We consider tomographic reconstruction using priors in the form of a\ndictionary learned from training images. The reconstruction has two stages:\nfirst we construct a tensor dictionary prior from our training data, and then\nwe pose the reconstruction problem in terms of recovering the expansion\ncoefficients in that dictionary. Our approach differs from past approaches in\nthat a) we use a third-order tensor representation for our images and b) we\nrecast the reconstruction problem using the tensor formulation. The dictionary\nlearning problem is presented as a non-negative tensor factorization problem\nwith sparsity constraints. The reconstruction problem is formulated in a convex\noptimization framework by looking for a solution with a sparse representation\nin the tensor dictionary. Numerical results show that our tensor formulation\nleads to very sparse representations of both the training images and the\nreconstructions due to the ability of representing repeated features compactly\nin the dictionary.\n