publication . Other literature type . Article . 2007

Diffusion-based spatial priors for imaging.

William D. Penny; John Ashburner; Nelson J. Trujillo-Barreto; Karl J. Friston; Lee M. Harrison;
Open Access
  • Published: 01 Dec 2007
  • Publisher: Elsevier BV
Abstract
AbstractWe describe a Bayesian scheme to analyze images, which uses spatial priors encoded by a diffusion kernel, based on a weighted graph Laplacian. This provides a general framework to formulate a spatial model, whose parameters can be optimized. The application we have in mind is a spatiotemporal model for imaging data. We illustrate the method on a random effects analysis of fMRI contrast images from multiple subjects; this simplifies exposition of the model and enables a clear description of its salient features. Typically, imaging data are smoothed using a fixed Gaussian kernel as a pre-processing step before applying a mass-univariate statistical model (...
Subjects
free text keywords: Diffusion kernel, Weighted graph Laplacian, Spatial priors, Gaussian process model, fMRI, General linear model, Random effects analysis, Article, Cognitive Neuroscience, Neurology, Anisotropic diffusion, Image processing, Prior probability, Mathematics, Algorithm, Gaussian function, symbols.namesake, symbols, Smoothing, Statistical model, Artificial intelligence, business.industry, business, Bayesian inference, Machine learning, computer.software_genre, computer, Scale space
Funded by
WT
Project
  • Funder: Wellcome Trust (WT)
Communities
Neuroinformatics
60 references, page 1 of 4

Alvarez, L., Lions, P.L., Morel, J.M.. Image selective smoothing and edge-detection by nonlinear diffusion: 2. SIAM J. Numer. Anal.. 1992; 29: 845-866 [OpenAIRE]

Begelfor, E., Werman, M.. How to put probabilities on homographies. IEEE Trans. Pattern Anal. Mach. Intell.. 2005; 27: 1666-1670 [OpenAIRE] [PubMed]

Bishop, C.. 1995

Bishop, C.M., Jordan, M.I.. Learning in Graphical Models. 1999: 371-403

Chefd'hotel, C., Tschumperle, D., Deriche, R., Faugeras, O.. Constrained flows of matrix-valued functions: application to diffusion tensor regularization. Comput. Vis. - Eccv. 2002; 2350 (Pt 1): 251-265 [OpenAIRE]

ChefD'Hotel, C., Tschumperle, D., Deriche, R., Faugeras, O.. Regularizing flows for constrained matrix-valued images. J. Math. Imaging Vis.. 2004; 20: 147-162 [OpenAIRE]

Chung, F.. 1991

Chung, M.K., Worsley, K.J., Robbins, S., Paus, T., Taylor, J., Giedd, J.N., Rapoport, J.L., Evans, A.C.. Deformation-based surface morphometry applied to gray matter deformation. NeuroImage. 2003; 18: 198-213 [PubMed]

Coifman, R.R., Maggioni, M.. Diffusion wavelets. Appl. Comput. Harmon. Anal.. 2006; 21: 53-94

Cosman, E.R., Fisher, J.W., Wells, W.M.. Exact MAP activity detection in fMRI using a GLM with an Ising spatial prior. Med. Image Comput. Comput. -Assist. Interv. - Miccai. 2004; 3217 (Pt 2): 703-710

Faugeras, O., Adde, G., Charpiat, G., Chefd'Hotel, C., Clerc, M., Deneux, T., Deriche, R., Hermosillo, G., Keriven, R., Kornprobst, P.. Variational, geometric, and statistical methods for modeling brain anatomy and function. NeuroImage. 2004; 23: S46-S55 [PubMed]

Flandin, G., Penny, W.D.. Bayesian fMRI data analysis with sparse spatial basis function priors. NeuroImage. 2007; 34: 1108-1125 [OpenAIRE] [PubMed]

Friman, O., Borga, M., Lundberg, P., Knutsson, H.. Adaptive analysis of fMRI data. NeuroImage. 2003; 19: 837-845 [OpenAIRE] [PubMed]

Friston, K.J., Penny, W.. Posterior probability maps and SPMs. NeuroImage. 2003; 19: 1240-1249 [PubMed]

Friston, K.J., Penny, W., Phillips, C., Kiebel, S., Hinton, G., Ashburner, J.. Classical and Bayesian inference in neuroimaging: theory. NeuroImage. 2002; 16: 465-483 [OpenAIRE] [PubMed]

