Three-dimensional edge-preserving regularization for Compton camera reconstruction

Compton imaging is often recognized as a potentially more valuable 3-D technique than conventional emission tomography. However, due to the inherent complexity of massive data set computations for the conical projection-backprojection operation, most reconstruction algorithms have been based on analytical methods rather than statistical methods. In this paper, we investigate a maximum a posteriori (MAP) approach to Compton camera reconstruction, which provides reconstructions with superior noise characteristics compared to analytical methods. In order to preserve edges that can occur occasionally in the underlying object, we use a convex-nonquadratic smoothing prior and apply to a row-action based regularized maximum likelihood method, which is provably convergent to a true MAP solution. Our preliminary results indicate that, although the statistical methods considered in this paper are not as fast as analytical methods, they have a great potential to improve quantitative accuracy in Compton imaging.