Attenuation correction using SPECT emission data only

A major step towards quantitative SPECT imaging may be achieved if tissue attenuation and scatter effects are accounted for in the image reconstruction process. The current trend is to calculate the tissue attenuation map prior to inversion by performing a transmission scan in parallel with the SPECT session. Inverting the transmission data provides the attenuation coefficient distribution, and iterative reconstruction methods like the maximum likelihood expectation maximization (ML-EM) algorithm are then used to reconstruct the unknown emission source. Here we consider an alternative way to attack the SPECT reconstruction problem, which consists in estimating the attenuation map from the emission data only. This leads to an inverse mathematical problem, which could no longer be solved by the notorious iterative procedures. Instead, an optimization-based approach is used. We present a successful strategy, and compare several optimization-based methods.