Accurate estimation of motion in fluoroscopic imaging sequences is critical for improved frame interpolation/extrapolation, tracking of surgical instruments, and Digital Subtraction Angiography (DSA). The projection of multiple transparent objects undergoing multiple complicated deformations in 3D onto a single 2D view makes this motion estimation problem quite challenging and ill-suited to existing techniques used in medical image analysis. We propose a novel method for jointly decomposing the observed image into a set of additive layers each associated with its corresponding smooth nonlinear deformation, which together model the non-smooth motion observed in the projection images across several frames. A total variation based regularization penalty is used to incorporate the known structure of the input frames for well posedness of the layer separation problem. We present the use of this model for frame interpolation and artifact reduction in DSA. Results are included from synthetic and real clinical datasets.