Dynamical system regularized object positioning from diffraction movie

We present a coupled nonlinear optimization framework that combines a physics-based dynamical model K with an optical propagation model H to perform dynamic low-dose characterization directly from time-resolved diffraction data. By embedding the equations of motion within the optical forward operator, we allow for mutual regularization between imaging and dynamics. The method converts the inverse imaging problem into a parameter-estimation task, thereby avoiding frame-by-frame phase retrieval and suppressing ill-conditionedness arising from noisy data. The approach is validated on synchrotron X-ray movies of a thermally actuated microelectro-mechanical (MEMS) oscillator. At a photon dose of ≈ 4 photons per pixel per frame, it simultaneously reconstructs the shuttle edge profile, partially coherent probe modes, and their temporal occupancies. With an incident flux of ≈ 0.015 photons per pixel per frame, the framework still recovers the MEMS shuttle displacement trajectory. Compared with conventional two-step pipelines, the joint treatment yields improved noise robustness by exploiting temporal correlations and enforcing physically admissible motion.