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A major step toward quantitative single photon emission computerized tomography (SPECT) imaging may be achieved if attenuation, scatter, and blurring effects are accounted for in the reconstruction process. Here we consider an approach which simultaneously estimates the unknown attenuation coefficient and the emission source using the emission data only. This leads to an inverse mathematical problem which may no longer be solved via iterative procedures like the well-known EM-algorithm. Instead, a regularization approach based on nonlinear optimization techniques is used. We present a successful strategy and test it in a simulated case study and a physical phantom experiment.