Attenuation of ultrasound waves traversing a medium is not only a result of absorption and scattering within a given tissue, but also of coherent scattering, including diffraction, refraction, and reflection of the acoustic wave at tissue boundaries. This leads to edge enhancement and other artifacts in most reconstruction algorithms, other than 3D wave migration with currently impractical, implementations. The presented approach accounts for energy loss at tissue boundaries by normalizing data based on variable sound speed, and potential density, of the medium using a k-space wave solver. Coupled with a priori knowledge of major sound speed distributions, physical attenuation values within broad ranges, and the assumption of homogeneity within segmented regions, an attenuation image representative of region bulk properties is constructed by solving a penalized weighted least squares optimization problem. This is in contradistinction to absorption or to conventional attenuation coefficient based on overall insertion loss with strong dependence on sound speed and impedance mismatches at tissue boundaries. This imaged property will be referred to as the bulk attenuation coefficient. The algorithm is demonstrated on an opposed array setup, with mean-squared-error improvements from 0.6269 to 0.0424 (dB/cm/MHz) 2 for a cylindrical phantom, and 0.1622 to 0.0256 (dB/cm/MHz) 2 for a windowed phantom.