Regularising limited view tomography using anatomical reference images and information theoretic similarity metrics

This paper is concerned with limited view tomography. Inspired by the application of digital breast tomosynthesis (DBT), which is but one of an increasing number of applications of limited view tomography, we concentrate primarily on cases where the angular range is restricted to a narrow wedge of approximately ±30°, and the number of views is restricted to 10-30. The main challenge posed by these conditions is undersampling, also known as the null space problem. As a consequence of the Fourier Slice Theorem, a limited angular range leaves large swathes of the object's Fourier space unsampled, leaving a large space of possible solutions, reconstructed volumes, for a given set of inputs. We explore the feasibility of using same- or different-modality images as anatomical priors to constrain the null space, hence the solution. To allow for different-modality priors, we choose information theoretic measures to quantify the similarity between reconstructions and their priors. We demonstrate the limitations of two popular choices, namely mutual information and joint entropy, and propose robust alternatives that overcome their limitations. One of these alternatives is essentially a joint mixture model of the image and its prior. Promising mitigation of the data insufficiency problem is demonstrated using 2D synthetic as well as clinical phantoms. This work initially assumes a priori registered priors, and is then extended to allow for the registration to be performed simultaneously with the reconstruction.