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Paper Abstract and Keywords
Presentation 2021-07-09 14:30
Construction of Dimension Reduction Matrix for Signal Recovery of Multivariate Gaussian Vectors
Kento Yokoyama, Tadashi Wadayama, Satoshi Takabe (NIT) IT2021-26
Abstract (in Japanese) (See Japanese page) 
(in English) In compressed sensing, we discuss the problem of estimating the sparse original signal $¥bm{x} ¥in ¥mathbb{R}^n$ from the linear observational signal $¥bm{y} = ¥bm{Ax}+ ¥bm{n} ¥in ¥mathbb{R}^m$.
This signal reconstruction problem is an inferior decision problem in which the observed signal length $m$ is shorter than the original signal length $n$.
As a signal reconstruction problem based on the same linear observation, in this paper, we consider the case where original signal $¥bm{x}$ is a signal that follows the multivariate Gaussian distribution $¥mathcal{N}(¥bm{0}, ¥bm{K})$.
The MMSE estimator function is used for signal reconstruction.
In this paper, we consider the optimal design problem of the observation matrix $¥bm A$.
That is, on the premise that we can design the observation matrix $¥bm {A}$, we propose a method of constructing $¥bm{A}$ that minimizes the estimation error.
Based on the singular value representation of the MMSE estimation error (MSE), the proposed observation matrix can be obtained by optimizing the singular value of the observation matrix by the method of Lagrange multiplier.
Experiments have shown that the proposed observation matrix gives a smaller estimation error than the existing method.
Keyword (in Japanese) (See Japanese page) 
(in English) compressed sensing / MMSE estimation / dimension reduction / multivariate Gaussian distribution / singular value representation / / /  
Reference Info. IEICE Tech. Rep., vol. 121, no. 96, IT2021-26, pp. 63-68, July 2021.
Paper # IT2021-26 
Date of Issue 2021-07-01 (IT) 
ISSN Online edition: ISSN 2432-6380
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 IT2021-26

Conference Information
Committee IT  
Conference Date 2021-07-08 - 2021-07-09 
Place (in Japanese) (See Japanese page) 
Place (in English) Online 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Freshman session, General 
Paper Information
Registration To IT 
Conference Code 2021-07-IT 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Construction of Dimension Reduction Matrix for Signal Recovery of Multivariate Gaussian Vectors 
Sub Title (in English)  
Keyword(1) compressed sensing  
Keyword(2) MMSE estimation  
Keyword(3) dimension reduction  
Keyword(4) multivariate Gaussian distribution  
Keyword(5) singular value representation  
1st Author's Name Kento Yokoyama  
1st Author's Affiliation Nagoya Institute of Technology (NIT)
2nd Author's Name Tadashi Wadayama  
2nd Author's Affiliation Nagoya Institute of Technology (NIT)
3rd Author's Name Satoshi Takabe  
3rd Author's Affiliation Nagoya Institute of Technology (NIT)
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Speaker Author-1 
Date Time 2021-07-09 14:30:00 
Presentation Time 25 minutes 
Registration for IT 
Paper # IT2021-26 
Volume (vol) vol.121 
Number (no) no.96 
Page pp.63-68 
Date of Issue 2021-07-01 (IT) 

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