Summary: A penalized least-squares algorithm is presented for simultaneously estimating Single Photon Emission Computed Tomography (SPECT) activity and attenuation distributions from emission data alone. The algorithm uses the Differential Attenuation Information (DAI), obtained from acquiring data at two different emission energies to estimate the attenuation map. The method is thus called the Differential Attenuation Method (DAM). The target application for this reconstruction scheme is cardiac imaging, where a highly non-uniform attenuation distribution is present, and thus a compensation of attenuation is most beneficial for diagnosis improvements. For cardiac studies the isotope 201Tl is predominantly used, but most of the development in this work is done by using 111In. The distant dependent collimator response is modeled as a Gaussian, and built into a five dimensional rotation tensor, computed prior reconstruction, providing a part of the projection kernel. Compton Scattering within the body is mainly responsible for obscuring the Differential Attenuation Information. An energy window based scatter correction method is used to estimate the scatter content and compensate for it prior reconstruction. A technique, based on Monte Carlo Simulation and experiment is presented to optimize the scatter correction method. Measured data from a clinical SPECT imaging system is obtained, scatter corrected, reconstructed, and the results then analyzed. For ideal, but noisy data DAM performs superior to conventional methods, but the implementation of a pre-computed Gaussian rotator, modeling the measured projection yields to an undesired attenuation artifact. A different, but more time consuming implementation of DAM is proposed, which will likely remedy this deficiency.