Sparse-Laplace hybrid graph manifold method for fluorescence molecular tomography

<i>Objective.</i>Fluorescence molecular tomography (FMT) holds promise for early tumor detection by mapping fluorescent agents in three dimensions non-invasively with low cost. However, since ill-posedness and ill-condition due to strong scattering effects in biotissues and limited measurable data, current FMT reconstruction is still up against unsatisfactory accuracy, including location prediction and morphological preservation.<i>Approach.</i>To strike the above challenges, we propose a novel Sparse-Laplace hybrid graph manifold (SLHGM) model. This model integrates a hybrid Laplace norm-based graph manifold learning term, facilitating a trade-off between sparsity and preservation of morphological features. To address the non-convexity of the hybrid objective function, a fixed-point equation is designed, which employs two successive resolvent operators and a forward operator to find a converged solution.<i>Main results.</i>Through numerical simulations and<i>in vivo</i>experiments, we demonstrate that the SLHGM model achieves an improved performance in providing accurate spatial localization while preserving morphological details.<i>Significance.</i>Our findings suggest that the SLHGM model has the potential to advance the application of FMT in biological research, not only in simulation but also in<i>in vivo</i>studies.