  Bones are always wrapped by soft tissues. As a result, bones in their X-ray
images are obscured and become unclear. In this paper, we tackle this problem
and propose a novel task to virtually decompose the soft tissue and bone by
image processing algorithms. This task is fundamentally different from
segmentation because the decomposed images share the same imaging domain. Our
decomposition task is also fundamentally different from the conventional image
enhancement. We propose a new mathematical model for such decomposition. Our
model is ill-posed and thus it requires some priors. With proper assumptions,
our model can be solved by solving a standard Laplace equation. The resulting
bone image is theoretically guaranteed to have better contrast than the
original input image. Therefore, the details of bones get enhanced and become
clearer. Several numerical experiments confirm the effective and efficiency of
our method. Our approach is important for clinical diagnosis, surgery planning,
recognition, deep learning, etc.
