  We describe and examine an algorithm for tomographic image reconstruction
where prior knowledge about the solution is available in the form of training
images. We first construct a nonnegative dictionary based on prototype elements
from the training images; this problem is formulated as a regularized
non-negative matrix factorization. Incorporating the dictionary as a prior in a
convex reconstruction problem, we then find an approximate solution with a
sparse representation in the dictionary. The dictionary is applied to
non-overlapping patches of the image, which reduces the computational
complexity compared to other algorithms. Computational experiments clarify the
choice and interplay of the model parameters and the regularization parameters,
and we show that in few-projection low-dose settings our algorithm is
competitive with total variation regularization and tends to include more
texture and more correct edges.
