Ultrasound Computer Tomography (UCT) is an imaging technique which has proved effective for soft-tissue (breast, liver,...) characterization. More recently, the use of UCT has been envisaged for bone imaging. In this field, the large variations of impedance distribution (high contrast) require that a finer model of wave propagation be integrated into the reconstruction scheme. Here, the tomographic procedure used is adapted to broadband data acquired in scattering configurations while the heterogeneous objects (Born approximation) are probed by spherical waves. An "elliptical" Fourier transform has been derived to solve the near-field inverse problem. This transform differs from the standard Fourier Transform in that, instead of plane waves, families of harmonic ellipsoidal waves are considered. For soft tissues it is possible to separate the impedance and speed of sound contributions and to reconstruct their cartographies using dedicated near-field Radon transforms. In the case of highly heterogeneous media such as bones, iterative inversion schemes are proposed. The various reconstruction procedures are set against experiments. © 2012 SPIE.