Study On The Diffuse Optical Tomography Based On The Steady Radiative Transfer Equation

Diffuse optical tomography is a new imaging modality with extensive application prospect.Compared with other imaging techniques,diffuse optical tomography has the advantages of noninvasive imaging modality,fast data collection and providing anatomy as well as physiological functional information of tissues and so on.The near infrared light is used as source to illuminate tissues,the photons are absorbed and scattered in tissues and some will go through the boundary of tissues,the intensity of the outgoing photons are detected on the surface of tissues,then the optical parameters can be deduced based on appropriate forward model and reconstruction algorithm.Radiative transfer e-quation and diffusion approximation are most widely used to describe the propagation,where the radiative transfer equation is regarded as the“gold standard”,while diffuse approximation can not accurately describe the process of photon transport in low scatter-ing region and also has a limit of distance between sources and detectors,thus diffusion approximation has limitations in practical application.In diffuse optical tomography,the reconstruction problems of optical parameters present highly ill-posed because of the multiple scattering of photons,noise interference in experiments and insufficient measure-ments.In order to alleviate the ill-posedness of reconstruction and improve the imaging accuracy and efficiency,the radiative transfer equation is used as the forward model in this paper,several suitable regularization reconstruction frameworks are developed,the well-posedness of the proposed regularization methods are proved,the corresponding fast algorithms are proposed and the feasibility as well as effectiveness of the proposed meth-ods are verified through numerical simulations.Iterative regularization method is one of the effective methods for solving ill-posed inverse problems.With angular variables and space variables,the imaging problem based on radiative transfer equation is a problem with large scale for numerical calculation,therefore it is crucial to study fast and efficient iterative methods for the development of diffuse optical tomography.Based on the homotopy perturbation iteration with fast convergence,the Nesterov acceleration method is combined to construct the accelerated homopoty perturbation iteration.Under the classical assumptions of iterative regulariza-tion,its convergence is proved.The proposed accelerated homopoty perturbation iterative method is applied to diffuse optical tomography,then some comparisons with the original homotopy perpurbation and the existing two point gradient method are carried out on the aspects of reconstruction accuracy and speed.The results show that accelerated homopoty perturbation method significantly reduced the imaging time.In order to simultaneously meet the description of sparse characterization of opti-cal parameters on the targets and the imaging requirement of edge preservation,the TV mixed with L1 regularization reconstruction framework is proposed,and the existence,stableness,convergence of its minimizers are provided.In numerical calculation,the reweighted strategy is introduced to TV norm to promote gradient sparsity,and the split-Bregman algorithm is used for both TV-penalty and L1 penalty.Through the comparison between TV regularization and L1 regularization,the proposed mixed regularization has more accurate reconstruction results,it has the effect of boundary preservation of TV reg-ularization as well as the effective identification capability of details of L1 regularization such as“sharp points”.In addition,the numerical simulation on the background of breast imaging presents the feasibility of mixed regularization in practical application.For the problem of identifying multi parameters of the complex tissue containing void layer or clear layer,an edge-guided TVp(0<p<1)regularization is proposed for further enhancement of boundary identification,the existence of its minimizers is proved with the regularity of H1(X)space.In numerical calculation,lagged diffusion-Newton algorithm is proposed for finding the solutions.Moreover,normalizing strategy is used to reduce the cross talk in multi parameters identification,which helps to improve the reconstruction accuracy.Numerical simulations show that the edge-guided TVp(0<1)regularization has obvious advantages in keeping shape,size and quantifying optical parameter value of targets in comparison with lp and TV regularization,it can provide the efficient imaging information of the tissue containing clear layer or void layer,and it is still able to obtain useful reconstruction results with half measurements.