Lp regularization for early gate fluorescence molecular tomography

Time domain fluorescence molecular tomography (TD-FMT) provides a unique dataset for enhanced quantification and spatial resolution. The time-gate dataset can be divided into two temporal groups around the maximum counts gate, which are early gates and late gates. It is well established that early gates allow for improved spatial resolution and late gates are essential for fluorophore unmixing and concentration quantification. However, the inverse problem of FMT is ill-posed and typically underdetermined, which makes image reconstruction highly susceptible to data noise. More specifically, photon counts are inherently very low at early gates due to high absorption and scattering of tissue, resulting in a low signal-to-noise ratio and unstable reconstructions. In this work, an L_p regularization-based reconstruction algorithm was developed and tested with our wide-field mesh-based MonteCarlo simulation strategy. We compared the early time-gate reconstructions obtained with the different p (p ∈ {1/16; 1/8; 1/4; 1/3; 1/2; 1; 2}) from a synthetic murine model simulating the fluorophore uptake in the kidneys and preclinical data. The results from a 3D mouse atlas and a mouse experiment show that our L_1/4 regularization methods give the best performance for early time gates reconstructions.