Image reconstruction from limited angle Compton camera data

The Compton camera is used for imaging the distributions of gamma ray direction in a gamma ray telescope for astrophysics and for imaging radioisotope distributions in nuclear medicine without the need for collimators. The integration of gamma rays on a cone is measured with the camera, so that some sort of inversion method is needed. Parra found an analytical inversion algorithm based on spherical harmonics expansion of projection data. His algorithm is applicable to the full set of projection data. In this paper, six possible reconstruction algorithms that allow image reconstruction from projections with a finite range of scattering angles are investigated. Four algorithms have instability problems and two others are practical. However, the variance of the reconstructed image diverges in these two cases, so that window functions are introduced with which the variance becomes finite at a cost of spatial resolution. These two algorithms are compared in terms of variance. The algorithm based on the inversion of the summed back-projection is superior to the algorithm based on the inversion of the summed projection.