Improvement of image quality of time-domain diffuse optical tomography with lp sparsity regularization

An l(p) (0 < p ≤ 1) sparsity regularization is applied to time-domain diffuse optical tomography with a gradient-based nonlinear optimization scheme to improve the spatial resolution and the robustness to noise. The expression of the l(p) sparsity regularization is reformulated as a differentiable function of a parameter to avoid the difficulty in calculating its gradient in the optimization process. The regularization parameter is selected by the L-curve method. Numerical experiments show that the l(p) sparsity regularization improves the spatial resolution and recovers the difference in the absorption coefficients between two targets, although a target with a small absorption coefficient may disappear due to the strong effect of the l(p) sparsity regularization when the value of p is too small. The l(p) sparsity regularization with small p values strongly localizes the target, and the reconstructed region of the target becomes smaller as the value of p decreases. A phantom experiment validates the numerical simulations.