In this study, we investigate the inverse source problem arising in bioluminescence tomography, the objective of which is to reconstruct both the support and the intensity of an internal light source from boundary measurements governed by an elliptic model. A shape optimization framework is developed in which the source intensity and its support are decoupled through first-order optimality conditions. To enhance the stability of the reconstruction, we incorporate a parameter-dependent coupled complex boundary method together with perimeter and volume regularizations. Source support is represented by a level set function, allowing the algorithm to naturally accommodate topological changes and recover multiple, closely spaced, or nested source regions. Theoretical justifications for the proposed formulation and regularization strategy are established, and extensive numerical experiments are performed to assess the reconstruction accuracy for both noise-free and noisy data. The results demonstrate that our method achieves robust and accurate recovery of source geometry and intensity, exhibits clear advantages over existing approaches.

Publication:

INVERSE PROBLEMS

http://dx.doi.org/10.1088/1361-6420/ae5086

Author:

Qianqian Wu

School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, Jiangsu, People’s Republic of China

Rongfang Gong

School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, Jiangsu, People’s Republic of China

Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing 211106, Jiangsu, People’s Republic of China

Author to whom any correspondence should be addressed.

E-mail: grf_math@nuaa.edu.cn

Wei Gong

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

Ziyi Zhang

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China

Shengfeng Zhu

School of Mathematical Sciences & Key Laboratory of Ministry of Education & Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai 200241, People’s Republic of China