A Student-t based sparsity enforcing hierarchical prior for linear inverse problems and its efficient Bayesian computation for 2D and 3D Computed Tomography
Résumé
In many imaging systems and in particular in X ray
Computed Tomography (CT) the reconstruction problem can be
written as a linear inverse problem. In these problems, one property
which can often be exploited is sparsity of the solution in an
appropriate basis. In this work we consider the Student-t model in
its hierarchical Normal-Inverse Gamma with an appropriate dictionary
based coefficient. Then, thanks to the hierarchical generative
model of the observation, we derive the expression of the joint
posterior law of all the unknowns and an alternate optimisation algorithm
for obtaining the joint MAP solution. We then detail the
implementation issues of this algorithms for parallel computation
and show the results on real size 2D and 3D phantoms.
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