A variational model for SPECT reconstruction with a nonlinearly transformed attenuation prototype
This work deals with the single photon emission computed tomography (SPECT) reconstruction process. As a SPECT measurement also depends on unknown attenuation properties of the tissue, such a process is challenging. Furthermore, the given attenuation may not be a good approximation to the true attenuation field. Reasons are repositioning or movement of the patient such as relaxation during scan time or even breathing. We propose a novel model for an attenuation correction in SPECT reconstruction, which is a natural extension of an idea of Natterer in that way, as the linear transformation of a so-called attenuation prototype is enhanced to an arbitrary transformation. We present numerical results for a non-linear spline transformation model which clearly indicate the superiority of the proposed reconstruction model compared to the case of no motion correction and the correction with a linear transformation model.