Sound speed inversions made using simulated time of flight data from a numerical limb-mimicking phantom comprised of soft tissue and a bone inclusion demonstrate that wave front tracking forward modeling combined with ??1 regularization could lead to accurate estimates of bone sound-speed. Ultrasonic tomographic imaging of limbs has the potential to impact prosthetic socket fitting, as well as detect and track muscular dystrophy diseases, osteoporosis and bone fractures at low cost and without radiation exposure. Research in ultrasound tomography of bones has increased in the last 10 years, however, methods delivering clinically useful sound-speed inversions are lacking. Inversions for the sound-speed of the numerical phantoms using ??1and ??2 regularizations are compared using wave front forward models. The simulations are based on a custom-made cylindrically-scanning tomographic medical ultrasound system (0.5 – 5 MHz) consisting of two acoustic transducers capable of collecting pulse echo and travel time measurements over the entire 360° aperture.