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Different methods for determination of quantitative acoustical tissue parameters, based on the analysis of raw or RF data, are well established. With a minimum size of 1 cm in the axial direction, the usual procedures for parameter estimation require large regions of interest (ROI) to obtain reliable data. On the other hand, parameter imaging applications in ultrasound tissue characterization require both smaller resolution cells and reliable parameter estimates. The hypothesis that ultrasound attenuation estimates based on multidirectional scans in combination with tomographic procedures could decrease the size of the resolution cells is verified in theory, with simulations as well as phantom measurements. In comparison to conventional scans, the effective ROI size could reduced down to 3 mm in theory. In first clinical tests, parameter images from homogenous tissues like testis and parotid gland, based on raw data, were obtained.