Research On Choosing Parameters Of Regularization Methods For Inverse Problem Of Electrical Resistance Tomography

Electrical resistance tomography(ERT)as one kind of tomography techniques reconstructs the conductivity distribution from the boundary changes of electrical measurements.ERT attracts much attention with the merits of non-invasion,non-radiation,low cost and high speed in recent years.However,due to the serious ill-posedness of the inverse problem of ERT,it is hard to implement the reconstruction in a fast and accuracy way.The regularization methods have an outstanding performance in dealing with the ill-posedness of the inverse problem,but they are critically affected by the choice of regularization parame ter.Therefore some systematical investigates about an appropriate choice of the regularization parameter in the regularization methods are carried out here.The main contents are as follows:(1)A brief discussion on choosing a proper regularization parameter for Tikhonov regularization is introduced and three of the most commonly known methods-discrepancy principle,generalized cross validation,L-curve method-are tested with some simulations of ERT.(2)Do some further survey on the application of the L-curve method in solving the inverse problem of ERT.And propose a modified strategy to overcome the situations where the L-curve method fails.Combining with the traditional L-curve method,the modified strategy extends the application of L-curve in the field of choosing regularization parameter and achieves an efficient solution for the inverse problem to improve reconstruction quality of ERT.(3)Most approaches to the parameter selection in the literature only concern a fixed predetermined scale value as regularization parameter over the whole measured field and ignore the spatial characteristic of the measured field distribution.A spatially adaptive regularization parameter choice method is proposed for ERT based on Tikhonov regularization.And the parameters concerned in the proposed method are also discussed.The adaptive method makes full use of the spatial characteristic of the measured field,achieves an efficient and reliable regularization solution for the inverse problem and improves the quality of the reconstructed objects in all the size,location,number and the boundary.(4)The Lp regularization method(??21 p)as one kind of sparse regularization methods,has been used in image reconstruction of ERT.A spatial adaptive method is proposed for determining the parameter p.And combining with the adaptive regularization parameter choice method,Lp regularization method can select both parameter p and regularization parameter automatically.(5)In order to improve the speed and save the running time of ERT,a projection method based on Krylov subspace is applied on the inverse problem of ERT.And combining with Krylov subspace,all methods mentioned above further improve the imaging speed without losing the accuracy.This lays a foundation of the real-time imaging.