  This work presents an approach for image reconstruction in clinical low-dose
tomography that combines principles from sparse signal processing with ideas
from deep learning. First, we describe sparse signal representation in terms of
dictionaries from a statistical perspective and interpret dictionary learning
as a process of aligning distribution that arises from a generative model with
empirical distribution of true signals. As a result we can see that sparse
coding with learned dictionaries resembles a specific variational autoencoder,
where the decoder is a linear function and the encoder is a sparse coding
algorithm. Next, we show that dictionary learning can also benefit from
computational advancements introduced in the context of deep learning, such as
parallelism and as stochastic optimization. Finally, we show that
regularization by dictionaries achieves competitive performance in computed
tomography (CT) reconstruction comparing to state-of-the-art model based and
data driven approaches.
