Efficient reconstruction algorithms for three-dimensional tomographic imaging

作     者：Helle Majander 

作者单位：Aalto University 

学位级别：博士

导师姓名：Nuutti Hyvonen

授予年度：2016年

主      题：parameter estimation problem tomographic imaging edge-enhancing regularization modeling errors priorconditioning LSQR electrical impedance tomography complete electrode model diffuse optical tomography quantitative photoacoustic tomography 

摘      要：This thesis considers nonlinear parameter estimation problems arising from tomographic imaging modalities governed by elliptic partial differential equations. These are ill-posed inverse problems and hence their solution requires regularization or, in the Bayesian frame- work, incorporation of prior information about the to-be-reconstructed spatially varying parameter. In particular, if the parameter is known to have distinct inclusions in a constant background, we quantify such information by assuming that after discretization the parameter follows an edge-enhancing prior distribution. Moreover, we study how to recover from differ- ent kinds of errors in the data, since even small ones can be enough to ruin the reconstruction for an ill-posed tomographic imaging problem. We consider the solution ofthe investigated inverse problem to be the maximum a posteriori estimate for the parameter of interest, which can be found by solving a minimization problem. We propose to search for the minimizer by an iterative algorithm based on combining lineariza- tions of the forward model, lagged diffusivity steps and a priorconditioned Krylov subspace method (LSQR). By presenting examples from electrical impedance tomography (EIT), diffuse optical tomography (DOT) and quantitative photoacoustic tomography (QPAT), we demon- strate that such a method can be implemented efficiently enough to be feasible for solving large-scale three-dimensional problems. In addition, we use a conformal invariance result for the complete electrode model (CEM) of EIT to compensate for geometric modeling errors.