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Attenuation correction is one of the most important issues in quantitative SPECT. A current trend in SPECT systems development is to employ transmission scanning for estimation of the attenuation map. An alternative approach is to use emission data for this purpose. Both approaches, however, are not free from drawbacks. Transmission data acquired on a SPECT system often suffer from incompleteness and truncation and may exhibit poor statistical properties, whereas determination of the attenuation map from emission projections may require redundant emission measurements and is sensitive to photon statistics. The key idea of the suggested approach is to combine transmission and emission data in order to extract more information from the measurements and therefore provide a better estimation of the attenuation map. The proposed algorithm is based on constrained optimization of the discrete consistency conditions for the emission data, where the transmission data play the role of linear equality constraints. Application to experimental torso phantom data is discussed.