On support sizes of restricted isometry constants
A generic tool for analyzing sparse approximation algorithms is the restricted isometry property (RIP) introduced by Candès and Tao (2005) [11]. If <i>R(k, n, N)</i> is the RIP constant with support size <i>k</i> for an <i>n × N</i> measurement matrix, we invest...
| Päätekijät: | , |
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| Aineistotyyppi: | Journal article |
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Elsevier
2010
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| _version_ | 1826263309747224576 |
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| author | Blanchard, J Thompson, A |
| author_facet | Blanchard, J Thompson, A |
| author_sort | Blanchard, J |
| collection | OXFORD |
| description | A generic tool for analyzing sparse approximation algorithms is the restricted isometry property (RIP) introduced by Candès and Tao (2005) [11]. If <i>R(k, n, N)</i> is the RIP constant with support size <i>k</i> for an <i>n × N</i> measurement matrix, we investigate the trend of reducing the support size of the RIP constants for qualitative comparisons between sufficient conditions. For example, which condition is easier to satisfy, <i>R</i>(4<i>k, n, N</i>) < 0.1 or <i>R</i>(<i>2k, n, N</i>) < 0.025? Using a quantitative comparison via phase transitions for Gaussian measurement matrices, three examples from the literature of such support size reduction are considered. In each case, utilizing a larger support size for the RIP constants results in a sufficient condition for exact sparse recovery that is satisfied by a significantly larger subset of Gaussian matrices. |
| first_indexed | 2024-03-06T19:49:43Z |
| format | Journal article |
| id | oxford-uuid:238dfc8e-33aa-4b47-a56c-4b6c1126efb4 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:49:43Z |
| publishDate | 2010 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:238dfc8e-33aa-4b47-a56c-4b6c1126efb42022-03-26T11:44:52ZOn support sizes of restricted isometry constantsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:238dfc8e-33aa-4b47-a56c-4b6c1126efb4Symplectic Elements at OxfordElsevier2010Blanchard, JThompson, AA generic tool for analyzing sparse approximation algorithms is the restricted isometry property (RIP) introduced by Candès and Tao (2005) [11]. If <i>R(k, n, N)</i> is the RIP constant with support size <i>k</i> for an <i>n × N</i> measurement matrix, we investigate the trend of reducing the support size of the RIP constants for qualitative comparisons between sufficient conditions. For example, which condition is easier to satisfy, <i>R</i>(4<i>k, n, N</i>) < 0.1 or <i>R</i>(<i>2k, n, N</i>) < 0.025? Using a quantitative comparison via phase transitions for Gaussian measurement matrices, three examples from the literature of such support size reduction are considered. In each case, utilizing a larger support size for the RIP constants results in a sufficient condition for exact sparse recovery that is satisfied by a significantly larger subset of Gaussian matrices. |
| spellingShingle | Blanchard, J Thompson, A On support sizes of restricted isometry constants |
| title | On support sizes of restricted isometry constants |
| title_full | On support sizes of restricted isometry constants |
| title_fullStr | On support sizes of restricted isometry constants |
| title_full_unstemmed | On support sizes of restricted isometry constants |
| title_short | On support sizes of restricted isometry constants |
| title_sort | on support sizes of restricted isometry constants |
| work_keys_str_mv | AT blanchardj onsupportsizesofrestrictedisometryconstants AT thompsona onsupportsizesofrestrictedisometryconstants |