TY - GEN

T1 - Probabilistic image processing by extended Gauss-Markov random fields

AU - Tanaka, Kazuyuki

AU - Morin, Nicolas

AU - Yasuda, Muneki

AU - Titterington, D. M.

PY - 2009

Y1 - 2009

N2 - We propose an extension of the Gauss-Markov random field (GMRF) models by introducing next-nearest neighbour interactions. The values of the next-nearest neighbour interactions are set to positive real numbers with the expectation that this will lead to some noise reduction while preserving the edges. Values for the hyperparameters in the proposed model are determined by using the EM algorithm in order to maximize the marginal likelihood. In addition, a measure of mean squared error, which quantifies the statistical performance of our proposed model, is derived analytically as an exact explicit expression by means of the multi-dimensional Gaussian integral formulas.

AB - We propose an extension of the Gauss-Markov random field (GMRF) models by introducing next-nearest neighbour interactions. The values of the next-nearest neighbour interactions are set to positive real numbers with the expectation that this will lead to some noise reduction while preserving the edges. Values for the hyperparameters in the proposed model are determined by using the EM algorithm in order to maximize the marginal likelihood. In addition, a measure of mean squared error, which quantifies the statistical performance of our proposed model, is derived analytically as an exact explicit expression by means of the multi-dimensional Gaussian integral formulas.

KW - Bayesian image analysis

KW - Bayesian network

KW - Gauss-Markov random fields

UR - http://www.scopus.com/inward/record.url?scp=72349087793&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=72349087793&partnerID=8YFLogxK

U2 - 10.1109/SSP.2009.5278499

DO - 10.1109/SSP.2009.5278499

M3 - Conference contribution

AN - SCOPUS:72349087793

SN - 9781424427109

T3 - IEEE Workshop on Statistical Signal Processing Proceedings

SP - 618

EP - 621

BT - 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09

T2 - 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09

Y2 - 31 August 2009 through 3 September 2009

ER -