On Model-Based RIP-1 Matrices
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Indyk_On model.pdf
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03ed765abe088ca0a16a71d4f1e9a57a
Author(s)
Indyk, Piotr
Razenshteyn, Ilya
Date Issued
2013
Journal
Automata, Languages, and Programming
Publisher
Springer-Verlag Berlin Heidelberg
Citation
Indyk, Piotr, and Ilya Razenshteyn. “On Model-Based RIP-1 Matrices.” Automata, Languages, and Programming (Lecture Notes in Computer Science; volume 7965) Springer Berlin Heidelberg. (2013): 564–575.
Version
Author's final manuscript
Abstract
The Restricted Isometry Property (RIP) is a fundamental property of a matrix enabling sparse recovery [5]. Informally, an m ×n matrix satisfies RIP of order k in the ℓ p norm if ∥ Ax ∥ p ≈ ∥ x ∥ p for any vector x that is k-sparse, i.e., that has at most k non-zeros. The minimal number of rows m necessary for the property to hold has been extensively investigated, and tight bounds are known. Motivated by signal processing models, a recent work of Baraniuk et al [3] has generalized this notion to the case where the support of x must belong to a given model, i.e., a given family of supports. This more general notion is much less understood, especially for norms other than ℓ2.
In this paper we present tight bounds for the model-based RIP property in the ℓ1 norm. Our bounds hold for the two most frequently investigated models: tree-sparsity and block-sparsity. We also show implications of our results to sparse recovery problems.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1007/978-3-642-39206-1_48
