Bioluminescence Tomography Based On Non-convex L_1-2 Regularization

Bioluminescence tomography(BLT)is a new type of optical imaging mode.It use s the intensity information on the surface to retrieve the distribution information of inte rnal source(fluorescently labeled target),and thus realizing non-invasive in vivo obser vation of the physiological and pathological process occurred at the molecular level.It has many advantages,such as low cost,high sensitivity,non-ionizing radiation and so on.It is very promising in the pre-clinical application of drug development and early d etection of tumor.BLT is a typical inverse source problem with a high degree of ill-posedness.In ad dition,the measurement information obtained is very limited,which increases the diffi culty of reconstruction.How to solve the ill-posedness of BLT inverse problem and rec onstruct the internal source accurately and efficiently remain a hot topic of research.In order to overcome the ill-posedness of BLT and achieve stable source reconstruction,this paper mainly studies the reconstruction methods based on regularization techniqu es.The main contents include:(1)Automatic selection of regularization parametersAs we all know,the regularization parameter has a great influence on the results o f the regularization method,hence it is necessary to select an optimal regularization par ameter to ensure the good solution.In this paper,three automatic selection methods of regularization parameters are studied:generalized cross validation(GCV),L-curve met hod and U-curve method.The three methods are combined with the classical Tikhonov regularization method and the incomplete variables truncated conjugate gradient meth od to solve the inverse problem of BLT.The digital mouse experiment is designed to v erify the effectiveness of the three methods in dealing with the problem of high ill-pose dness of BLT.The simulation result shows that the regularization parameter selected by the GCV and the L-curve method can yield good source reconstruction,while the regu larization parameter selected by the U-curve method is not proper.(2)BLT reconstruction based on nonconvex L1-2 regularizationIn order to further improve the precision of source reconstruction,this paper prop ose a new BLT reconstruction method based on nonconvex L1-2 regularization and use the difference of convex algorithm to solve the minimization objective function.In eac h iteration,we effectively solve problem through an alternating direction method of mu ltiplier with adaptive penalty,and the regularized parameter selection is carried out wit h the L-curve method.In order to verify the positioning ability and source resolving po wer of the reconstruction method,multiple groups of the experiment of single source a nd double source on digital mouse are designed and compared with several typical reco nstruction methods based on L1-norm regularization.The simulation results show that the proposed method can further improve the accuracy of reconstruction and the ability to distinguish two targets.