[OMTE 2008/2009] GPU speed-up of a 3D Bayesian CT algorithm : reconstruction of a real foam
Résumé
Challenge: 3D CT cone beam reconstructions from limited number of projections (like in dose reduction context) require alternative methods to standard analytical filtered backproprojection method. Proposed method: A Bayesian iterative algorithm based on a Gauss-Markov-Potts prior model. Beyond limitations: Parallelization on a 8 GPUs server has allowed us to go beyond the computing time limitations. 2 A Bayesian approach Inverse problem: Getting the object f from the projections data g collected from a cone beam 3D CT: g = Hf + (1) Prior model: Object f(r) is composed of K regions R k corresponding to K materials labeled by a hidden variable z(r)=k. A Markov/Potts model corresponding to the compactness of materials is used for z. It's A Gaussian model corresponding to the homogeneity of materials is used for each region R k. p(f (r)/z(r)) = k) = N (m k , n k) (2) Steps of the Iterative method: 1) Reconstruction step: Updating f by computing f (i+1) = arg max f {p(f|z, θ, g)}. This is done by using a gradient type optimization algorithm: f (i+1) = f (i) + α H t (g − Hf (i)) + λD t Df (i) (3) 2) Segmentation step: Updating z by generating a sample from p(z|f, θ, g) with a sampling algorithm from a Potts-Markov model. 3) Characterization step: Updating the hyperparameters using p(θ|f, z, g). Backprojection Regularization Projection Segmentation Characterization −> N iterations −> M iterations 1 −> I iterations Reconstruction Volume 3 Reconstruction 2 g z (i,m+1) z (i,m) ˆ f (i) δf (n) M C δf (n) regˆf regˆ regˆf (i,n+1)
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