The Family of Regularized Parametric Projection Filters for Digital Image Restoration

Hideyuki IMAI; Akira TANAKA; Masaaki MIYAKOSHI

The Family of Regularized Parametric Projection Filters for Digital Image Restoration

Hideyuki IMAI, Akira TANAKA, Masaaki MIYAKOSHI

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Optimum filters for an image restoration are formed by a degradation operator, a covariance operator of original images, and one of noise. However, in a practical image restoration problem, the degradation operator and the covariance operators are estimated on the basis of empirical knowledge. Thus, it appears that they differ from the true ones. When we restore a degraded image by an optimum filter belonging to the family of Projection Filters and Parametric Projection Filters, it is shown that small deviations in the degradation operator and the covariance matrix can cause a large deviation in a restored image. In this paper, we propose new optimum filters based on the regularization method called the family of Regularized Projection Filters, and show that they are stable to deviations in operators. Moreover, some numerical examples follow to confirm that our description is valid.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.3 pp.527-534

Publication Date: 1999/03/25

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Type of Manuscript: PAPER

Category: Image Theory

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Hideyuki IMAI, Akira TANAKA, Masaaki MIYAKOSHI, "The Family of Regularized Parametric Projection Filters for Digital Image Restoration" in IEICE TRANSACTIONS on Fundamentals, vol. E82-A, no. 3, pp. 527-534, March 1999, doi: .
Abstract: Optimum filters for an image restoration are formed by a degradation operator, a covariance operator of original images, and one of noise. However, in a practical image restoration problem, the degradation operator and the covariance operators are estimated on the basis of empirical knowledge. Thus, it appears that they differ from the true ones. When we restore a degraded image by an optimum filter belonging to the family of Projection Filters and Parametric Projection Filters, it is shown that small deviations in the degradation operator and the covariance matrix can cause a large deviation in a restored image. In this paper, we propose new optimum filters based on the regularization method called the family of Regularized Projection Filters, and show that they are stable to deviations in operators. Moreover, some numerical examples follow to confirm that our description is valid.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_3_527/_p

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@ARTICLE{e82-a_3_527,
author={Hideyuki IMAI, Akira TANAKA, Masaaki MIYAKOSHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Family of Regularized Parametric Projection Filters for Digital Image Restoration},
year={1999},
volume={E82-A},
number={3},
pages={527-534},
abstract={Optimum filters for an image restoration are formed by a degradation operator, a covariance operator of original images, and one of noise. However, in a practical image restoration problem, the degradation operator and the covariance operators are estimated on the basis of empirical knowledge. Thus, it appears that they differ from the true ones. When we restore a degraded image by an optimum filter belonging to the family of Projection Filters and Parametric Projection Filters, it is shown that small deviations in the degradation operator and the covariance matrix can cause a large deviation in a restored image. In this paper, we propose new optimum filters based on the regularization method called the family of Regularized Projection Filters, and show that they are stable to deviations in operators. Moreover, some numerical examples follow to confirm that our description is valid.},
keywords={},
doi={},
ISSN={},
month={March},}

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TY - JOUR
TI - The Family of Regularized Parametric Projection Filters for Digital Image Restoration
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 527
EP - 534
AU - Hideyuki IMAI
AU - Akira TANAKA
AU - Masaaki MIYAKOSHI
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 1999
AB - Optimum filters for an image restoration are formed by a degradation operator, a covariance operator of original images, and one of noise. However, in a practical image restoration problem, the degradation operator and the covariance operators are estimated on the basis of empirical knowledge. Thus, it appears that they differ from the true ones. When we restore a degraded image by an optimum filter belonging to the family of Projection Filters and Parametric Projection Filters, it is shown that small deviations in the degradation operator and the covariance matrix can cause a large deviation in a restored image. In this paper, we propose new optimum filters based on the regularization method called the family of Regularized Projection Filters, and show that they are stable to deviations in operators. Moreover, some numerical examples follow to confirm that our description is valid.
ER -