Multisensor Data Fusion And The Multiscale Solving Of Linear Inverse Problem

In many fields, such as remote sensing, nuclear medical, computer tomography, geophysical prospecting, groundwater hydrology, global ocean modeling, image processing, tumor detection, nondestructive detection, the objective of applied sciences and engineering is the recovery of the original signal given a collection of noisy observations of the original signal; we call these problems inverse problem. Now the two issues we are confronted with are:First, a reasonable regularization technique is required to overcome the ill-posedness of the problem;Second, we are required to develop a computational efficient technique to reduce the complexity of the solving, which in turn promotes the implementation of the solving algorithm.This is due to the following two facts: the ill-posedness induced by the incompleteness of the observation data can make the solving much more difficult; In addition, the observation system involved multiple sensors are required to compensate the inaccuracy of the observation equipment, which will inevitably make the cost of the computation prohibitively expensive.In this paper, we combine the multi-scale representation and the multi-sensor data fusion technique with the solving of the inverse problem. The main contributions of this paper are as follows:1. A multi-sensor distributed data fusion algorithm is developed in chapter 3, and the theoretical proving is presented;2. A sub-optimal Kalman filter is presented in chapter 3, and the relative error covariance matrix (RECM) is introduced to evaluate the performance of the fusion process;3. Based on the multi-scale representation theory, we present a reduced ordermodel for the solving of the inverse problem. Also the relative error covariance matrix is used to analyze the performance of models with different orders;4. For those inverse problems with multiple observation processes, we present a distributed hierarchical fusion algorithm. Using the RECM to evaluate the performance, we conclude that the performance of the distributed hierarchical fusion algorithm is comparable to that of the centralized fusion algorithm, while the computational burden of the solving is obviously alleviated.