Application of multigrid techniques to image restoration problems

R. H. CHAN; M. DONATELLI; S. SERRA-CAPIZZANO; C. TABLINO-POSSIO

doi:10.1117/12.452469

Application of multigrid techniques to image restoration problems

R. H. CHAN^*, M. DONATELLI, S. SERRA-CAPIZZANO, C. TABLINO-POSSIO

^*Corresponding author for this work

Research output: Book Chapters | Papers in Conference Proceedings › Conference paper (refereed) › Research › peer-review

2 Citations (Scopus)

Abstract

We briefly describe a multigrid strategy for unilevel and two-level linear systems whose coefficient matrix A_n belongs either to the Toeplitz class or to the cosine algebra of type III and such that A_n can be naturally associated, in the spectral sense, with a polynomial function f. The interest of the technique is due to its optimal cost of O(N) arithmetic operations, where N is the size of the algebraic problem. We remark that these structures arise in certain 2D image restoration problems or can be used as preconditioners for more complicated image restoration problems.

Original language	English
Title of host publication	Proceedings Volume 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII
Editors	Franklin T. LUK
Publisher	SPIE
Pages	210-221
Number of pages	12
Volume	4791
DOIs	https://doi.org/10.1117/12.452469
Publication status	Published - 6 Dec 2002
Externally published	Yes
Event	International Symposium on Optical Science and Technology 2002 - Seattle, United States Duration: 7 Jul 2002 → 11 Jul 2002

Symposium

Symposium	International Symposium on Optical Science and Technology 2002
Country/Territory	United States
City	Seattle
Period	7/07/02 → 11/07/02

Keywords

Cosine transform
DCT-III matrix algebra
Multigrid and preconditioning
Toeplitz matrices
Two-level structures

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10.1117/12.452469

Cite this

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title = "Application of multigrid techniques to image restoration problems",

abstract = "We briefly describe a multigrid strategy for unilevel and two-level linear systems whose coefficient matrix An belongs either to the Toeplitz class or to the cosine algebra of type III and such that An can be naturally associated, in the spectral sense, with a polynomial function f. The interest of the technique is due to its optimal cost of O(N) arithmetic operations, where N is the size of the algebraic problem. We remark that these structures arise in certain 2D image restoration problems or can be used as preconditioners for more complicated image restoration problems.",

keywords = "Cosine transform, DCT-III matrix algebra, Multigrid and preconditioning, Toeplitz matrices, Two-level structures",

author = "CHAN, {R. H.} and M. DONATELLI and S. SERRA-CAPIZZANO and C. TABLINO-POSSIO",

year = "2002",

month = dec,

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doi = "10.1117/12.452469",

language = "English",

volume = "4791",

pages = "210--221",

editor = "LUK, {Franklin T.}",

booktitle = "Proceedings Volume 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII",

publisher = "SPIE",

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note = "International Symposium on Optical Science and Technology 2002 ; Conference date: 07-07-2002 Through 11-07-2002",

}

CHAN, RH, DONATELLI, M, SERRA-CAPIZZANO, S & TABLINO-POSSIO, C 2002, Application of multigrid techniques to image restoration problems. in FT LUK (ed.), Proceedings Volume 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII. vol. 4791, SPIE, pp. 210-221, International Symposium on Optical Science and Technology 2002, Seattle, Washington, United States, 7/07/02. https://doi.org/10.1117/12.452469

Application of multigrid techniques to image restoration problems. / CHAN, R. H.; DONATELLI, M.; SERRA-CAPIZZANO, S. et al.
Proceedings Volume 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII. ed. / Franklin T. LUK. Vol. 4791 SPIE, 2002. p. 210-221.

Research output: Book Chapters | Papers in Conference Proceedings › Conference paper (refereed) › Research › peer-review

TY - GEN

T1 - Application of multigrid techniques to image restoration problems

AU - CHAN, R. H.

AU - DONATELLI, M.

AU - SERRA-CAPIZZANO, S.

AU - TABLINO-POSSIO, C.

PY - 2002/12/6

Y1 - 2002/12/6

N2 - We briefly describe a multigrid strategy for unilevel and two-level linear systems whose coefficient matrix An belongs either to the Toeplitz class or to the cosine algebra of type III and such that An can be naturally associated, in the spectral sense, with a polynomial function f. The interest of the technique is due to its optimal cost of O(N) arithmetic operations, where N is the size of the algebraic problem. We remark that these structures arise in certain 2D image restoration problems or can be used as preconditioners for more complicated image restoration problems.

AB - We briefly describe a multigrid strategy for unilevel and two-level linear systems whose coefficient matrix An belongs either to the Toeplitz class or to the cosine algebra of type III and such that An can be naturally associated, in the spectral sense, with a polynomial function f. The interest of the technique is due to its optimal cost of O(N) arithmetic operations, where N is the size of the algebraic problem. We remark that these structures arise in certain 2D image restoration problems or can be used as preconditioners for more complicated image restoration problems.

KW - Cosine transform

KW - DCT-III matrix algebra

KW - Multigrid and preconditioning

KW - Toeplitz matrices

KW - Two-level structures

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VL - 4791

SP - 210

EP - 221

BT - Proceedings Volume 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII

A2 - LUK, Franklin T.

PB - SPIE

T2 - International Symposium on Optical Science and Technology 2002

Y2 - 7 July 2002 through 11 July 2002

ER -

Application of multigrid techniques to image restoration problems

Abstract

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Keywords

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