IEICE TRANSACTIONS on Information
Optimal Sampling Operator for Signal Restoration in the Presence of Signal Space and Observation Space Noises
Summary :
The partial projection filter (PTPF) for a given observation operator provides an optimal signal restoration in the presence of both the signal space and observation space noises. However, restoration error by the filter still depends on the observation operator which consists of measurement and sampling processes. In this paper, we determine a sampling operator which minimizes the restoration error by the PTPF. We see that under some assumptions about noise statistics, the restoration error by the PTPF is divided into two terms corresponding to the error arising from the signal space noise and that from the observation space noise. It has been found that although the restoration error due to the signal space noise is independent of the sampling operator, the restoration error arising from the observation space noise can arbitrarily be decreased by increasing the number of sample points in the proposed sampling operator. An illustrative example of optimal sampling in the trigonometric polynomial space is also given.
- Publication
- IEICE TRANSACTIONS on Information Vol.E88-D No.12 pp.2828-2838
- Publication Date
- 2005/12/01
- Publicized
- Online ISSN
- DOI
- 10.1093/ietisy/e88-d.12.2828
- Type of Manuscript
- PAPER
- Category
- Image Processing and Video Processing
Authors
Keyword
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Aqeel SYED, Hidemitsu OGAWA, "Optimal Sampling Operator for Signal Restoration in the Presence of Signal Space and Observation Space Noises" in IEICE TRANSACTIONS on Information,
vol. E88-D, no. 12, pp. 2828-2838, December 2005, doi: 10.1093/ietisy/e88-d.12.2828.
Abstract: The partial projection filter (PTPF) for a given observation operator provides an optimal signal restoration in the presence of both the signal space and observation space noises. However, restoration error by the filter still depends on the observation operator which consists of measurement and sampling processes. In this paper, we determine a sampling operator which minimizes the restoration error by the PTPF. We see that under some assumptions about noise statistics, the restoration error by the PTPF is divided into two terms corresponding to the error arising from the signal space noise and that from the observation space noise. It has been found that although the restoration error due to the signal space noise is independent of the sampling operator, the restoration error arising from the observation space noise can arbitrarily be decreased by increasing the number of sample points in the proposed sampling operator. An illustrative example of optimal sampling in the trigonometric polynomial space is also given.
URL: https://global.ieice.org/en_transactions/information/10.1093/ietisy/e88-d.12.2828/_p
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@ARTICLE{e88-d_12_2828,
author={Aqeel SYED, Hidemitsu OGAWA, },
journal={IEICE TRANSACTIONS on Information},
title={Optimal Sampling Operator for Signal Restoration in the Presence of Signal Space and Observation Space Noises},
year={2005},
volume={E88-D},
number={12},
pages={2828-2838},
abstract={The partial projection filter (PTPF) for a given observation operator provides an optimal signal restoration in the presence of both the signal space and observation space noises. However, restoration error by the filter still depends on the observation operator which consists of measurement and sampling processes. In this paper, we determine a sampling operator which minimizes the restoration error by the PTPF. We see that under some assumptions about noise statistics, the restoration error by the PTPF is divided into two terms corresponding to the error arising from the signal space noise and that from the observation space noise. It has been found that although the restoration error due to the signal space noise is independent of the sampling operator, the restoration error arising from the observation space noise can arbitrarily be decreased by increasing the number of sample points in the proposed sampling operator. An illustrative example of optimal sampling in the trigonometric polynomial space is also given.},
keywords={},
doi={10.1093/ietisy/e88-d.12.2828},
ISSN={},
month={December},}
Copy
TY - JOUR
TI - Optimal Sampling Operator for Signal Restoration in the Presence of Signal Space and Observation Space Noises
T2 - IEICE TRANSACTIONS on Information
SP - 2828
EP - 2838
AU - Aqeel SYED
AU - Hidemitsu OGAWA
PY - 2005
DO - 10.1093/ietisy/e88-d.12.2828
JO - IEICE TRANSACTIONS on Information
SN -
VL - E88-D
IS - 12
JA - IEICE TRANSACTIONS on Information
Y1 - December 2005
AB - The partial projection filter (PTPF) for a given observation operator provides an optimal signal restoration in the presence of both the signal space and observation space noises. However, restoration error by the filter still depends on the observation operator which consists of measurement and sampling processes. In this paper, we determine a sampling operator which minimizes the restoration error by the PTPF. We see that under some assumptions about noise statistics, the restoration error by the PTPF is divided into two terms corresponding to the error arising from the signal space noise and that from the observation space noise. It has been found that although the restoration error due to the signal space noise is independent of the sampling operator, the restoration error arising from the observation space noise can arbitrarily be decreased by increasing the number of sample points in the proposed sampling operator. An illustrative example of optimal sampling in the trigonometric polynomial space is also given.
ER -
English
