Attenuation correction using a three-dimensional template and the consistency conditions

Attenuation correction is required in positron emission tomography (PET) for accurate quantitation and to reduce artifacts. In previous work we have shown that consistency information can be used to perform attenuation correction in the absence of any transmission measurements. In that work a separate object was used for each slice and was transformed in two dimensions. Here, we introduce an extension of this work to perform three-dimensional transformations on a single object over many slices. The aim is to produce a useful attenuation correction in situations where either it is impractical to acquire transmission data or there is significant misregistration between the transmission and emission data. The method is tested using simulated data, with both uniform and nonuniform attenuation, and experimental data, using a nonuniform cardiac phantom. Results show that for most cases the consistency conditions method will produce a useful correction but not necessarily towards a quantitatively better solution.