Preconditioned iterative methods for high-resolution image reconstruction with multisensors

Raymond Hon-fu Chan; Tony F. Chan; Michael K. Ng; Wun-Cheung Tang; Chiu-Kwong T. Wong

doi:10.1117/12.325695

Preconditioned iterative methods for high-resolution image reconstruction with multisensors

Raymond Hon-fu Chan
, Tony F. Chan
, Michael K. Ng
, Wun-Cheung Tang
, Chiu-Kwong T. Wong

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

22 Citations (Scopus)

Abstract

We study the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors. The corresponding reconstruction operator H is a spatially variant operator. In this paper, instead of using the usual zero boundary condition (corresponding to a dark background outside the scene), the Neumann boundary condition (corresponding to a reflection of the original scene at the boundary) is imposed on the images. The resulting discretization matrix of H is a block-Toeplitz-Toeplitz-block-like matrix. We apply the preconditioned conjugate gradient (PCG) method with cosine transform preconditioners to solve the discrete problems. Preliminary results show that the image model under the Neumann boundary condition gives better reconstructed high-resolution images than that under the zero boundary condition, and the PCG method converges very fast.

Original language	English
Title of host publication	Advanced Signal Processing Algorithms, Architectures, and Implementations VIII
Editors	Franklin T. Luk
Publisher	SPIE
Pages	348-357
ISBN (Print)	0819429163
DOIs	https://doi.org/10.1117/12.325695
Publication status	Published - 2 Oct 1998
Externally published	Yes
Event	International Symposium on Optical Science, Engineering, and Instrumentation, 1998: Advance Signal Processing Algorithms, Atchitectures, and Implementations VIII - San diego, CA, United States Duration: 22 Jul 1998 → 24 Jul 1998 https://www.amazon.com/Advanced-Processing-Algorithms-Architectures-Implementations/dp/0819429163

Publication series

Name	Proceedings of SPIE
Volume	3461
ISSN (Print)	0277-786X

Conference

Conference	International Symposium on Optical Science, Engineering, and Instrumentation, 1998
Place	United States
City	San diego, CA
Period	22/07/98 → 24/07/98
Internet address	https://www.amazon.com/Advanced-Processing-Algorithms-Architectures-Implementations/dp/0819429163

Research Keywords

Block-Toeplitz-Toeplitz-block-like matrix
Cosine transform preconditioner
High-resolution image reconstruction
Neumann boundary condition
Preconditioned conjugate gradient
Regularization

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Cite this

@inproceedings{12c195da734f4aaab58209851ebc13d8,

title = "Preconditioned iterative methods for high-resolution image reconstruction with multisensors",

abstract = "We study the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors. The corresponding reconstruction operator H is a spatially variant operator. In this paper, instead of using the usual zero boundary condition (corresponding to a dark background outside the scene), the Neumann boundary condition (corresponding to a reflection of the original scene at the boundary) is imposed on the images. The resulting discretization matrix of H is a block-Toeplitz-Toeplitz-block-like matrix. We apply the preconditioned conjugate gradient (PCG) method with cosine transform preconditioners to solve the discrete problems. Preliminary results show that the image model under the Neumann boundary condition gives better reconstructed high-resolution images than that under the zero boundary condition, and the PCG method converges very fast.",

keywords = "Block-Toeplitz-Toeplitz-block-like matrix, Cosine transform preconditioner, High-resolution image reconstruction, Neumann boundary condition, Preconditioned conjugate gradient, Regularization",

author = "Chan, \{Raymond Hon-fu\} and Chan, \{Tony F.\} and Ng, \{Michael K.\} and Wun-Cheung Tang and Wong, \{Chiu-Kwong T.\}",

year = "1998",

month = oct,

day = "2",

doi = "10.1117/12.325695",

language = "English",

isbn = "0819429163",

series = "Proceedings of SPIE ",

publisher = "SPIE",

pages = "348--357",

editor = "Luk, \{Franklin T.\}",

booktitle = "Advanced Signal Processing Algorithms, Architectures, and Implementations VIII",

address = "United States",

note = "International Symposium on Optical Science, Engineering, and Instrumentation, 1998 : Advance Signal Processing Algorithms, Atchitectures, and Implementations VIII ; Conference date: 22-07-1998 Through 24-07-1998",

url = "https://www.amazon.com/Advanced-Processing-Algorithms-Architectures-Implementations/dp/0819429163",

}

Chan, RH, Chan, TF, Ng, MK, Tang, W-C & Wong, C-KT 1998, Preconditioned iterative methods for high-resolution image reconstruction with multisensors. in FT Luk (ed.), Advanced Signal Processing Algorithms, Architectures, and Implementations VIII. Proceedings of SPIE , vol. 3461, SPIE, pp. 348-357, International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San diego, CA, United States, 22/07/98. https://doi.org/10.1117/12.325695

Preconditioned iterative methods for high-resolution image reconstruction with multisensors. / Chan, Raymond Hon-fu; Chan, Tony F.; Ng, Michael K. et al.
Advanced Signal Processing Algorithms, Architectures, and Implementations VIII. ed. / Franklin T. Luk. SPIE, 1998. p. 348-357 (Proceedings of SPIE ; Vol. 3461).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Preconditioned iterative methods for high-resolution image reconstruction with multisensors

AU - Chan, Raymond Hon-fu

AU - Chan, Tony F.

AU - Ng, Michael K.

AU - Tang, Wun-Cheung

AU - Wong, Chiu-Kwong T.

PY - 1998/10/2

Y1 - 1998/10/2

N2 - We study the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors. The corresponding reconstruction operator H is a spatially variant operator. In this paper, instead of using the usual zero boundary condition (corresponding to a dark background outside the scene), the Neumann boundary condition (corresponding to a reflection of the original scene at the boundary) is imposed on the images. The resulting discretization matrix of H is a block-Toeplitz-Toeplitz-block-like matrix. We apply the preconditioned conjugate gradient (PCG) method with cosine transform preconditioners to solve the discrete problems. Preliminary results show that the image model under the Neumann boundary condition gives better reconstructed high-resolution images than that under the zero boundary condition, and the PCG method converges very fast.

AB - We study the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors. The corresponding reconstruction operator H is a spatially variant operator. In this paper, instead of using the usual zero boundary condition (corresponding to a dark background outside the scene), the Neumann boundary condition (corresponding to a reflection of the original scene at the boundary) is imposed on the images. The resulting discretization matrix of H is a block-Toeplitz-Toeplitz-block-like matrix. We apply the preconditioned conjugate gradient (PCG) method with cosine transform preconditioners to solve the discrete problems. Preliminary results show that the image model under the Neumann boundary condition gives better reconstructed high-resolution images than that under the zero boundary condition, and the PCG method converges very fast.

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KW - Cosine transform preconditioner

KW - High-resolution image reconstruction

KW - Neumann boundary condition

KW - Preconditioned conjugate gradient

KW - Regularization

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BT - Advanced Signal Processing Algorithms, Architectures, and Implementations VIII

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PB - SPIE

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Y2 - 22 July 1998 through 24 July 1998

ER -

Preconditioned iterative methods for high-resolution image reconstruction with multisensors

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