In various applications of signals transmission and processing, there is always a possibility of loss of samples. The iterative algorithm of Papoulis-Gerchberg (PG) is famous for solving the band-limited lost samples recovery problem. Two problems are known in this domain: (1) a band-limited signal practically is difficult to be obtained and (2) the convergence rate is too slow. By inserting a subtraction by a polynomial in the PG algorithm, using boundary-matched concept, a significant increase in performance and speed of its convergence has been achieved. In this paper, we propose an efficient approach to restore lost samples by adding a preprocess which meets the periodic boundary conditions of Fast Fourier transform in the iteration method. The accuracy of lost samples reconstruction by using the PG algorithm can be greatly improved with the aid of mapping the input data sequence of satisfying the boundary conditions. Further, we also developed another approach that force the signal to meet a new critical boundary conditions in Fourier domain that make the parameters of the preprocessing can be easily obtained. The simulation indicates that the mean square error (MSE) of the recovery and the convergence rate with the preprocess concept is better and faster than the one without preprocess concept. Our both proposed approaches can also be applied to other cases of signal restoration, which allow Cadzow's iterative processing method, with more convenience and flexibility.
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Chau-Yun HSU, Tsung-Ming LO, "Signal Reconstruction with Boundary-Matching via Iterative Algorithm" in IEICE TRANSACTIONS on Fundamentals,
vol. E89-A, no. 11, pp. 3283-3289, November 2006, doi: 10.1093/ietfec/e89-a.11.3283.
Abstract: In various applications of signals transmission and processing, there is always a possibility of loss of samples. The iterative algorithm of Papoulis-Gerchberg (PG) is famous for solving the band-limited lost samples recovery problem. Two problems are known in this domain: (1) a band-limited signal practically is difficult to be obtained and (2) the convergence rate is too slow. By inserting a subtraction by a polynomial in the PG algorithm, using boundary-matched concept, a significant increase in performance and speed of its convergence has been achieved. In this paper, we propose an efficient approach to restore lost samples by adding a preprocess which meets the periodic boundary conditions of Fast Fourier transform in the iteration method. The accuracy of lost samples reconstruction by using the PG algorithm can be greatly improved with the aid of mapping the input data sequence of satisfying the boundary conditions. Further, we also developed another approach that force the signal to meet a new critical boundary conditions in Fourier domain that make the parameters of the preprocessing can be easily obtained. The simulation indicates that the mean square error (MSE) of the recovery and the convergence rate with the preprocess concept is better and faster than the one without preprocess concept. Our both proposed approaches can also be applied to other cases of signal restoration, which allow Cadzow's iterative processing method, with more convenience and flexibility.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.11.3283/_p
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@ARTICLE{e89-a_11_3283,
author={Chau-Yun HSU, Tsung-Ming LO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Signal Reconstruction with Boundary-Matching via Iterative Algorithm},
year={2006},
volume={E89-A},
number={11},
pages={3283-3289},
abstract={In various applications of signals transmission and processing, there is always a possibility of loss of samples. The iterative algorithm of Papoulis-Gerchberg (PG) is famous for solving the band-limited lost samples recovery problem. Two problems are known in this domain: (1) a band-limited signal practically is difficult to be obtained and (2) the convergence rate is too slow. By inserting a subtraction by a polynomial in the PG algorithm, using boundary-matched concept, a significant increase in performance and speed of its convergence has been achieved. In this paper, we propose an efficient approach to restore lost samples by adding a preprocess which meets the periodic boundary conditions of Fast Fourier transform in the iteration method. The accuracy of lost samples reconstruction by using the PG algorithm can be greatly improved with the aid of mapping the input data sequence of satisfying the boundary conditions. Further, we also developed another approach that force the signal to meet a new critical boundary conditions in Fourier domain that make the parameters of the preprocessing can be easily obtained. The simulation indicates that the mean square error (MSE) of the recovery and the convergence rate with the preprocess concept is better and faster than the one without preprocess concept. Our both proposed approaches can also be applied to other cases of signal restoration, which allow Cadzow's iterative processing method, with more convenience and flexibility.},
keywords={},
doi={10.1093/ietfec/e89-a.11.3283},
ISSN={1745-1337},
month={November},}
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TY - JOUR
TI - Signal Reconstruction with Boundary-Matching via Iterative Algorithm
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 3283
EP - 3289
AU - Chau-Yun HSU
AU - Tsung-Ming LO
PY - 2006
DO - 10.1093/ietfec/e89-a.11.3283
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2006
AB - In various applications of signals transmission and processing, there is always a possibility of loss of samples. The iterative algorithm of Papoulis-Gerchberg (PG) is famous for solving the band-limited lost samples recovery problem. Two problems are known in this domain: (1) a band-limited signal practically is difficult to be obtained and (2) the convergence rate is too slow. By inserting a subtraction by a polynomial in the PG algorithm, using boundary-matched concept, a significant increase in performance and speed of its convergence has been achieved. In this paper, we propose an efficient approach to restore lost samples by adding a preprocess which meets the periodic boundary conditions of Fast Fourier transform in the iteration method. The accuracy of lost samples reconstruction by using the PG algorithm can be greatly improved with the aid of mapping the input data sequence of satisfying the boundary conditions. Further, we also developed another approach that force the signal to meet a new critical boundary conditions in Fourier domain that make the parameters of the preprocessing can be easily obtained. The simulation indicates that the mean square error (MSE) of the recovery and the convergence rate with the preprocess concept is better and faster than the one without preprocess concept. Our both proposed approaches can also be applied to other cases of signal restoration, which allow Cadzow's iterative processing method, with more convenience and flexibility.
ER -