In this paper, we study the problem of noise with regard to the perfect reconstruction of non-bandlimited signals, the class of signals having a finite number of degrees of freedom per unit time. The finite rate of innovation (FRI) method provides a means of recovering a non-bandlimited signal through using of appropriate kernels. In the presence of noise, however, the reconstruction function of this scheme may become ill-conditioned. Further, the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity. In this paper, to obtain improved noise robustness, we propose the matrix pencil (MP) method for sample signal reconstruction, which is based on principal component analysis (PCA). Through the selection of an adaptive eigenvalue, a non-bandlimited signal can be perfectly reconstructed via a stable solution of the Yule-Walker equation. The proposed method can obtain a high signal-to-noise-ratio (SNR) for the reconstruction results. Herein, the method is applied to certain non-bandlimited signals, such as a stream of Diracs and nonuniform splines. The simulation results demonstrate that the MP and PCA are more effective than the FRI method in suppressing noise. The FRI method can be used in many applications, including those related to bioimaging, radar, and ultrasound imaging.
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Yujie SHI, Li ZENG, "Signal Reconstruction Algorithm of Finite Rate of Innovation with Matrix Pencil and Principal Component Analysis" in IEICE TRANSACTIONS on Fundamentals,
vol. E100-A, no. 3, pp. 761-768, March 2017, doi: 10.1587/transfun.E100.A.761.
Abstract: In this paper, we study the problem of noise with regard to the perfect reconstruction of non-bandlimited signals, the class of signals having a finite number of degrees of freedom per unit time. The finite rate of innovation (FRI) method provides a means of recovering a non-bandlimited signal through using of appropriate kernels. In the presence of noise, however, the reconstruction function of this scheme may become ill-conditioned. Further, the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity. In this paper, to obtain improved noise robustness, we propose the matrix pencil (MP) method for sample signal reconstruction, which is based on principal component analysis (PCA). Through the selection of an adaptive eigenvalue, a non-bandlimited signal can be perfectly reconstructed via a stable solution of the Yule-Walker equation. The proposed method can obtain a high signal-to-noise-ratio (SNR) for the reconstruction results. Herein, the method is applied to certain non-bandlimited signals, such as a stream of Diracs and nonuniform splines. The simulation results demonstrate that the MP and PCA are more effective than the FRI method in suppressing noise. The FRI method can be used in many applications, including those related to bioimaging, radar, and ultrasound imaging.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.761/_p
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@ARTICLE{e100-a_3_761,
author={Yujie SHI, Li ZENG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Signal Reconstruction Algorithm of Finite Rate of Innovation with Matrix Pencil and Principal Component Analysis},
year={2017},
volume={E100-A},
number={3},
pages={761-768},
abstract={In this paper, we study the problem of noise with regard to the perfect reconstruction of non-bandlimited signals, the class of signals having a finite number of degrees of freedom per unit time. The finite rate of innovation (FRI) method provides a means of recovering a non-bandlimited signal through using of appropriate kernels. In the presence of noise, however, the reconstruction function of this scheme may become ill-conditioned. Further, the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity. In this paper, to obtain improved noise robustness, we propose the matrix pencil (MP) method for sample signal reconstruction, which is based on principal component analysis (PCA). Through the selection of an adaptive eigenvalue, a non-bandlimited signal can be perfectly reconstructed via a stable solution of the Yule-Walker equation. The proposed method can obtain a high signal-to-noise-ratio (SNR) for the reconstruction results. Herein, the method is applied to certain non-bandlimited signals, such as a stream of Diracs and nonuniform splines. The simulation results demonstrate that the MP and PCA are more effective than the FRI method in suppressing noise. The FRI method can be used in many applications, including those related to bioimaging, radar, and ultrasound imaging.},
keywords={},
doi={10.1587/transfun.E100.A.761},
ISSN={1745-1337},
month={March},}
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TY - JOUR
TI - Signal Reconstruction Algorithm of Finite Rate of Innovation with Matrix Pencil and Principal Component Analysis
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 761
EP - 768
AU - Yujie SHI
AU - Li ZENG
PY - 2017
DO - 10.1587/transfun.E100.A.761
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2017
AB - In this paper, we study the problem of noise with regard to the perfect reconstruction of non-bandlimited signals, the class of signals having a finite number of degrees of freedom per unit time. The finite rate of innovation (FRI) method provides a means of recovering a non-bandlimited signal through using of appropriate kernels. In the presence of noise, however, the reconstruction function of this scheme may become ill-conditioned. Further, the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity. In this paper, to obtain improved noise robustness, we propose the matrix pencil (MP) method for sample signal reconstruction, which is based on principal component analysis (PCA). Through the selection of an adaptive eigenvalue, a non-bandlimited signal can be perfectly reconstructed via a stable solution of the Yule-Walker equation. The proposed method can obtain a high signal-to-noise-ratio (SNR) for the reconstruction results. Herein, the method is applied to certain non-bandlimited signals, such as a stream of Diracs and nonuniform splines. The simulation results demonstrate that the MP and PCA are more effective than the FRI method in suppressing noise. The FRI method can be used in many applications, including those related to bioimaging, radar, and ultrasound imaging.
ER -