Compressive sensing using locality-preserving matrices
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Indyk_Compressive sensing.pdf
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198 KB
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Adobe PDF
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68379f4facd68179bfb2b27c054d1cba
Author(s)
Grant, Elyot
Indyk, Piotr
Date Issued
June 2013
Journal
Proceedings of the 29th annual symposium on Symposuim on computational geometry (SoCG '13)
Publisher
Association for Computing Machinery (ACM)
Citation
Elyot Grant and Piotr Indyk. 2013. Compressive sensing using locality-preserving matrices. In Proceedings of the twenty-ninth annual symposium on Computational geometry (SoCG '13). ACM, New York, NY, USA, 215-222.
Version
Author's final manuscript
Abstract
Compressive sensing is a method for acquiring high dimensional signals (e.g., images) using a small number of linear measurements. Consider an n-pixel image x ∈ R[superscript n], where each pixel p has value x[subscript p]. The image is acquired by computing the measurement vector Ax, where A is an m x n measurement matrix, for some m << n. The goal is to design the matrix A and the recovery algorithm which, given Ax, returns an approximation to x. It is known that m=O(k log(n/k)) measurements suffices to recover the k-sparse approximation of x. Unfortunately, this result uses matrices A that are random. Such matrices are difficult to implement in physical devices. In this paper we propose compressive sensing schemes that use matrices A that achieve the near-optimal bound of m=O(k log n), while being highly "local". We also show impossibility results for stronger notions of locality.
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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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1145/2462356.2462405
