The quantitative and visual interpretation of SPECT myocardial perfusion images is limited by physical factors such as photon attenuation, Compton scatter, and finite resolution effects. A method of attenuation correction is described for use in nonhomogeneous media and applied to cardiac SPECT imaging. This method, termed multiplicative variable attenuation compensation (MVAC), uses tissue contours determined from segmentation of a transmission scan to assign a priori determined attenuation coefficients to different tissue regions of the transaxial images. An attenuation correction map is then constructed using a technique inspired by Chang's method that includes regionally dependent attenuation within the chest cavity and is applied after reconstruction by filtered backprojection. Scatter correction using the subtraction of a simultaneously acquired scatter window image enables the use of narrow beam attenuation coefficients. Experimental measurements to evaluate these methods were conducted for 201Tl and 99mTc SPECT using a homomorphic cardiac phantom. Finite resolution effects were included in the evaluation of results by computer simulation of the three-dimensional activity distribution. The correction methodology was shown to substantially improve both relative and absolute quantification of uniform and nonuniform regions of activity in the phantom's myocardial wall.