Noise Reduction for NMR FID Signals via Oversampled Real-Valued Discrete Gabor Transform
Summary :
An efficient algorithm to reduce the noise from the Nuclear Magnetic Resonance Free Induction Decay (NMR FID) signals is presented, in this paper, via the oversampled real-valued discrete Gabor transform using the Gaussian synthesis window. An NMR FID signal in the Gabor transform domain (i.e., a joint time-frequency domain) is concentrated in a few number of Gabor transform coefficients while the noise is fairly distributed among all the coefficients. Therefore, the NMR FID signal can be significantly enhanced by performing a thresholding technique on the coefficients in the transform domain. Theoretical and simulation experimental analyses in this paper show that the oversampled Gabor transform using the Gaussian synthesis window is more suitable for the NMR FID signal enhancement than the critically-sampled one using the exponential synthesis window, because both the Gaussian synthesis window and its corresponding analysis window in the oversampling case can have better localization in the frequency domain than the exponential synthesis window and its corresponding analysis window in the critically-sampling case. Moreover, to speed up the transform, instead of the commonly-used complex-valued discrete Gabor transform, the real-valued discrete Gabor transform presented in our previous work is adopted in the proposed algorithm.
- Publication
- IEICE TRANSACTIONS on Information Vol.E88-D No.7 pp.1511-1518
- Publication Date
- 2005/07/01
- Publicized
- Online ISSN
- DOI
- 10.1093/ietisy/e88-d.7.1511
- Type of Manuscript
- Special Section PAPER (Special Section on Recent Advances in Circuits and Systems--Part 1)
- Category
- Adaptive Signal Processing
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Liang TAO, Hon Keung KWAN, "Noise Reduction for NMR FID Signals via Oversampled Real-Valued Discrete Gabor Transform" in IEICE TRANSACTIONS on Information,
vol. E88-D, no. 7, pp. 1511-1518, July 2005, doi: 10.1093/ietisy/e88-d.7.1511.
Abstract: An efficient algorithm to reduce the noise from the Nuclear Magnetic Resonance Free Induction Decay (NMR FID) signals is presented, in this paper, via the oversampled real-valued discrete Gabor transform using the Gaussian synthesis window. An NMR FID signal in the Gabor transform domain (i.e., a joint time-frequency domain) is concentrated in a few number of Gabor transform coefficients while the noise is fairly distributed among all the coefficients. Therefore, the NMR FID signal can be significantly enhanced by performing a thresholding technique on the coefficients in the transform domain. Theoretical and simulation experimental analyses in this paper show that the oversampled Gabor transform using the Gaussian synthesis window is more suitable for the NMR FID signal enhancement than the critically-sampled one using the exponential synthesis window, because both the Gaussian synthesis window and its corresponding analysis window in the oversampling case can have better localization in the frequency domain than the exponential synthesis window and its corresponding analysis window in the critically-sampling case. Moreover, to speed up the transform, instead of the commonly-used complex-valued discrete Gabor transform, the real-valued discrete Gabor transform presented in our previous work is adopted in the proposed algorithm.
URL: https://global.ieice.org/en_transactions/information/10.1093/ietisy/e88-d.7.1511/_p
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@ARTICLE{e88-d_7_1511,
author={Liang TAO, Hon Keung KWAN, },
journal={IEICE TRANSACTIONS on Information},
title={Noise Reduction for NMR FID Signals via Oversampled Real-Valued Discrete Gabor Transform},
year={2005},
volume={E88-D},
number={7},
pages={1511-1518},
abstract={An efficient algorithm to reduce the noise from the Nuclear Magnetic Resonance Free Induction Decay (NMR FID) signals is presented, in this paper, via the oversampled real-valued discrete Gabor transform using the Gaussian synthesis window. An NMR FID signal in the Gabor transform domain (i.e., a joint time-frequency domain) is concentrated in a few number of Gabor transform coefficients while the noise is fairly distributed among all the coefficients. Therefore, the NMR FID signal can be significantly enhanced by performing a thresholding technique on the coefficients in the transform domain. Theoretical and simulation experimental analyses in this paper show that the oversampled Gabor transform using the Gaussian synthesis window is more suitable for the NMR FID signal enhancement than the critically-sampled one using the exponential synthesis window, because both the Gaussian synthesis window and its corresponding analysis window in the oversampling case can have better localization in the frequency domain than the exponential synthesis window and its corresponding analysis window in the critically-sampling case. Moreover, to speed up the transform, instead of the commonly-used complex-valued discrete Gabor transform, the real-valued discrete Gabor transform presented in our previous work is adopted in the proposed algorithm.},
keywords={},
doi={10.1093/ietisy/e88-d.7.1511},
ISSN={},
month={July},}
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TY - JOUR
TI - Noise Reduction for NMR FID Signals via Oversampled Real-Valued Discrete Gabor Transform
T2 - IEICE TRANSACTIONS on Information
SP - 1511
EP - 1518
AU - Liang TAO
AU - Hon Keung KWAN
PY - 2005
DO - 10.1093/ietisy/e88-d.7.1511
JO - IEICE TRANSACTIONS on Information
SN -
VL - E88-D
IS - 7
JA - IEICE TRANSACTIONS on Information
Y1 - July 2005
AB - An efficient algorithm to reduce the noise from the Nuclear Magnetic Resonance Free Induction Decay (NMR FID) signals is presented, in this paper, via the oversampled real-valued discrete Gabor transform using the Gaussian synthesis window. An NMR FID signal in the Gabor transform domain (i.e., a joint time-frequency domain) is concentrated in a few number of Gabor transform coefficients while the noise is fairly distributed among all the coefficients. Therefore, the NMR FID signal can be significantly enhanced by performing a thresholding technique on the coefficients in the transform domain. Theoretical and simulation experimental analyses in this paper show that the oversampled Gabor transform using the Gaussian synthesis window is more suitable for the NMR FID signal enhancement than the critically-sampled one using the exponential synthesis window, because both the Gaussian synthesis window and its corresponding analysis window in the oversampling case can have better localization in the frequency domain than the exponential synthesis window and its corresponding analysis window in the critically-sampling case. Moreover, to speed up the transform, instead of the commonly-used complex-valued discrete Gabor transform, the real-valued discrete Gabor transform presented in our previous work is adopted in the proposed algorithm.
ER -
English
