Applications Of Probabilistic And Statistical Methods In Microwave Biomedical Imaging And Evaluation Of Lightning Electromagnetic Effects

The research contents of this thesis include two parts: microwave biomedical imaging and evaluation of lightning electromagnetic effects. Microwave imaging (MWI) is a typical electromagnetic inverse scattering (IS) problem of a great theoretical importance, and its potential advantages in biomedical imaging make it of great application value, too. On the other hand, the trend toward micro-miniaturization in electronic systems development brings an increasing sensitivity to transient phenomena, the major one of which is lightning activity. Consequently, study of the evaluation of lightning electromagnetic effects has attracted more and more attention. The main work addressed in this thesis includes the following aspects.1. We investigated the general mathematical theory and algorithms of MWI (IS), and pointed out that 1) the essential solution to ill-posedness of inverse scattering problem is to increase effective information including measurement one and a-prior (additional) one; 2) study on quality of measurement information can help choosing more reasonable and effective measurement mode; 3) the existing two kinds of IS algorithms - deterministic methods combining with regularization technique, and stochastic methods capable of searching globally - all contained the process of adding additional information in spite of whether or not the researchers had the subjective intent; 4) when the error between the so-called optimal solution in certainsense and the real solution is difficult to determine, considering the whole set of solutions (i.e. ensemble inference) is shown important.2. The quality of measurement information in reconstruction of layered medium inside coaxial line was studied primarily. Firstly, according to the model deduced by the theory of transmission line, we investigated the ill-posedness of this reconstruction problem using a method combining mathematical analysis with numerical experiments, and further considered how to obtain more effective information so as to remedy the ill-posedness. The conclusion from theoretical analysis agrees with numerical results that compared with multi-impedancemeasurements, multi-frequencies measurements are easier to get more effectiveinformation so as to ensure the uniqueness of reconstruction solution and weaken the instability. This conclusion can direct the practical reconstruction.3. The problem of microwave imaging was solved under the framework of Bayesian method. Representing prior information about permittivity distribution of observed object by prior probability density and combining measurements information of scattering field described as likelihood function, we obtained posterior probability density that included synthetic informjation about the observed object. And then, Gibbs sampler, one of Markov Chain Monte Carlo method, was used to sample the posterior probability density. The sample mean was regarded as an evaluation of the permittivity distribution. The results of simulation imaging with "blocky" objects showed that this set of methods makes use of information efficiently, and has the advantages of feasibility and very strong anti-noise ability. In addition, its other features include: capable of describing (definite or indefinite) prior information in a convenient and controllable way, as well as capable of giving the "complete" solution, i.e., the occurrence probability of every permittivity distribution. On the other hand, because of its high computational cost, the quick solver of the direct problem is very important. Fortunately, the permittivity in only one subregion could be disturbed at each substep in Gibbs sampler, which makes it possible to design the quick solver.4. Lightning electromagnetic field (EMF) and its effects on electronic receiverare discussed under a general probabilistic framework. The formulas of probability distribution functions of peak amplitude of lightning EMF and maximal received power of the receiving antenna were presented. The numerical simulations show that the evaluation results obtained from the formulas are in good agreement with the MC simulation results. The set of methods are not confined to certain lightning current waveform, lightning return stroke model, or the number and the probability distributions of the random variables considered, although these factors can affect the calculation results. This work forms a base for further investigating the effects of lightning on electronic systems, e.g., probability of failure.