Summer School on

Sparsity in Image and Signal Analysis

At Hólar, Iceland, August 16 - 20, 2010 (both days included)

Sami Brandt

Total Variation Regularization and Large Scale Volume Reconstructions in Tomography

In tomography, a usual goal is to reconstruct 3D object from 2D projections where the 2D projections represent an attenuation measurement of rays transmitting through the imaged object. The related volume reconstruction problem from a small number of projections is ill-posed and needs to be regularized. We have studied a Bayesian approach for these type of inverse problems where the regularization is provided by certain types of convex, spatial derivative priors, like the total variation, which favour sparse solutions in the first or second derivative. Moreover, this kind of volume reconstruction problems require efficient optimization methodology, since the problems typically have very high dimensionality with millions of variables and the positivity constraint for the variables. To perform the large scale statistical optimization we have considered, for instance, an extension of the Skilling-Bryan method to obtain the solution in a relatively small number of iterations.

Summer School on Sparsity in Image and Signal Analysis, Hólar, Iceland