Method Research For Multiscale Representation Of Stochastic Dynamic Processes

Multisensor data fusion technology has been applied broadly in practice, Such as automated target recognition, control of autonomous vehicles and medical diagnosis etc. However, the key of the data fusion is the design for modeling and the algorithm for fusing.A large number of phenomena or processes possess features and physically significant effects at multiple scales. At the same time, the available data are collected at several different resolutions. Thus, it is very necessary to built multiscale dynamic model based on pyramidally organized trees for stochastic processes. The multiscale model is not only capturing the several important ways in which a data analysis or signal processing problem can have multiscale characteristic, but also leading to an efficient and highly parallelizable algorithm for optimal estimation of stochastic processes. The multiscale modeling we describe in this dissertation has been employed in a wide variety of applications, including: geophysical remote sense imaging, ocean height estimation, surface reconstruction, image denoising, texture discrimination, image segmentation, object recognition and multisensor fusion for groundwater hydrology.In this dissertation, we develop the research work of the following three aspects based on existed work.First, using the scale-invariant property of multiscale model, i.e. Markovian among scales, a method of qth-order tree-based for multiscale representation of a class of 1-D stochastic process is presented. The multiscale stochastic model is established. The representation forms of parameter matrices, such as, the state transition matrix, the disturbance matrix, the initial state and the corresponding covariance matrix are deduced in detail. The multiscale sample paths based on distinctive order tree are presented by computer simulation.Second, we present the method of 3x3 -order tree-based of redundant multiscale representation for 2-D Markov random fields, and we propose a class of non-redundantmultiscale model for reduced-order approximately representing Gaussian Markov random fields making ties to multiscale analysis.At last, aimed at the stochastic system in which the uniform target at the same periods is observed by sensors possessing different characters at multiple scales, we present a method of the multiscale representation based on unregular tree. We develop the multiscale stochastic model based on scale sequence at odd- and even-numbered scale and on different order trees.The models described in this dissertation lay the theoretic foundation for multi-sensor multiscale dada fusion.