Radar Super Resolution Imaging Technology Based On Statistical Sampling Machine Learning

Synthetic Aperture Radar（SAR）has the characteristics of all-day,all-weather and long operating range,which can carry out high-resolution imaging of detection targets in complex environment,and has been widely used in practical scenes.In the actual work,the resolution of SAR imaging directly affects the quality of radar imaging performance,so how to effectively improve the imaging resolution is the core content of SAR imaging algorithm.However,due to the limitation of the response function,the traditional SAR imaging algorithm using Fourier transform will widen the main lobe and enlarge the side lobe of the echo data.This seriously limits the improvement of radar accuracy and is not conducive to target detection and feature extraction.This thesis aims at improving the accuracy of high resolution SAR imaging recovery.In this thesis,the original radar echo data and Bayesian statistical machine learning method are used.Then the probability density distribution is used for modeling.Finally,statistical sampling techniques,mainly Markov Chain Monte Carlo（MCMC）sampling techniques,are used to realize Bayesian inference.The research contents can be divided into the following points:1.This thesis studies the problem of complex parameter adjustment in the optimized imaging algorithm.Traditional optimized sparse SAR imaging algorithms involve tedious regularization coefficient adjustment,which seriously limits the accuracy and convenience of SAR target superresolution imaging.In this paper,a hierarchical Bayesian probability model is established for the unconstrained Lasso regularization problem.Firstly,a Bayesian Lasso model for SAR imaging is established.Under the sparse prior assumption,the solution of the inhomogeneous underdetermined linear equations is transformed into the solution of the Lasso problem.Then,the sparse Laplace prior probabilistic modeling is implemented in the hierarchical Bayesian framework.Meanwhile,a conditional probabilistic dependent model is established for the sparse regulation coefficient of the corresponding ₁ norm regular term in the optimization process.Finally,the MCMC sampling algorithm is used to automatically learn the regular term coefficient from the data to realize the solution of the sparse features of the SAR target,and obtain the multi-parameter estimation including the regular term coefficient synchronously.Based on this research method,all parameters can be dependent through conditional probability,and the solution can be completed in MCMC sampling algorithm,so as to effectively avoid the cumbersome parameter adjustment process and improve the automation degree of the algorithm.2.This thesis studies the use of Bi-sparsity distribution to make statistical constraints on the prior distribution of the target scatterers,and to locate the target position and enhance the target amplitude from two aspects of Sparsity,so as to realize SAR high-resolution imaging.Firstly,considering that SAR imaging targets usually have obvious sparse characteristics,Bernoulli--Laplace（BL）hybrid sparse prior is used to model the statistical characteristics of the target,and Bi-sparsity is used to make statistical constraints on the target priors,so as to effectively simulate the statistical priors of the target scattering field.Secondly,in order to simplify the Bayesian inference and reduce the computational complexity,the prior is layered by introducing the hidden variable modeling under the Bayesian Hierarchy Model.Finally,in order to avoid tedious manual parameter adjustment and realize the self-adjustment of hyperparameters,conditional probability dependent model was established for each random variable,and MCMC sampling algorithm was used to solve the problems that high dimensional integration and posterior distribution were difficult to solve,so as to realize the estimation calculation of hyperparameters and improve the self-learning ability of the algorithm.The effectiveness of the algorithm is proved by the comparison of simulation and raw data.3.This thesis studies the problem that the flexibility of fixed priors is not high and it is difficult to simulate the statistical characteristics of complex SAR imaging target scene effectively.Firstly,a generalized Gaussian distribution（GGD）is used to build a statistical model of the target priori,and the target scattering field is fully simulated and modeled by adaptive matching of the target priori driven by the received echo data.Then the superparameters are introduced and the Bayesian hierarchy model is used to solve the non-conjugate problem between the likelihood function and the prior distribution so as to simplify the operation and improve the efficiency.Because the target’s posterior distribution is difficult to be obtained by direct analysis,this paper combines the idea of variable splitting of Alternating Direction Method of Multipliers（ADMM）,which is widely used in convex optimization,and introduces auxiliary variables to decompose the target’s posterior distribution into multiple subtasks for calculation.Finally,the combination of the proximal operator and the Hamiltonian Monte Carlo（HMC）sampling algorithm is used to construct the proximal Hamiltonian Monte Carlo（PHMC）sampling algorithm to solve the sampling problem of the non-smooth posterior distribution function,so as to effectively improve the efficiency of Bayesian inference.