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Today, the trend in SPECT attenuation correction is to acquire a transmission data set and reconstruct the corresponding attenuation map, for incorporating 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 transmission data can be consistent with given emission data. However it is necessary to include some a priori information so that the consistency conditions can be used in an efficient manner. Here, three types of priors are used: a uniform ellipse, a uniform spline curve, and a uniform spline curve knowing the untruncated part of the transmission sinogram. Once the corresponding attenuation map has been computed, it is used to correct for attenuation in the emission image reconstruction process. The three methods have been tested on both simulations and experimentally acquired data. The results show that the two first methods give equally acceptable results, while the third method provides reconstructions which are closer to reconstructions obtained when the attenuation map is computed from untruncated transmission data.