Use of Learned Dictionaries in Tomographic Reconstruction

We study the use and impact of a dictionary in a tomographic reconstruction setup. First, we build two different dictionaries: one using a set of bases functions (Discrete Cosine Transform), and the other that is learned using patches extracted from training images, similar to the image that we would like to reconstruct. We use K-SVD as the learning algorithm. These dictionaries being local, we convert them to global dictionaries, ready to be applied on whole images, by generating all possible shifts of each atom across the image. During the reconstruction, we minimize the reconstruction error by performing a gradient descent on the image representation in the dictionary space. Our experiments show promising results, allowing to eliminate standard artifacts in the tomographic reconstruction, and to reduce the number of measurements required for the inversion. However, the quality of the results depends on the convergence of the learning process, and on the parameters of the dictionaries (number of atoms, convergence criterion, atom size, etc.). The exact influence of each of these remains to be studied.