A state-space approach to dynamic tomography

tomography;Kalman filtering;Kalman smoothing;ensemble Kalman filtering;ensemble Kalman smoothing;solar tomography;solar corona;coronal electron density;state estimation;dynamic tomography;time-dependent tomography;ensemble Kalman filter convergence;covariance tapering

Butala, Mark D.

关键词: tomography;    Kalman filtering;    Kalman smoothing;    ensemble Kalman filtering;    ensemble Kalman smoothing;    solar tomography;    solar corona;    coronal electron density;    state estimation;    dynamic tomography;    time-dependent tomography;    ensemble Kalman filter convergence;    covariance tapering;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/18480/Butala_Mark.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The statistical inference of a hidden Markov random process is aproblem encountered in numerous signal processing applicationsincluding dynamic tomography.In dynamic tomography, the goal is toform images of an object that changes in time from its projectionmeasurements.This work focuses on the case where the object'stemporal evolution is significant and governed by a physical model.Solar tomography, the remote sensing problem concerned with thereconstruction of the dynamic solar atmosphere, has served as themotivating application throughout the development of the dissertation.The proposed state-space formulation provides a natural and generalstatistical framework for the systematic tomographic reconstruction ofdynamic objects when faced with inevitable measurement and modelinguncertainties.In addition, the dissertation offers signal processingmethods that scale to meet the computational demands ofhigh-dimensional state estimation problems such as dynamic tomography.Major contributions include a rigorous characterization of theconvergence of the ensemble Kalman filter, a new method for ensembleKalman smoothing and theory regarding its convergence, the firstfour-dimensional reconstruction of electron density in the solaratmosphere, a new method for dynamic tomography called theKalman-Wiener filter that has the same computational complexity asfiltered back-projection, and a means for characterizing thespatial-temporal resolution of dynamic reconstructions posed under thestate-space formulation.