Research On Flash Image Reconstruction Algorithm Based On MCMC Method

MCMC methods are effective means to solve high-dimensional nonlinear problems.High energy flash radiographs reconstruction is a typical high-dimensional nonlinear inversion pro-cess.However,most of the current reconstruction methods are based on a linear approximation model,which uses optical depth images for reconstruction.As radiographs are convolved by the system blur,images reconstructed with this linear model are blurred,especially at edges.The main difficulties of these methods are deconvolution and denoising.In this thesis,considering the complete flash radiography process,we focus on the effects of the system blur and noise on reconstructions,discuss the theories and methods of flash radiographs reconstruction in linear models and nonlinear models,and mainly study the flash radiographs reconstruction algorithms based on the MCMC methods.In the linear model,optical depth images are reconstructed by a MCMC method based on the Bayesian hierarchical model.The numerical experiments show that it is feasible to use the MCMC method for flash radiographs reconstruction.However,the MCMC reconstructions are seriously affected by the system blur and their resolutions are low,especially at edges,similar to the other reconstruction algorithms based on this linear model.To overcome this shortcom-ing of the linear reconstructions,assuming that the system blur is known,a nonlinear least squares reconstruction model for transmittance images is proposed and optimized by the Lev-enberg-Marquardt algorithm with non-negativity constraints and smoothing constraints.The numerical experiments show that the reconstruction error of this approach is greatly reduced and the edges sharpness is significantly improved,compared with linear reconstructions,indi-cating the advantage of nonlinear reconstruction model in deconvolution.Finally,to accurately obtain the reconstruction uncertainty which could improve the quantitative use value of results,we propose the nonlinear Bayes model for flash radiographs reconstruction.The results of the nonlinear least squares are taken as prior knowledge,and MCMC methods are used to solve this Bayes model.MCMC reconstructions are smoothing and their edges are sharp.Furthermore,the uncertainty are quantified accurately.In conclusion,compared with current reconstruction methods,our nonlinear MCMC algorithms can not only effectively reduce the effects of the system blur on reconstructions,but also quantify uncertainty in reconstructions,and show a promising prospect in high energy flash radiographs reconstruction.