Research On Reconstruction Methods For Diffuse Optical Tomography

Diffuse optical tomography is an emerging noninvasive imaging modality which utilizes visible light or near infrared light in certain spectral region to excite the tissues, and reconstructs the distribution of optical parameters of internal organizations through the measurement of intensity distribution on the surface of organization. In order to obtain high quality imaging, first of all we need the model which can accurately describe the photon transportation in tissues. At present diffusion equation is widely used as the forward model in diffuse optical tomography. Diffusion equation is an diffusion approximation of radiative transfer equation, it has some limitations in application. On the other hand,the measurement data is usually insu?cient in diffuse optical tomography and effected by noise, which makes the solving process seriously ill-posed. In order to reconstruct the optical parameters steadily, and improve the imaging quality, this article studies the diffuse optical tomography reconstruction algorithms based on radiative transfer equation.Based on homotopy perturbation technique, we provide a new iterative format for diffuse optical tomography problems, which can be regarded as an improvement version of classic Landweber method. This iterative format which has simple form can be implemented easily, it is an iterative regularization method. Because the optical parameter distribution in diffuse optical tomography reconstruction is usually continuous or piecewise constant, non-smooth phenomenon and oscillations will happen in discontinuous areas. In order to improve the quality of reconstructed image of these cases, we introduce the total variation regularization method that can denoise and keep the edge information.Nevertheless, total variation function is non-differentiable at zero point, we construct a new iterative format based on the homotopy perturbation technique and Bregman distance to solve the total variation regularization problem, and prove the convergence of the proposed method. The method transforms the optimization problem with total variation items into optimization problem of Bregman distance, this progress avoids the differential at zero point. This iterative method can effectively reconstruct the absorb coe?cient and scattering coe?cient separately.Based on step by step linearization of the physical model, and considering the spatial sparsity of optical parameter perturbation, we study the reconstruction problem with sparse constraint, and put forward a sparse reconstruction model with l1 norm of optical parameters perturbation and a sparse reconstruction model with SCAD function of optical parameters perturbation as regularization constraint penalty, i.e. l1 norm regularization and SCAD regularization. Considering the reconstruction problems of optical parameters perturbation which have sparse distribution in space, several examples are given to analyze the reconstruction performance of two given regularization methods.The numerical simulation shows that both of two methods can get clear edge of the inclusion with the constant background with certain noise resistant ability. Because the SCAD regularization has good statistical properties, the images reconstructed by SCAD regularization have better quality than that of l1 norm regularization. Because l1 norm regularization method requires minimization of non-differentiable objective functional,while the objective functional of SCAD regularization is non-convex, in order to solve these regularization problems, the split-Bregman algorithm is introduced for fast image reconstruction of high quality. Compared with other popular algorithms for solving sparse regularization, it can be seen that l1 norm regularization and SCAD regularization based on split-Bregman algorithm have advantages in the inversion precision and computational e?ciency through the numerical simulations.Inspired by idea of the smoothed l0 norm, to deal with the reconstruction of optical parameter perturbation distribution which is sparse in space, this article proposes a sparse reconstruction model with the l0 norm of optical parameters perturbation as regularization constraint penalty. Through a series of smooth function with gradually reduced parameters to approximate l0 norm, the l0 norm minimization problem is converted into the smooth function minimization problem. Combining with the algebraic reconstruction method, a new algorithm for solving smoothed l0 regularization is presented. An improved algebraic reconstruction algorithm is provided to accelerate the computing speed,combined with conjugate gradient method in each iterative step. The above progress constructs an algorithm that can quickly solve problems of linear systems generated by diffuse optical tomography. Then the algorithm is parallelized to effectively reduce the calculation time. Computation with GPU can improve the computation e?ciency and save the cost of computing devices. Considering limitation and particularity of parallel computing on GPU, we optimize the structure of the algorithm. A computing method combined with GPU single precision and double precision arithmetic is provided to make full use of respective advantages of GPU single and double precision arithmetic, this technique promotes the e?ciency of calculation at the cost of little double precision arithmetic on GPU. Finally, the proposed algorithm is applied to reconstruct the absorption coe?cient and scattering coe?cient simultaneously to verify its performance. And effective inversion tactics are given to alleviate “cross talking” phenomenon when multiple parameters are inverted simultaneously.