Electrical impedance tomography (EIT) aims to reconstruct the conductivity distribution using the boundary measured voltage potential. Traditional regularization based method would suffer from error propagation due to...Electrical impedance tomography (EIT) aims to reconstruct the conductivity distribution using the boundary measured voltage potential. Traditional regularization based method would suffer from error propagation due to the iteration process. The statistical inverse problem method uses statistical inference to estimate unknown parameters. In this article, we develop a nonlinear weighted anisotropic total variation (NWATV) prior density function based on the recently proposed NWATV regularization method. We calculate the corresponding posterior density function, i.e., the solution of the EIT inverse problem in the statistical sense, via a modified Markov chain Monte Carlo (MCMC) sampling. We do numerical experiment to validate the proposed approach.展开更多
In this paper, a low-dose CT denoising method based on L1/L2regularization method of Markov chain Monte Carlo is studied. Firstly, the mathematical model and regularization method of low-dose CT denoising are summariz...In this paper, a low-dose CT denoising method based on L1/L2regularization method of Markov chain Monte Carlo is studied. Firstly, the mathematical model and regularization method of low-dose CT denoising are summarized, and then the theoretical basis of MCMC method and its application in image denoising are introduced. We evaluated the performance of various regularization strategies by comparing the denoising effects of L1, L2, and L1/L2regularization terms in MCMC sampling at Gaussian noise levels. The experimental results show that L1/L2regularization has the best performance in balancing noise removal and image detail retention, significantly superior to single L1and L2regularization, which proves its effectiveness for low-dose CT denoising.展开更多
A review of ten-year's practice in developing the improved simultaneous physical retrieval method(ISPRM)is given in the hope that some creative ideas can be drawn from it.The improvement upon the SPRM is associate...A review of ten-year's practice in developing the improved simultaneous physical retrieval method(ISPRM)is given in the hope that some creative ideas can be drawn from it.The improvement upon the SPRM is associated with the under-determinedness of this ill-posed inverse problem.In our experiment,the precondition is observed that prior information must be independent of the satellite measurements.The well-posed retrieval theory has told us that the forward process is fundamental for the retrieval,and it is the bridge between the input of satellite radiance and the output of retrievals.In order to obtain a better result from the forward process. the full advantage of every prior information available must be taken.It is necessary to turn the ill- posed inverse problem into the well-posed one.Then by using the Ridge regression or Bayes algorithm to find the optimal combination among the first guess,the theoretical analogue information and the satellite observations,the impact of the under-determinedness of this inverse problem on the numerical solution is minimized.展开更多
文摘Electrical impedance tomography (EIT) aims to reconstruct the conductivity distribution using the boundary measured voltage potential. Traditional regularization based method would suffer from error propagation due to the iteration process. The statistical inverse problem method uses statistical inference to estimate unknown parameters. In this article, we develop a nonlinear weighted anisotropic total variation (NWATV) prior density function based on the recently proposed NWATV regularization method. We calculate the corresponding posterior density function, i.e., the solution of the EIT inverse problem in the statistical sense, via a modified Markov chain Monte Carlo (MCMC) sampling. We do numerical experiment to validate the proposed approach.
文摘In this paper, a low-dose CT denoising method based on L1/L2regularization method of Markov chain Monte Carlo is studied. Firstly, the mathematical model and regularization method of low-dose CT denoising are summarized, and then the theoretical basis of MCMC method and its application in image denoising are introduced. We evaluated the performance of various regularization strategies by comparing the denoising effects of L1, L2, and L1/L2regularization terms in MCMC sampling at Gaussian noise levels. The experimental results show that L1/L2regularization has the best performance in balancing noise removal and image detail retention, significantly superior to single L1and L2regularization, which proves its effectiveness for low-dose CT denoising.
基金Supported by NNSF of China under Grant(49794030#)National"973"Program No.4 (G1998040909#).
文摘A review of ten-year's practice in developing the improved simultaneous physical retrieval method(ISPRM)is given in the hope that some creative ideas can be drawn from it.The improvement upon the SPRM is associated with the under-determinedness of this ill-posed inverse problem.In our experiment,the precondition is observed that prior information must be independent of the satellite measurements.The well-posed retrieval theory has told us that the forward process is fundamental for the retrieval,and it is the bridge between the input of satellite radiance and the output of retrievals.In order to obtain a better result from the forward process. the full advantage of every prior information available must be taken.It is necessary to turn the ill- posed inverse problem into the well-posed one.Then by using the Ridge regression or Bayes algorithm to find the optimal combination among the first guess,the theoretical analogue information and the satellite observations,the impact of the under-determinedness of this inverse problem on the numerical solution is minimized.
