title: Mixed Total Variation andL1Regularization Method for Optical Tomography Based on Radiative Transfer Equation.
abstract: Optical tomography is an emerging and important molecular imaging modality. The aim of optical tomography is to reconstruct optical properties of human tissues. In this paper, we focus on reconstructing the absorption coefficient based on the radiative transfer equation (RTE). It is an ill-posed parameter identification problem. Regularization methods have been broadly applied to reconstruct the optical coefficients, such as the total variation (TV) regularization and theL1regularization. In order to better reconstruct the piecewise constant and sparse coefficient distributions, TV andL1norms are combined as the regularization. The forward problem is discretized with the discontinuous Galerkin method on the spatial space and the finite element method on the angular space. The minimization problem is solved by a Jacobian-based Levenberg-Marquardt type method which is equipped with a split Bregman algorithms for theL1regularization. We use the adjoint method to compute the Jacobian matrix which dramatically improves the computation efficiency. By comparing with the other imaging reconstruction methods based on TV andL1regularizations, the simulation results show the validity and efficiency of the proposed method.
authors.affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, China.
authors.forename: Jinping
authors.identifier: 0000-0002-9789-3751
authors.initials: J
authors.lastname: Tang
authors.affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, China.
authors.forename: Bo
authors.identifier: 0000-0002-8828-791X
authors.initials: B
authors.lastname: Han
authors.affiliation: Department of Mathematics, University of Iowa, Iowa City, IA, USA.
authors.forename: Weimin
authors.identifier: 0000-0002-0960-2281
authors.initials: W
authors.lastname: Han
authors.affiliation: School of Mathematics and Statistics, Northeast Petroleum University, Daqing, Heilongjiang Province, China.
authors.forename: Bo
authors.initials: B
authors.lastname: Bi
authors.affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, China.
authors.forename: Li
authors.initials: L
authors.lastname: Li
mesh_terms: D000465:Algorithms; D016880:Anisotropy; D003198:Computer Simulation; D003936:Diagnosis, Computer-Assisted; D020342:Finite Element Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods; D008490:Medical Informatics / Q000379:methods; D015233:Models, Statistical; D055095:Optics and Photonics; D019047:Phantoms, Imaging; D041622:Tomography, Optical / Q000379:methods*