Transcranial ultrasound has been used to image the brain since 1942. Currently, it is regaining interest and full-waveform inversion (FWI) methods are now employed to reconstruct speed-of-sound profiles of the brain. Many of these methods require a good starting model. Here, we test the applicability of contrast source inversion (CSI) as a FWI method to reconstruct two-dimensional speed-of-sound profiles of the soft brain tissue enclosed by the skull. The advantage of CSI is that it can handle large acoustic contrasts without the need for a good starting model. To test the performance of CSI, we first compute synthetic data. The resulting pressure field clearly shows a significant amount of multiple scattering caused by the skull that acts as a hard acoustic contrast. Next we invert the resulting synthetic data within the Born approximation as well as by applying CSI as a FWI method. The results clearly show that Born inversion can only image the soft brain tissue in the absence of the skull whereas it generates erroneous results when the skull is present. On the other hand, with CSI it is feasible to reconstruct both the skull and the soft brain tissue accurately. Importantly, as compared to other methods CSI does not require any a priori information about the contrast, a mask or a heterogeneous starting model to reconstruct the soft tissue enclosed by the skull.@en