Today, the trend in SPECT attenuation correction is to acquire a transmissi
on data set and reconstruct the corresponding attenuation map, for incorpor
ating into the emission reconstruction. Recently, some techniques have been
developed to determine the attenuation map directly from the emission data
, by exploiting the fact that in the absence of noise only some specific tr
ansmission data can be consistent with given emission data. However it is n
ecessary to include some a priori information so that the consistency condi
tions can be used in an efficient manner. In this paper, three types of pri
ors are used: a uniform ellipse, a uniform spline curve, and a uniform spli
ne curve knowing the untruncated part of the transmission sinogram. Once th
e corresponding attenuation map has been computed, it is used to correct fo
r attenuation in the emission image reconstruction process. The three metho
ds have been tested on both simulations and experimentally acquired data. T
he results show that the two first methods give equally acceptable results,
while the third method provides reconstructions which are closer to recons
tructions obtained when the attenuation map is computed from untruncated tr
ansmission data.