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Accurate correction for nonuniform attenuation in SPECT requires knowledge of the patient-specific attenuation map. Currently, attenuation maps are either measured using a radioactive external source mounted on the SPECT system, or derived from images from other modalities, such as CT. We have developed a method for reconstructing attenuation maps from emission data in energy windows below the photopeak window. We derived a linear relation between the number of photons detected in the scatter windows and the values of the voxel attenuation coefficients, making it possible to reconstruct attenuation maps using statistical techniques such as MLEM. Our approach is based on the assumption that all photons detected in the selected scatter windows have been singly scattered. The algorithm requires multiple passes with alternating updates of the estimated emission distribution and the attenuation map. To test the feasibility of this approach, we acquired projection datasets of a torso phantom using a Siemens e.cam scanner. Sixty one-minute projections over 360 degrees were obtained. Counts were acquired in a 140-keV photopeak window (15% wide) and in five scatter windows centered at 126, 120, 114, 108, and 102 keV (each 4% wide). In our initial evaluation, the attenuation maps were successfully reconstructed without major artifacts in the first pass of the algorithm. The spatial resolution of the attenuation map appeared to be similar to that of SPECT, because details on the order of 1 cm could be seen. This new approach is promising, and may provide an alternative to transmission-based attenuation maps in SPECT imaging.