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In the clinical field of diagnostic emission tomography SPECT imaging currently covers a large part of the whole functional imaging market and first clinical PET/MR systems have been developed to open up novel clinical applications. For both, commonly used and future diagnostic imaging systems, the correction for photon attenuation and scattering is the key technology for reliable and accurate quantitative functional imaging. While additional scanner equipment for transmission measurements is commonly used for the acquisition of the attenuation information, this thesis is based on the basic approach to extract information about the hidden phantom attenuation directly from the emission data to support its accurate correction during the reconstruction. By this, the approach used in this thesis also allows for attenuation corrected functional image acquisition but without applying additional radiation dose to the patient which also avoids costs for expensive dedicated hardware equipment. Two novel generic methods were investigated and developed for some of the most common and promising applications in emission tomography, myocardium perfusion SPECT and combined (whole-body) PET/MR imaging. On both simulated and measured clinical data, the performance analyses of the proposed methods demonstrate a great potential to perform accurate attenuation corrected reconstruction of the activity distribution. Moreover, the results achieved using the novel methods for both SPECT and PET indicate a valuable improvement over existing approaches which are either based on additional transmission scans are less generic and reliable in respect of whole-body PET and thorax SPECT imaging. Since both novel methods automatically adapt to patient specific anatomy, they provide special robustness which makes them applicable for a large variety of patient types (e.g., regarding size, weight, extent of the organs, anatomical anomalies, etc.) and future applications. Compared to other simultaneous reconstruction approaches, the here proposed use of typical attenuation coefficients and predefined anatomical structures in SPECT, and the segmented anatomical data for PET, have shown to effectively avoid symptomatical cross-talk effects between the activity and the attenuation estimates which prevented former approaches from being clinically accepted.