Bayesian Spatial Autoregressive for Reducing Blurring Effect in Image

Siana Halim

doi:10.20965/jaciii.2007.p0308

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JACIII Vol.11 No.3 pp. 308-311

doi: 10.20965/jaciii.2007.p0308

(2007)

Paper:

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Bayesian Spatial Autoregressive for Reducing Blurring Effect in Image

Siana Halim

Industrial Engineering Department, Petra Christian University, Indonesia

Received:

April 17, 2006

Accepted:

September 6, 2006

Published:

March 20, 2007

Keywords:

Spatial Autoregressive, Bayesian statistics, Gibbs sampler

Abstract

We apply the Bayesian Spatial Autoregressive, which is developed by Geweke and LeSage, for reducing the blurring effect in the image. This blurring effect, particularly comes from the synthesizing semi regular texture via, e.g., two dimensional block bootstrap. We model the error, i.e., the difference between the true image and the synthesis one, as the Bayesian Spatial Autoregressive (SAR). Moreover, the weight matrix is defined in a specific manner, such that the problem in the computational for a very large matrix can be avoided. Finally, we use the error estimate, as the result of Bayesian SAR modelling, for reducing the blurring effect in the synthesis image.

Cite this article as:

S. Halim, “Bayesian Spatial Autoregressive for Reducing Blurring Effect in Image,” J. Adv. Comput. Intell. Intell. Inform., Vol.11 No.3, pp. 308-311, 2007.

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References

[1] L. Anselin, “Spatial Econometrics: Methods and Models,” Kluwer Academic Publisher, Dordrecht, 1981.
[2] N. A. C. Cressie, “Statistics for Spatial Data,” John Wiley & Sons, New York, Chichester, Brisbane, Singapore, 1991.
[3] J. Geweke, “Bayesian Treatment of the Independent Student t linear Model,” Journal of Applied Econometrics, 8, pp. 19-40, 1993.
[4] S. Halim, “Spatially adaptive detection of local disturbances in time series and stochastic processes on the integer lattice Z²,” Ph.D. thesis, Universitaet Kaiserslautern-Germany, Department of Mathematics, 2005.
[5] J. P. LeSage, “Bayesian Estimation of Spatial Autoregressive Models,” International Regional Science Review, 20, 1&2, pp. 113-129, 1997.
[6] J. P. LeSage, “Spatial Econometrics,” Website, 1999.
http://www.rri.wvu.edu/WebBook/LeSage/spatial/spatial.html
[7] R. Mead, “A mathematical model for the estimation of inter-plant competition,” Biometrics, 23(2), pp. 189-205, 1967.
[8] B. D. Ripley, “Spatial Statistics,” John Wiley & Sons, New York, Chichester, Brisbane, Toronto, 1981.
[9] P. Whittle, “On Stationary Processes in the Plane,” Biometrika, 41, pp. 434-449, 1954.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] L. Anselin, “Spatial Econometrics: Methods and Models,” Kluwer Academic Publisher, Dordrecht, 1981.

[2] [2] N. A. C. Cressie, “Statistics for Spatial Data,” John Wiley & Sons, New York, Chichester, Brisbane, Singapore, 1991.

[3] [3] J. Geweke, “Bayesian Treatment of the Independent Student t linear Model,” Journal of Applied Econometrics, 8, pp. 19-40, 1993.

[4] [4] S. Halim, “Spatially adaptive detection of local disturbances in time series and stochastic processes on the integer lattice Z²,” Ph.D. thesis, Universitaet Kaiserslautern-Germany, Department of Mathematics, 2005.

[5] [5] J. P. LeSage, “Bayesian Estimation of Spatial Autoregressive Models,” International Regional Science Review, 20, 1&2, pp. 113-129, 1997.

[6] [6] J. P. LeSage, “Spatial Econometrics,” Website, 1999.
http://www.rri.wvu.edu/WebBook/LeSage/spatial/spatial.html

[7] [7] R. Mead, “A mathematical model for the estimation of inter-plant competition,” Biometrics, 23(2), pp. 189-205, 1967.

[8] [8] B. D. Ripley, “Spatial Statistics,” John Wiley & Sons, New York, Chichester, Brisbane, Toronto, 1981.

[9] [9] P. Whittle, “On Stationary Processes in the Plane,” Biometrika, 41, pp. 434-449, 1954.