Research On The Statistical Inversion Approach For Aperture Synthesis Microwave Radiometric Imaging

The statistical inversion theory is induced into aperture synthesis radiometers (ASRs) extended source imaging researches. According the statistical inversion theory, the following knowledge about the ASRs imaging is explored and modeled:the prior information about the extended source's brightness temperature distribution (ESBTD) of the extended source, the ASRs' physical properties, and the information in the ASRs' measurement processes. Different SIAs have been developed according to the natures of different ESBTD prior information. The common theoretical problems of SIA itself and the special applicable background of ASRs imaging has been researched. Main works are given below:1 The deterministic inversion approaches (DIAs) for ASRs imaging are analyzed in the viewpoint of statistics. The statistical properties about the ESBTD and the visibilities implicitly used in the DIAs are presented and compared with the actual ones. The difficulties of the regularization parameter determination and the discretization error analysis for DIAs are also discussed. In SIAs, the unkown parameters can be estimated using statistical inference method, which can avoid the difficulty on regularization parameter determination. The quality of reconstruction can be improved by taking advantage the statistical properties about the ESBTD prior information. According to the properties of SIA, the researches about the ASRs imaging in the statistical form are done as the following parts:â‘ constructing the likelihood function to model the relationship between the visibilities and ESBTD;â‘¡constructing the prior probability distribution to model the ESBTD prior information;â‘¢developing the posteriori probability estimation method according to the relationship between the likelihood and the prior probability distribution.2 According to the different impacts on the reconstructions, the ASRs'imperfections are classified by the instrument errors and the noise errors.The measurement uncertainty is introduced to evaluate the quality of the visibilities. The analytic relationship between the calibration parameters and the combination uncertainty is established, which can synthetically take into account the impacts of the errors and the error calibration on the visibilities' quality.3 According to the nature of prior probability distribution, two kinds of SIAs, i.e., the Gaussian prior information based SIA and the non-Gaussian prior information based SIA are developed. The works about the Gaussian prior information based SIAs are given below:(1) A Gaussian prior information based SIA is proposed. Based on the analysis about the ESBTD's prior covariance matrix, a novel Gaussian prior model of the ESBTD is presented, which is robust to the noise errors. The statistical inversion model of ASRs is deduced and constructed. A SIA is proposed according to the Gaussian ESBTD prior information and the Gaussian visibility noise, which can effectively improve the image quality of ASRs.(2) A multi-resolution SIA for ASRs is proposed. The discretization errors and its impact on the visibilities' statistical properties are analyzed using multi-resolution technique. Correspondingly, a multi-resolution inverse problem model is constructed. Based on the works mentioned above, the multi-resolution SIA for ASRs is presented, which can seamlessly accounts for the knowledge about the ESBTD prior information and the statistical properties of discretization error, and improve the quality of the reconstructions. Additionally, the multi-resolution SIA can generate the multi-resolution maximum posteriori estimation of the ESBTD.The works about the non-Gaussian prior information based SIAs are given below:(1) The (?)1 prior information based SIAs are proposed. Conditioned the extended source, a space transformation method is proposed to explored the implicit (?)1 prior information about the ESBTD. An equivalent hierarchical prior model for the (?)1 prior information is constructed, and the methods for hyperparamter estimation about the hierarchical prior model are presented. Compared with the ASRs' DIAs, the (?)1 prior information based SIAs are robust to the ASRs' imperfections, and can greatly improve the reconstruction's radiometric accuracy and reduce the reconstruction's noise.(2) A compressive sensing theory based SIA for ASRs is proposed. It's difficult to satisfy the sparsity and the restricted isometry property (RIP) in the application of the compressive sensing theory for ASRs extended source imaging. For the ESBTD with structure features, a compressive basis is proposed for tradeoff between the sparsity and the RIP. Furthermore, the whiting operation and random baseline selection are carried out to improve the RIP. Compared with the ASRs'DIAs, the compressive sensing theory based SIA can provide exact ESBTD in high probability conditioned less visibilities, and reduce the computation complexity for ASRs imaging.Compared with the ASRs' DIAs, the SIAs developed conditioned different ESBTD prior information can efficiently reduce the impact of ASRs' imperfections on the reconstructions, and greatly improve the ASRs'imaging performance. Additionally, the research in this paper is much of help in performance evaluation and parameter design of ASRs.