Reconstruction And Bayesian Inference Of Radiation In Atmospheric Medium

The composition of the atmospheric medium is complex,and different atmospheric medium will have different effects on the radiative transfer of light scattering,which will seriously affect human activities and the global climate change.For example,aerosols in the atmosphere will seriously affect the environment and cause harm to human health.Therefore,the research on the atmospheric medium is very important.In this paper,the radiative transfer problem of light scattering in the atmospheric medium is considered.In the first part of our study,a new scheme for sampling and reconstructing the bidirectional scattering distribution function(BSDF)is proposed.The Fibonacci point set method,which is suitable for calculating integral on sphere,and Monte Carlo method are used to sampling the observation points.Then the Monte Carlo simulation of radiative transfer is used to obtain the observation data of BSDF,and the compressed sensing theory is applied to reconstruct the BSDF.The sparsity of the signal is vital for compressed sensing,it enable to recover the signal by using fewer samples than the Nyquist sampling theorem.In this study,the sparsity of the BSDF is explored by using spherical harmonic basic functions and the BSDF is reconstructed by solving a ₁l-norm minimizing problem.A logarithmic transformation of the BSDF data is introduced to improve the accuracy of reconstruction.The numerical results show that the proposed reconstruction scheme has higher accuracy with lower the sampling cost.In the second part of our study,Bayesian inference is used to estimate the atmospheric parameters,such as optical thickness,albedo and asymmetry factor.Firstly,the samples are obtained by simulating the radiative transfer.Then the Bayesian estimation is made with the uniform distribution as prior.Finally,the MCMC sampling method is used to sampling from the posterior distribution,and the statistics of posterior distribution,such as sample mean,median,standard deviation and 95%confidence interval,are estimated according to the samples.The numerical results show that the MCMC Bayesian method can give good estimation of atmospheric parameters.