  We consider tomographic reconstruction using priors in the form of a
dictionary learned from training images. The reconstruction has two stages:
first we construct a tensor dictionary prior from our training data, and then
we pose the reconstruction problem in terms of recovering the expansion
coefficients in that dictionary. Our approach differs from past approaches in
that a) we use a third-order tensor representation for our images and b) we
recast the reconstruction problem using the tensor formulation. The dictionary
learning problem is presented as a non-negative tensor factorization problem
with sparsity constraints. The reconstruction problem is formulated in a convex
optimization framework by looking for a solution with a sparse representation
in the tensor dictionary. Numerical results show that our tensor formulation
leads to very sparse representations of both the training images and the
reconstructions due to the ability of representing repeated features compactly
in the dictionary.
