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| Presentation | 2013-07-25 14:55 Interpolation of Reconstruction Condition for Compressed Sensing -- Extended Implications of Restricted Isometry Property -- Shinsuke Nakajima, Tsutomu Kawabata (UEC)  IT2013-15 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | It is fundamental in the compressed sensing, to consider a sufficient reconstruction condition in $l_{1}$ norm of a sparse signal, with sparsity given by a constant $s$. Among several approaches, Cand`es consider the restricted isometry property$(RIP)$, in particular the restricted isometry coefficient which is defined firstly by the given linear observation mapping $A$ and secondly by the set of restricted observation signal. For the latter he considered the signal set which has sparsity $2s$. The corresponding restricted isometry coefficient is described by $delta_{2s}$. In this report, we consider to interpolate the series $delta_{2s}$. For this purpose, we consider a fixed index subset $N$, and introduce a partition of size $s-left|Nright|$, and derive a new sufficient condition which is prescribed through $delta_{(2s-left|Nright|,N)}$, which corresponds to $delta_{2s-left|Nright|}$ We give an example which demonstrate the effectiveness of our condition. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | compressive sensing / restricted isometory property / sparse vector / $l_{1}$ restruction / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 113, no. 153, IT2013-15, pp. 23-26, July 2013. | |
| Paper # | IT2013-15 | |
| Date of Issue | 2013-07-18 (IT) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | IT2013-15 |
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| Conference Information | |
| Committee | IT |
| Conference Date | 2013-07-25 - 2013-07-26 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Nishi-Waseda campus, Waseda University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | freshman session, general |
| Paper Information | |
| Registration To | IT |
| Conference Code | 2013-07-IT |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Interpolation of Reconstruction Condition for Compressed Sensing |
| Sub Title (in English) | Extended Implications of Restricted Isometry Property |
| Keyword(1) | compressive sensing |
| Keyword(2) | restricted isometory property |
| Keyword(3) | sparse vector |
| Keyword(4) | $l_{1}$ restruction |
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| 1st Author's Name | Shinsuke Nakajima |
| 1st Author's Affiliation | University of Electro-Communications (UEC) |
| 2nd Author's Name | Tsutomu Kawabata |
| 2nd Author's Affiliation | University of Electro-Communications (UEC) |
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| Speaker | Author-1 |
| Date Time | 2013-07-25 14:55:00 |
| Presentation Time | 25 minutes |
| Registration for | IT |
| Paper # | IT2013-15 |
| Volume (vol) | vol.113 |
| Number (no) | no.153 |
| Page | pp.23-26 |
| #Pages | 4 |
| Date of Issue | 2013-07-18 (IT) |
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