse system transfer matrix using an inverse discrete Fourier transform (DFT) operation, which leads to…

Signal Processing · Electrical Eng. & Systems 2023-09-04 Yiwen Mao , Dawei Gao , Qinghua Guo , Ming Jin

We propose strongly consistent algorithms for reconstructing the characteristic function 1_K of an unknown convex body K in R^n from possibly noisy measurements of the modulus of its Fourier transform \hat{1_K}. This represents a complete…

Metric Geometry · Mathematics 2016-05-02 Gabriele Bianchi , Richard J. Gardner , Markus Kiderlen

We address the problem of joint sparsity pattern recovery based on low dimensional multiple measurement vectors (MMVs) in resource constrained distributed networks. We assume that distributed nodes observe sparse signals which share the…

Information Theory · Computer Science 2015-06-16 Thankshila Wimalajeewa , Pramod K. Varshney

Given an overcomplete dictionary $A$ and a signal $b$ that is a linear combination of a few linearly independent columns of $A$, classical sparse recovery theory deals with the problem of recovering the unique sparse representation $x$ such…

Machine Learning · Statistics 2015-07-07 C. You , R. Vidal

We study sparse polynomials with bounded individual degree and their factors, obtaining the following structural and algorithmic results. 1. A deterministic polynomial-time algorithm to find all sparse divisors of a sparse polynomial of…

Computational Complexity · Computer Science 2026-03-10 Aminadav Chuyoon , Amir Shpilka

Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention. In this paper, we propose a \underline{sto}chastic alte\underline{r}nating \underline{m}inimizing method for…

Machine Learning · Statistics 2019-06-17 Jianfeng Cai , Yuling Jiao , Xiliang Lu , Juntao You

In this paper, we solve the l2-l1 sparse recovery problem by transforming the objective function of this problem into an unconstrained differentiable function and apply a limited-memory trust-region method. Unlike gradient projection-type…

Numerical Analysis · Mathematics 2016-03-01 Lasith Adhikari , Jennifer B. Erway , Shelby Lockhart , Roummel F. Marcia

The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…

Optimization and Control · Mathematics 2009-12-10 William Hager , Dzung Phan , Hongchao Zhang

Dictionary learning, the problem of recovering a sparsely used matrix $\mathbf{D} \in \mathbb{R}^{M \times K}$ and $N$ $s$-sparse vectors $\mathbf{x}_i \in \mathbb{R}^{K}$ from samples of the form $\mathbf{y}_i = \mathbf{D}\mathbf{x}_i$, is…

Machine Learning · Computer Science 2023-03-29 Alexei Novikov , Stephen White

Orthogonal matching pursuit~(OMP) is a commonly used greedy algorithm for recovering sparse signals from compressed measurements. In this paper, we introduce a variant of the OMP algorithm to reduce the complexity of reconstructing a class…

Signal Processing · Electrical Eng. & Systems 2025-11-25 Xinwei Zhao , Jinming Wen , Hongqi Yang , Xiao Ma

We present a pursuit-like algorithm that we call the "superset method" for recovery of sparse vectors from consecutive Fourier measurements in the super-resolution regime. The algorithm has a subspace identification step that hinges on the…

Information Theory · Computer Science 2013-06-11 Laurent Demanet , Deanna Needell , Nam Nguyen

Exact recovery of $K$-sparse signals $x \in \mathbb{R}^{n}$ from linear measurements $y=Ax$, where $A\in \mathbb{R}^{m\times n}$ is a sensing matrix, arises from many applications. The orthogonal matching pursuit (OMP) algorithm is widely…

Information Theory · Computer Science 2020-08-13 Jinming Wen , Rui Zhang , Wei Yu

We (nearly) settle the time complexity for computing vertex fault-tolerant (VFT) spanners with optimal sparsity (up to polylogarithmic factors). VFT spanners are sparse subgraphs that preserve distance information, up to a small…

Data Structures and Algorithms · Computer Science 2022-09-08 Merav Parter