Combined constraints for efficient algebraic regularized methods in fully 3D reconstruction

SPECT systems incorporate the use of one or more rotating gamma cameras which can be equipped with cone-beam collimators to improve the trade-off between spatial resolution and sensitivity. The geometry of the cone-beam collimators implies that a specific 3D reconstruction algorithm must be applied. Algebraic methods provide the possibility of including the physical characteristics, such as attenuation, Compton scatter and detector response, in the reconstruction process. However, the reconstruction problem is an ill-posed problem which should be regularized. This paper presents a 3D algebraic method that combines three regularizing constraints. These constraints deal respectively with penalizing negative voxels, local noise smoothing and missing data compensation. The results presented were obtained from imaging simulations, phantom data and from a thyroid clinical study of a normal volunteer.