| The statistical inference of a hidden Markov random process is a problem encountered in numerous signal processing applications including dynamic tomography. In dynamic tomography, the goal is to form images of an object that changes in time from its projection measurements. This work focuses on the case where the object's temporal evolution is significant and governed by a physical model. Solar tomography, the remote sensing problem concerned with the reconstruction of the dynamic solar atmosphere, has served as the motivating application throughout the development of the dissertation.;The proposed state-space formulation provides a natural and general statistical framework for the systematic tomographic reconstruction of dynamic objects when faced with inevitable measurement and modeling uncertainties. In addition, the dissertation offers signal processing methods that scale to meet the computational demands of high-dimensional state estimation problems such as dynamic tomography. Major contributions include a rigorous characterization of the convergence of the ensemble Kalman filter, a new method for ensemble Kalman smoothing and theory regarding its convergence, the first four-dimensional reconstruction of electron density in the solar atmosphere, a new method for dynamic tomography called the Kalman-Wiener filter that has the same computational complexity as filtered backprojection, and a means for characterizing the spatial-temporal resolution of dynamic reconstructions posed under the state-space formulation. |
