An iterative reconstruction algorithm for single photon emission computed tomography with cone beam geometry

An iterative EM reconstruction algorithm for single photon emission computed tomography is implemented for cone beam geometry that uses a ray‐driven projector‐backprojector. The cone beam projector‐backprojector models the attenuated Radon transform of a source distributed within an attenuator as line integrals of discrete voxels representing the source and attenuation distributions. The attenuation coefficient distribution for each voxel is assumed to be equal to the average value over a cubical region, and the integral of the source concentration through each voxel is obtained by interpolating between the source values at eight neighboring voxels. The calculation of the attenuation factors requires a specification of the attenuation distribution, estimated either from an assumed constant distribution with an estimated body outline or from transmission measurements. The distribution of attenuation coefficients is stored in memory, and the attenuation factors are calculated for each voxel during the projection and backprojection operations instead of using precalculated values. Computer simulations of half‐scan and full‐scan reconstructions show that the algorithm is able to compensate for attentuation and to suppress the propagation of artifacts that can result with limited angular sampling. The simulations verify that the algorithm has important application to cardiac SPECT imaging; because of variable attentuation through the thorax, it is necessary to use an iterative algorithm with an attenuation map in order to quantify radiopharmaceutical distributions in the heart.