Bioluminescence tomography: A new regularized shape optimization method

Abstract: In this paper, we investigate an inverse source problem arising in bioluminescence tomography (BLT), where the objective is to recover both the support and intensity of the light source from boundary measurements. A shape optimization framework is developed, in which the source strength 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(CCBM) scheme together with perimeter and volume regularizations. The level-set representation naturally accommodates topological changes, enabling the reconstruction of multiple, closely located, or nested sources. Theoretical justifications are provided, and a series of numerical experiments are conducted to validate the proposed method. The results demonstrate the robustness, accuracy, and noise-resistance of the algorithm, as well as its advantages over existing approaches.