Total variation regularization for 3D reconstruction in fluorescence tomography: experimental phantom studies

Abstract

Fluorescence tomography (FT) is depth-resolved three-dimensional (3D) localization and quantification of fluorescence distribution in biological tissue and entails a highly ill-conditioned problem as depth information must be extracted from boundary measurements. Conventionally, L2 regularization schemes that penalize the euclidean norm of the solution and possess smoothing effects are used for FT reconstruction. Oversmooth, continuous reconstructions lack high-frequency edge-type features of the original distribution and yield poor resolution. We propose an alternative regularization method for FT that penalizes the total variation (TV) norm of the solution to preserve sharp transitions in the reconstructed fluorescence map while overcoming ill-posedness. We have developed two iterative methods for fast 3D reconstruction in FT based on TV regularization inspired by Rudin-Osher-Fatemi and split Bregman algorithms. The performance of the proposed method is studied in a phantom-based experiment using a noncontact constant-wave trans-illumination FT system. It is observed that the proposed method performs better in resolving fluorescence inclusions at different depths.