Gradient domain layer separation under independent motion

Multi-exposure X-ray imaging can see through objects and separate different material into transparent layers. However, layer motion makes the separation task under-determined. Instead of aligning the non-rigid motion, we address the layer separation problem in gradient domain and propose an energy optimization framework to regularize it by explicitly enforcing independence constraint. It is shown that gradient domain allows more accurate and robust independence analysis between non-stationary signal using mutual information (MI) and hence achieves better separation. Furthermore, gradient fields contain sufficient information for full reconstruction of separated layers by solving the Poisson Equation. For efficient regularization of the gradient separation, energy terms based on the Taylor expansion of MI is further derived. Evaluation on both synthesized and real datasets proves the effectiveness of our algorithm and its robustness to complex tissue motion.