Solution to impedance distribution in electrical impedance tomography （EIT） is an ill-posed nonlinear inverse problem. It is especially difficult to reconstruct an EIT image in the center area of a measured object. ...Solution to impedance distribution in electrical impedance tomography （EIT） is an ill-posed nonlinear inverse problem. It is especially difficult to reconstruct an EIT image in the center area of a measured object. Tikhonov regularization with some prior information is a sound regnlarization method for static electrical impedance tomography under the condition that some true impedance distribution information is known a priori. This paper presents a direct search method （DSM） as pretreatment of image reconstruction through which one not only can construct a regularization matrix which may locate in areas of impedance change, but also can obtain an initial impedance distribution more similar to the true impedance distribution, as well as better current modes which can better distinguish the initial distribution and the true distribution. Simulation results indicate that, by using DSM, resolution in the center area of the measured object can be improved significantly.展开更多
In this paper, we propose a new separable fractional interpolation model which can be established by 2n interpolation points where n is the number of variables. Based on this model, a new direct search method is prese...In this paper, we propose a new separable fractional interpolation model which can be established by 2n interpolation points where n is the number of variables. Based on this model, a new direct search method is presented. In this method, a new iterate is determined by solving the fractional interpolation model in trust region. Under mild assumptions, the convergence results of this method are given and proved, Numerical experiments show that the new method is promising.展开更多
文摘Solution to impedance distribution in electrical impedance tomography （EIT） is an ill-posed nonlinear inverse problem. It is especially difficult to reconstruct an EIT image in the center area of a measured object. Tikhonov regularization with some prior information is a sound regnlarization method for static electrical impedance tomography under the condition that some true impedance distribution information is known a priori. This paper presents a direct search method （DSM） as pretreatment of image reconstruction through which one not only can construct a regularization matrix which may locate in areas of impedance change, but also can obtain an initial impedance distribution more similar to the true impedance distribution, as well as better current modes which can better distinguish the initial distribution and the true distribution. Simulation results indicate that, by using DSM, resolution in the center area of the measured object can be improved significantly.
基金Supported by the National Natural Science Foundation of China(Nos.11071117 and 11001128)ChinaRussia(NSFC RFBR)Cooperation Program(No.11211120155)
文摘In this paper, we propose a new separable fractional interpolation model which can be established by 2n interpolation points where n is the number of variables. Based on this model, a new direct search method is presented. In this method, a new iterate is determined by solving the fractional interpolation model in trust region. Under mild assumptions, the convergence results of this method are given and proved, Numerical experiments show that the new method is promising.
