Comparison of l_p-regularization-based reconstruction methods for time domain fluorescence molecular tomography on early time gates

Time domain florescence molecular tomography (TD-FMT) allows 3D visualization of multiple fluorophores based on lifetime contrast and provides a unique data set for enhanced quantification and spatial resolution. The time-gate data set can be divided into two groups around the maximum gate, which are early gates and late gates. It is well-established that early gates allow for improved spatial resolution of reconstruction. However, photon counts are inherently very low at early gates due to the high absorption and scattering of tissue. It makes image reconstruction highly susceptible to the effects of noise and numerical errors. Moreover, the inverse problem of FMT is the ill-posed and underdetermined. These factors make reconstruction difficult for early time gates. In this work, l_p (0<p≤1) regularization based reconstruction algorithm was developed within our wide-field mesh-based Monte Carlo reconstruction strategy. The reconstructions performances were validated on a synthetic murine model simulating the fluorophores uptake in the kidneys and with experimental preclinical data. We compared the early time-gate reconstructed results using l_1/3, l_1/2 and l₁ regularization methods in terms of quantification and resolution. The regularization parameters were selected by the Lcurve method. The simulation results of a 3D mouse atlas and mouse experiment show that l₉ (0<p<1) regularization method obtained more sparse and accurate solutions than l₁ regularization method for early time gates.