Improvement of Semi-Random Measurement Matrix for Compressed Sensing

Wentao LV; Junfeng WANG; Wenxian YU; Zhen TAN

doi:10.1587/transfun.E97.A.1426

Improvement of Semi-Random Measurement Matrix for Compressed Sensing

Wentao LV, Junfeng WANG, Wenxian YU, Zhen TAN

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In compressed sensing, the design of the measurement matrix is a key work. In order to achieve a more precise reconstruction result, the columns of the measurement matrix should have better orthogonality or linear incoherence. A random matrix, like a Gaussian random matrix (GRM), is commonly adopted as the measurement matrix currently. However, the columns of the random matrix are only statistically-orthogonal. By substituting an orthogonal basis into the random matrix to construct a semi-random measurement matrix and by optimizing the mutual coherence between dictionary columns to approach a theoretical lower bound, the linear incoherence of the measurement matrix can be greatly improved. With this optimization measurement matrix, the signal can be reconstructed from its measures more precisely.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.6 pp.1426-1429

Publication Date: 2014/06/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E97.A.1426

Type of Manuscript: LETTER

Category: Digital Signal Processing

Authors

Wentao LV
  Shanghai Jiao Tong University
Junfeng WANG
  Shanghai Jiao Tong University
Wenxian YU
  Shanghai Jiao Tong University
Zhen TAN
  Shanghai Jiao Tong University

Keyword

compressed sensing, measurement matrix, semi-random matrix, mutual coherence, complex image compression

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Wentao LV, Junfeng WANG, Wenxian YU, Zhen TAN, "Improvement of Semi-Random Measurement Matrix for Compressed Sensing" in IEICE TRANSACTIONS on Fundamentals, vol. E97-A, no. 6, pp. 1426-1429, June 2014, doi: 10.1587/transfun.E97.A.1426.
Abstract: In compressed sensing, the design of the measurement matrix is a key work. In order to achieve a more precise reconstruction result, the columns of the measurement matrix should have better orthogonality or linear incoherence. A random matrix, like a Gaussian random matrix (GRM), is commonly adopted as the measurement matrix currently. However, the columns of the random matrix are only statistically-orthogonal. By substituting an orthogonal basis into the random matrix to construct a semi-random measurement matrix and by optimizing the mutual coherence between dictionary columns to approach a theoretical lower bound, the linear incoherence of the measurement matrix can be greatly improved. With this optimization measurement matrix, the signal can be reconstructed from its measures more precisely.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.1426/_p

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@ARTICLE{e97-a_6_1426,
author={Wentao LV, Junfeng WANG, Wenxian YU, Zhen TAN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Improvement of Semi-Random Measurement Matrix for Compressed Sensing},
year={2014},
volume={E97-A},
number={6},
pages={1426-1429},
abstract={In compressed sensing, the design of the measurement matrix is a key work. In order to achieve a more precise reconstruction result, the columns of the measurement matrix should have better orthogonality or linear incoherence. A random matrix, like a Gaussian random matrix (GRM), is commonly adopted as the measurement matrix currently. However, the columns of the random matrix are only statistically-orthogonal. By substituting an orthogonal basis into the random matrix to construct a semi-random measurement matrix and by optimizing the mutual coherence between dictionary columns to approach a theoretical lower bound, the linear incoherence of the measurement matrix can be greatly improved. With this optimization measurement matrix, the signal can be reconstructed from its measures more precisely.},
keywords={},
doi={10.1587/transfun.E97.A.1426},
ISSN={1745-1337},
month={June},}

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TY - JOUR
TI - Improvement of Semi-Random Measurement Matrix for Compressed Sensing
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1426
EP - 1429
AU - Wentao LV
AU - Junfeng WANG
AU - Wenxian YU
AU - Zhen TAN
PY - 2014
DO - 10.1587/transfun.E97.A.1426
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2014
AB - In compressed sensing, the design of the measurement matrix is a key work. In order to achieve a more precise reconstruction result, the columns of the measurement matrix should have better orthogonality or linear incoherence. A random matrix, like a Gaussian random matrix (GRM), is commonly adopted as the measurement matrix currently. However, the columns of the random matrix are only statistically-orthogonal. By substituting an orthogonal basis into the random matrix to construct a semi-random measurement matrix and by optimizing the mutual coherence between dictionary columns to approach a theoretical lower bound, the linear incoherence of the measurement matrix can be greatly improved. With this optimization measurement matrix, the signal can be reconstructed from its measures more precisely.
ER -