Research On The Statistical Inference Methods For Synthetic Aperture Interferometric Radiometry Inversion

According to the law of thermomechanics,any material whose temperature is higher than absolute zero radiates electromagnetic energy.In the microwave band,the radiometer is a passive receiver with high radiometric sensitivity.The synthetic aperture interferometric radiometer(SAIR)is a kind of sparse array system,which consists of several small sized antennas.The synthetic aperture is equivalent to the largest filled real aperture and the SAIR can fulfill radiometric measurement simultaneously without scanning.At present,the SAIR technique has been widely investigated and applied in the field of radio astronomy,geophysical remote sensing,safety inspection and military reconnaissance.The radiometer measures the energy accumulation of natural random thermal radiation and outputs a physical quantity with the unit dimension of power.In particular,the SAIR measures the cross-correlation between the signals received by pairs of spatially separated antennas,which have overlapping fields of view,obtaining samples of visibility function of the brightness temperature of the observed scene.In order to solve the key issues about brightness temperature(BT)reconstruction and radio frequency interference(RFI)localiza-tion,this dissertation focuses on the research of the SAIR visibility function and involves the following aspects:With the regard to the limitation of deterministic regularization methods in solving the ill-posed inverse problems,this dissertation elaborates a probability theoretical framework on the SAIR inversion drawn support from the theory context combined by the probability and the Hilbert space.This framework is also based on the statistical learning theory and provides a criterion on evaluating the risk functional quality of the SAIR inversion model under the condition of small sample set.The relationship between the kernel methods and the deterministic regularization methods is analysed.Then the probability equations with re-spect to the deterministic regularization methods is exhibited and the internal mathematical meaning is explained.Finally,the statistical feature of the signal in the SAIR measurement is verified through some interferometric experiments and numerical simulations.Based on the theoretical analysis of statistical inference and the consecutive probabilis-tic description of the BT distribution and the visibility function,this dissertation provides a Bayesian inference estimation method for BT reconstruction in the SAIR.In order to resolve the difficulty of determining the optimal parameters in the deterministic regularization meth-ods,this method establishes the statistical regression model for SAIR inversion and uses Bayesian inference theory to estimate the reconstructed BT,without introducing the dilem-ma of over-regularization or under-regularization.The method can relief the ill-posedness of the model operator adjusted to the visibility function,and obtain the reconstructed BT more effectively in the case of ensuring inversion accuracy.Furthermore,the presented method can also provide a way to evaluate the quality of BT reconstruction with the help of confidence interval.In consideration of the adverse impact caused by RFI sources in microwave radiom-etry,inspired by the sparseness of RFI distribution in the spatial domain,this dissertation presents a RFI localization method by the means of sparse prior modeling.On the basis of the equivalence property between the visibility function in the SAIR and the covariance matrix in the conventional sensor array for beamforming technique,the Laplace sparse prior probability model for sparsely distributed RFI sources in the spatial domain is established,and the subsequent hierarchical probability model for RFI sources' DOA estimation is con-ducted.As a result,the problem of RFI localization is translated to maximum a posterior(MAP)estimation for sparse index vector.Finally,the quantity and the locations of RFI sources in BT images can be obtained.In this dissertation,all the related research work on the statistical inference methods for brightness temperature inversion and radio frequency interference sources localization has included strict mathematical theory deviation,as well as sufficient simulations and experiments.