Algorithms and lower bounds for sparse recovery
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2011
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| Online Access: | http://hdl.handle.net/1721.1/62668 |
| _version_ | 1811091099568046080 |
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| author | Price, Eric (Eric C.) |
| author2 | Piotr Indyk. |
| author_facet | Piotr Indyk. Price, Eric (Eric C.) |
| author_sort | Price, Eric (Eric C.) |
| collection | MIT |
| description | Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010. |
| first_indexed | 2024-09-23T14:57:00Z |
| format | Thesis |
| id | mit-1721.1/62668 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T14:57:00Z |
| publishDate | 2011 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/626682019-04-12T16:10:32Z Algorithms and lower bounds for sparse recovery Price, Eric (Eric C.) Piotr Indyk. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Electrical Engineering and Computer Science. Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010. Cataloged from PDF version of thesis. Includes bibliographical references (p. 69-71). We consider the following k-sparse recovery problem: design a distribution of m x n matrix A, such that for any signal x, given Ax with high probability we can efficiently recover x satisfying IIx - x l, </-Cmink-sparse x' IIx - x'II. It is known that there exist such distributions with m = O(k log(n/k)) rows; in this thesis, we show that this bound is tight. We also introduce the set query algorithm, a primitive useful for solving special cases of sparse recovery using less than 8(k log(n/k)) rows. The set query algorithm estimates the values of a vector x [epsilon] Rn over a support S of size k from a randomized sparse binary linear sketch Ax of size O(k). Given Ax and S, we can recover x' with IIlx' - xSII2 </- [theta]IIx - xsII2 with probability at least 1 - k-[omega](1). The recovery takes O(k) time. While interesting in its own right, this primitive also has a number of applications. For example, we can: * Improve the sparse recovery of Zipfian distributions O(k log n) measurements from a 1 + [epsilon] approximation to a 1 + o(1) approximation, giving the first such approximation when k </- O(n1-[epsilon]). * Recover block-sparse vectors with O(k) space and a 1 + [epsilon] approximation. Previous algorithms required either w(k) space or w(1) approximation. by Eric Price. M.Eng. 2011-05-09T15:17:04Z 2011-05-09T15:17:04Z 2010 2010 Thesis http://hdl.handle.net/1721.1/62668 714249160 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 71 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Electrical Engineering and Computer Science. Price, Eric (Eric C.) Algorithms and lower bounds for sparse recovery |
| title | Algorithms and lower bounds for sparse recovery |
| title_full | Algorithms and lower bounds for sparse recovery |
| title_fullStr | Algorithms and lower bounds for sparse recovery |
| title_full_unstemmed | Algorithms and lower bounds for sparse recovery |
| title_short | Algorithms and lower bounds for sparse recovery |
| title_sort | algorithms and lower bounds for sparse recovery |
| topic | Electrical Engineering and Computer Science. |
| url | http://hdl.handle.net/1721.1/62668 |
| work_keys_str_mv | AT priceericericc algorithmsandlowerboundsforsparserecovery |