Studies of Sensitivity in the Dictionary Learning Approach to Computed Tomography: Simplifying the Reconstruction Problem, Rotation, and Scale

In this report, we address the problem of low-dose tomographic image reconstruction using dictionary priors learned from training images. In our recent work [22] dictionary learning is used to incorporate priors from training images and construct a dictionary, and then the reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the subspace spanned by the dictionary. The work in [22] has shown that using learned dictionaries in computed tomography can lead to superior image reconstructions comparing to classical methods. Our formulation in [22] enforces that the solution is an exact representation by the dictionary; in this report, we investigate this requirement. Furthermore, the underlying assumption that the scale and orientation of the training images are consistent with the unknown image of interest may not be realistic. We investigate the sensitivity and robustness of the reconstruction to variations of the scale and orientation in the training images and we suggest algorithms to estimate the correct relative scale and orientation of the unknown image to the training images from the data.