Exact emission SPECT reconstruction with truncated transmission data

It is common, even with new SPECT/CT systems, that the transmission data are truncated. This paper develops a method that obtains exact attenuation correction with truncated transmission data. The emission object (e.g., the heart) is assumed to have a finite, convex support, whose emission projections are not truncated. The transmission measurements over the support are available, but may be truncated outside the support (within the torso). A novel emission data reconstruction technique combines emission projections from conjugate views; a modified version of the ML-EM algorithm is used to reconstruct emission data. The attenuation map outside the support is not needed during reconstruction. The transmission measurements through the support are used to pre-scale the emission data and to reconstruct the attenuation map within the support. The attenuation map reconstruction within the support is an interior problem in which only a biased solution can be obtained using an iterative algorithm. The bias is then corrected by identifying a soft tissue region within the support and the known attenuation coefficient values of these pixels for the soft tissue. Proof of convergence of the new algorithm is provided. Computer simulations verify the accuracy of the new method. Conclusions: an exact attenuation map within the support can be obtained provided the attenuation coefficient is known at 1 pixel within the support. The method, which requires emission data over 360 deg., provides a means to perform attenuation correction in SPECT with truncated transmission data.