Robust identification of multiple point targets in time-domain fluorescence diffuse optical tomography

We present a reconstruction framework for time-domain fluorescence diffuse optical tomography (FDOT) to identify the locations of fluorescent point targets from boundary measurements. Unlike conventional approaches that rely on reduced temporal features, the proposed method utilizes the entire measured time-domain fluorescence response in the inverse reconstruction. The reconstruction is formulated as a gradient-based optimization problem in which candidate target locations are iteratively updated to match the observed temporal data. Numerical experiments demonstrate accurate and robust localization for both single- and multi-target configurations. Moreover, the proposed method remains effective when the number of targets is unknown a priori: In overparameterized reconstructions, redundant candidate points are automatically suppressed without the need for explicit regularization. This robustness makes the approach particularly suitable for practical FDOT settings, where the number of fluorescent targets is typically unknown. Furthermore, we demonstrate the practical feasibility of the framework through a comprehensive robustness analysis, confirming its stability under significant measurement noise and systematic mismatches in background optical properties. Finally, we show that the point-based optimization strategy can be successfully extended to localize extended volumetric targets and estimate their size, highlighting the versatility of the proposed method for complex geometric configurations.