Edge-guided TVp regularization for diffuse optical tomography based on radiative transport equation

摘要

An edge-guided TVp (0 p 1) regularization is introduced to recover scattering and absorption coefficients simultaneously in optical tomography, which combines the TVp minimizing scheme with an edge-guided strategy. The TVp minimizing scheme consists of a data fidelity term and an l(p )-norm (0 p 1) of the gradients of underlying optical coefficients. To make the minimization problem numerically tractable, the Huber function is utilized to locally smooth the l(p)-norm to obtain a differential objective function. The lagged diffusivity-Newton iteration is applied to find the minimizers of the above Huberized objective function. An edge-guided strategy is inserted into each iteration in the form of a weighted matrix. In addition, a normalizing technique is incorporated into our algorithm to reduce the cross-talk. Compared with l(p) regularization, the proposed edge-guided TVp regularization presents superiorities on keeping the shape as well as the size of targets and removing background undulations. Then the proposed method is applied to image the tissue in the presence of a non-scattering or a low-scattering layer. It is shown that our method is capable of imaging the targets in the tissue containing a non-scattering layer using reduced measurements data. Moreover, it holds promise for jointly imaging both targets and the low-scattering layer under a certain noise level.