Fluorescence Imaging Model And Algorithm Based On Diffusion Equation

Fluorescence diffusion optical tomography is a technology that uses externally applied emission light to excite specific fluorescence inside biological tissues,and uses a detector to capture the fluorescence information on the surface,thereby imaging the fluorescence distribution inside biological tissues.Under the background of experimental settings,the fluorescence imaging problem is studied based on the diffusion equation in the upper half of the unbounded region.When the medium of the emission field is isotropic and the photon density field can be approximated as a linear function with respect to the angle,the radiation transmission equation can be simplified to a diffusion equation independent of the angle direction.Assuming that the absorption coefficient of the fluorescence is much smaller than the absorption coefficient and scattering coefficient of the excitation light in the medium,the emission field and excitation field can be decoupled,and finally the fluorescence imaging positive process is the first type of linear integral with an explicit integral nucleus equation.The two-dimensional situation in space is dispersed by the method of collocation points,and the discrete approximate linear model of the system is obtained.Firstly,the serious ill-posedness of the fluorescence imaging problem is verified by the discrete Picard curve,and then Tikhonov regularization,l1 regularization,TV regularization of the spatial two-dimensional discrete system are given.Finally,considering the spatial three-dimensional imaging,assuming that the fluorescence has a special geometric shape and uniform distribution,it is transformed into a small-scale nonlinear optimization problem of geometric parameters and intensity values,and the theoretical basis for the selection of initial values is given.The numerical examples compare the reconstruction effects of various regularization algorithms from the depth position of the fluorescence and the error of the discrete model;it is numerically verified that the time corresponding to the maximum value of the horizontal position fixed integral core is linearly related to the depth position of the integral core;under the assumption that the fluorescence has a special geometric shape and uniform distribution,the numerical results of different detection point pairs at different times are given,which verifies the theoretical results of the nature of the observed extreme points.