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Cone-beam transmission imaging employing medium-energy photons which penetrate parallel-hole collimators can be used to rapidly estimate attenuation maps for use in reconstruction of cardiac SPECT images. Such a transmission imaging geometry offers the advantage of eliminating the need to mechanically move the point-sources during imaging, and enables fast sequential transmission scans. The axial extent over which artifact-free attenuation maps can be reconstructed is limited by the cone-beam geometry and point-source collimation. We investigated irradiation of a single head by multiple point-sources whose asymmetric cone-beam fields overlap in the axial direction as a method of extending the axial coverage of the patient. This study reports on the development and testing of a penalized-likelihood algorithm for transmission reconstruction of overlapping asymmetric cone-beams. We evaluated this algorithm and optimized the reconstruction parameters through MCAT phantom simulations. We then and applied the algorithm to transmission measurements of an anthropomorphic phantom. The experimental work consisted of performing a series of flood and transmission measurements on the anthropomorphic phantom with shifted axial locations of point-sources. We summed the projection data from individual measurements to simulate the projection data for a multiple point-source system. With the proposed penalized-likelihood algorithm, the full axial extent (20.5 cm) of the anthropomorphic phantom was reconstructed for the overlapping cone-beam geometry with two point-sources per camera head.