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In order to model the higher order dependencies in the disparity map, we model the disparity map in our energy function by another prior called sparsity prior E sparse(d).
Once the autoencoder is trained, d can be modeled by the sparsity prior E sparse(d) as follows: E_{text{sparse}}(d)=sum_{(x,y)}{left|{d^{(x,y }-fleft(U^{T}a^{(x,y }-fleftt)}right|}_{2}^{2}.
If the correct alignment between the anatomical and the PET dataset is in doubt and cannot be otherwise improved, it is recommended to proceed with a non-anatomical prior (e.g. TV) applied during reconstruction.
For some parameters, the posterior differs noticeably from the prior (e.g. N2, Ne1; Fig. 4A,B).
This prior carries more information than a typical non-informative variance prior (e.g., the above mentioned gamma distribution).
The cluster model takes the form of a mixture model, with a Dirichlet process (DP) prior (e.g. Rasmussen, 2000) to avoid having to specify the number of clusters (metabolites) a priori.
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