Application Of Sparse Regularization Methods In Electrical Tomography

Electrical Tomography(ET)attracts much attention due to its properties of non-invasion,non-radiative,low-cost and quick response.However,the ill-posedness and under-determinedness of image reconstruction becomes an important factor restricting the development of ET.The regularization methods have good performance in dealing with the ill-posedness of the inverse problem,and the sparse regularization methods based on L1 and Lp constraints are paid more attention in recent years and develop rapidly.In this paper,the applications of iterative shrinkage threshold algorithms for solving the sparse regularization problem are investigated systematically.In order to improve the applicability,accuracy and speed of the iterative shrinkage threshold algorithms,the following work is carried out:(1)The application of iterative shrinkage threshold algorithms(ISTA)for solving the inverse problem of ET is investigated.The relationship between iterative shrinkage threshold operator and the objective function of sparse regularizzation is deduced?Then an accelerating method of ISTA is introduced due to the low speed of ISTA and the feasibility of this kind of methods is tested with some simulations of ERT.Moreover,a non-negative process is added in the solution of ISTA,which solves the variegated background problem in reconstructed images and improves the quality of image reconctruction of ISTA.(2)A fast iterative shrinkage threshold algorithm(FIVTA)based on Firm threshold function is proposed to implement self-adaptive updating of threshold parameter.In order to solve the problem that the threshold parameter of ISTA is hard to be selected properly and the soft threshold iterative algorithm based on L1 regularization is sometimes over punished,the concept of sparsity is introduced here and the FIVTA based on a new Firm threshold function is proposed to achieve self-adaptive parameter updating.The imaging speed,accuracy and noise robustness of FIVTA are verified with simulated data and the practical ERT system.And the parameters concerned in FIVTA are also discussed.(3)As a sparse regularization method,Lp regularization has been widely studied and applied in image reconstruction of ET.However,the object function of Lp regularization is hard to solve,and the p value of Lp is always a fixed predetermined value which can not be properly selected in each step of iterations.So a new generalized p-threshold function,which can be seen as a mapping of a wide class of sparsity constraints,is proposed to solve the sparse regularization of ET.The proposed fast iterative shrinkage p-threshold algorithm(FIPTA)provides a general frame of solution for different object functions of different p values.Then combined with the effect of p value on reconstructed images,a strategy of self-adaptive approach for p value updating is proposed,which lays the foundation for the further study of the application of Lp regularization in ET.