@inproceedings{305f126173ee42b384643a2d88f96c1d,
title = "ℓ2/ℓ2-foreach sparse recovery with low risk",
abstract = "In this paper, we consider the {"}foreach{"} sparse recovery problem with failure probability p. The goal of the problem is to design a distribution over m x N matrices Φ and a decoding algorithm A such that for every x ∈ ℝN, we have with probability at least 1 - p ∥x - A(Φx∥2 ≤ C∥x - xk∥2, where xk is the best k-sparse approximation of x. Our two main results are: (1) We prove a lower bound on m, the number measurements, of Ω(k log(n/k) + log(1/p)) for 2-Θ(N) ≤ p < 1. Cohen, Dahmen, and DeVore [4] prove that this bound is tight. (2) We prove nearly matching upper bounds that also admit sub-linear time decoding. Previous such results were obtained only when p = Ω(1). One corollary of our result is an an extension of Gilbert et al. [6] results for information-theoretically bounded adversaries.",
author = "Gilbert, {Anna C.} and Ngo, {Hung Q.} and Ely Porat and Atri Rudra and Strauss, {Martin J.}",
year = "2013",
doi = "https://doi.org/10.1007/978-3-642-39206-1_39",
language = "الإنجليزيّة",
isbn = "9783642392054",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
number = "PART 1",
pages = "461--472",
booktitle = "Automata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Proceedings",
edition = "PART 1",
note = "40th International Colloquium on Automata, Languages, and Programming, ICALP 2013 ; Conference date: 08-07-2013 Through 12-07-2013",
}