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An Extension of Oblique Projection Sampling Theorem

平林 晃 (A. Hirabayashi), M. Unser

Proceedings of the Sixth International Workshop on Sampling Theory and Applications (SampTA'05), Samsun, Turkey, July 10-15, 2005, pp. 1-6.


In this paper, we discuss the sampling problem without a condition that was assumed in conventional sampling theorems. This means that we cannot perfectly reconstruct all functions in the reconstruction space. The perfect reconstruction is possible only for functions in an arbitrary complementary subspace of the intersection of the reconstruction space and the orthogonal complement of the sampling space. We propose a sampling theorem that reconstructs the oblique projection onto the complementary subspace along the orthogonal complement of the sampling space. The sampling theorem guarantees the perfect reconstruction of functions of special interest in the reconstruction space, such as the constant function in image processing applications. In addition, we explain why a conventional sampling theorem is not suitable for the present case.

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AUTHOR="Hirabayashi, A. and Unser, M.",
TITLE="An Extension of Oblique Projection Sampling Theorem",
BOOKTITLE="Proceedings of the Sixth International Workshop on Sampling
	Theory and Applications ({SampTA'05})",
YEAR="2005",
editor="",
volume="",
series="",
pages="1--6",
address="Samsun, Turkey",
month="July 10-15,",
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© 2005 SampTA. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from SampTA. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
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