This paper investigates the noise properties of SPECT images reconstructed with the attenuation correction methods of Bellini, Chang, and Tretiak and Metz. The general model for the image covariance matrix can be described by two terms, the first representing object variability, the second representing the object-dependent quantum noise. The model assumes the reconstruction operation is non-iterative and linear, and the noise in the projection data is nonstationary. All aspects of digital reconstruction are included in the model. The three attenuation correction methods are tested to demonstrate the noise character of SPECT images for a uniformly emitting and attenuating disk. In addition, image quality assessment is performed for the task of detecting a cold signal on a uniformly emitting and attenuating circular background. Comparing the local noise power spectrums for various pixel locations, it is shown that image noise is both globally and locally nonstationary for all three methods, except for a small, uniform region near the center of the disk. It is also seen that the noise properties of all three methods are similar in this region. The method of Tretiak-Metz increases the noise variance at the edge of the disk, whereas it is reduced with the Bellini and Chang methods. Finally, the ideal, nonprewhitening, and region-of-interest observers are shown to be invariant across reconstruction method, however the human observer performs better with the Bellini attenuation correction method.