Application of spherical harmonics to image reconstruction for the Compton camera

The Compton camera can collect SPECT data with high efficiency due to electronic collimation. The data acquired from a Compton camera are projections of source activity along cones and are approximated in this paper by cone-surface integrals. This paper proposes the use of an orthogonal spherical expansion to convert the cone-surface integrals into plane integrals. The conversion technique is efficient. Once the plane integrals are obtained, a 3D image can be reconstructed by the 3D Radon inversion formula. The algorithm is implemented and computer simulations are used to demonstrate the efficiency and accuracy of the proposed reconstruction algorithm.