Image reconstruction from limited angle Compton camera deta

The Compton camera is used for imaging the distributions of gamma-ray direction ingamma-ray telescope for astrophysics and for imaging radioisotope distributions innuclear medicine without the need for collimators. The integration of gamma-rayson a cone is measured with the camera, so that some sort of inversion methodis needed. Parra found an analytical inversion algorithm based on sphericalharmonics expansion of projection data. His algorithm is applicable to the fullset of projection data. In this paper, six possible reconstruction algorithms thatallow image reconstruction from projections with a finite range of scatteringangles are investigated. Four algorithms have instability problems and twoother are practical. However, the variance of the reconstructed image divergesin these two cases, so that window functions are introduced with which thevariance becomes finite at a cost of spatial resolution. These two algorithmsare compared in terms of variance. The algorithm based on the inversion of thesummed back-projection is superior to the algorithm based on the inversion ofthe summed projection