Statistical interior tomography

The long-standing interior problem has been recently revisited, leading to promising results on exact local reconstruction also referred to as interior tomography. To date, there are two key computational ingredients of interior tomography. The first ingredient is inversion of the truncated Hilbert transform with prior sub-region knowledge. The second is compressed sensing (CS) assuming a piecewise constant or polynomial region of interest (ROI). Here we propose a statistical approach for interior tomography incorporating the aforementioned two ingredients as well. In our approach, projection data follows the Poisson model, and an image is reconstructed in the maximum a posterior (MAP) framework subject to other interior tomography constraints including known subregion and minimized total variation (TV). A deterministic interior reconstruction based on the inversion of the truncated Hilbert transform is used as the initial image for the statistical interior reconstruction. This algorithm has been extensively evaluated in numerical and animal studies in terms of major image quality indices, radiation dose and machine time. In particular, our encouraging results from a low-contrast Shepp-Logan phantom and a real sheep scan demonstrate the feasibility and merits of our proposed statistical interior tomography approach.