60 references, page 1 of 4
Abstract
AbstractWe describe a Bayesian scheme to analyze images, which uses spatial priors encoded by a diffusion kernel, based on a weighted graph Laplacian. This provides a general framework to formulate a spatial model, whose parameters can be optimized. The application we have in mind is a spatiotemporal model for imaging data. We illustrate the method on a random effects analysis of fMRI contrast images from multiple subjects; this simplifies exposition of the model and enables a clear description of its salient features. Typically, imaging data are smoothed using a fixed Gaussian kernel as a pre-processing step before applying a mass-univariate statistical model (...
Subjects
free text keywords: Diffusion kernel, Weighted graph Laplacian, Spatial priors, Gaussian process model, fMRI, General linear model, Random effects analysis, Article, Cognitive Neuroscience, Neurology, Anisotropic diffusion, Image processing, Prior probability, Mathematics, Algorithm, Gaussian function, symbols.namesake, symbols, Smoothing, Statistical model, Artificial intelligence, business.industry, business, Bayesian inference, Machine learning, computer.software_genre, computer, Scale space
Funded by
WT
Project
  • Funder: Wellcome Trust (WT)
Communities
Neuroinformatics
60 references, page 1 of 4

Alvarez, L., Lions, P.L., Morel, J.M.. Image selective smoothing and edge-detection by nonlinear diffusion: 2. SIAM J. Numer. Anal.. 1992; 29: 845-866 [OpenAIRE]

Begelfor, E., Werman, M.. How to put probabilities on homographies. IEEE Trans. Pattern Anal. Mach. Intell.. 2005; 27: 1666-1670 [OpenAIRE] [PubMed]

Bishop, C.. 1995

Bishop, C.M., Jordan, M.I.. Learning in Graphical Models. 1999: 371-403

Chefd'hotel, C., Tschumperle, D., Deriche, R., Faugeras, O.. Constrained flows of matrix-valued functions: application to diffusion tensor regularization. Comput. Vis. - Eccv. 2002; 2350 (Pt 1): 251-265 [OpenAIRE]

ChefD'Hotel, C., Tschumperle, D., Deriche, R., Faugeras, O.. Regularizing flows for constrained matrix-valued images. J. Math. Imaging Vis.. 2004; 20: 147-162 [OpenAIRE]

Chung, F.. 1991

Chung, M.K., Worsley, K.J., Robbins, S., Paus, T., Taylor, J., Giedd, J.N., Rapoport, J.L., Evans, A.C.. Deformation-based surface morphometry applied to gray matter deformation. NeuroImage. 2003; 18: 198-213 [PubMed]

Coifman, R.R., Maggioni, M.. Diffusion wavelets. Appl. Comput. Harmon. Anal.. 2006; 21: 53-94

Cosman, E.R., Fisher, J.W., Wells, W.M.. Exact MAP activity detection in fMRI using a GLM with an Ising spatial prior. Med. Image Comput. Comput. -Assist. Interv. - Miccai. 2004; 3217 (Pt 2): 703-710

Faugeras, O., Adde, G., Charpiat, G., Chefd'Hotel, C., Clerc, M., Deneux, T., Deriche, R., Hermosillo, G., Keriven, R., Kornprobst, P.. Variational, geometric, and statistical methods for modeling brain anatomy and function. NeuroImage. 2004; 23: S46-S55 [PubMed]

Flandin, G., Penny, W.D.. Bayesian fMRI data analysis with sparse spatial basis function priors. NeuroImage. 2007; 34: 1108-1125 [OpenAIRE] [PubMed]

Friman, O., Borga, M., Lundberg, P., Knutsson, H.. Adaptive analysis of fMRI data. NeuroImage. 2003; 19: 837-845 [OpenAIRE] [PubMed]

Friston, K.J., Penny, W.. Posterior probability maps and SPMs. NeuroImage. 2003; 19: 1240-1249 [PubMed]

Friston, K.J., Penny, W., Phillips, C., Kiebel, S., Hinton, G., Ashburner, J.. Classical and Bayesian inference in neuroimaging: theory. NeuroImage. 2002; 16: 465-483 [OpenAIRE] [PubMed]

60 references, page 1 of 4
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