Log-sum Penalty-based Multispectral Bioluminescence Tomography

Bioluminescence tomography(BLT)can realize in-vivo visual observation of labeled cells in the body,so it is widely used in pre-clinical research such as understanding the process of disease occurrence and development,early detection of malignant tumors,quantitative evaluation of therapeutic drugs and protocols Application prospects.However,the reconstruction of BLT is to restore the position and intensity of the light source inside the organism through the photon distribution information obtained from the surface measurement.It is a typical ill-posed inverse source problem,and the absorption and scattering of light by biological tissues results in very limited measurements,increasing difficulty of numerical solution.In order to reduce the ill-posedness of BLT reconstruction,this paper combines multispectral measurement methods to obtain more photon distribution information,and considering the sparseness of the light source distribution,a non-convex Log-sum penalty term regularization model is introduced to solve the BLT inverse problem.The Log-sum penalty function can reduce the excessive contraction effect of the L1 norm,it is more closely approach to the L0 norm,and it can obtain a more accurate sparse solution in theory.In order to efficiently solve the non-convex multispectral sparse reconstruction model based on the log-sum penalty function,this paper presents two reconstruction algorithms,and designs simulation and mouse experiments to verify the feasibility and effectiveness of the algorithm.The research contents of this paper include:(1)A multi-spectral BLT sparse reconstruction model based on log-sum regular terms and multi-spectral measurement information is established.And a hybrid optimization algorithm is used to solve it.Different from the general iterative threshold shrinkage method for solving non-convex optimization models,this hybrid optimization method uses the quasi-Newton method or gradient descent method to selectively mix second-order information and first-order information for reconstruction in each iteration.This not only ensures the speed of the solution,but also makes it easier to obtain the global optimal solution.In order to evaluate the algorithm's convergence,robustness,light source reconstruction accuracy,and multi-light source discrimination ability in various aspects,we designed simulation experiments on multiple sets of digital mice and in vivo experiments with real mice.The reconstruction results compared with the typical Li norm reconstruction algorithm and non-convex sparse reconstruction algorithm.The experimental results show that compared with the L1 norm model,the Log-sum norm has a more sparse reconstruction result and also shows good anti-noise performance,which has great advantages in terms of positioning error and robustness.The experimental results show that,compared with the Li norm model,the log-sum norm has a more sparse reconstruction result and also shows good anti-noise performance,which has great advantages in terms of positioning error and robustness.(2)In order to reduce the morbidity of bioluminescence tomography,multi-spectral measurement is used to collect more source information.Although a priori information is added,the dimension of the measurement matrix has increased dramatically and the calculation cost is high.In order to further simplify the solution and improve the performance,a non-monotonic accelerate proximal gradient(nmAPG)method was used to solve the non-convex multispectral sparse reconstruction model based on the log-sum penalty function.The nmAPG method is an extension of accelerate proximal gradient method.It is adding a supervised term,the abandonment of the monotonicity of the objective function is made to make the objective function solution simpler,and required less calculation in each iteration.The simulation experiments on the digital mouse model show that,compared with the hybrid optimization algorithm,this method requires shortest time for reconstruction,and has higher positioning accuracy in reconstructing the three-dimensional image,and has great application potential.