Piecewise Weighted Tikhonov Regularization for Reconstructing Fluorophore Distribution in Tissue using Mesoscopic Epifluorescence Tomography

Piecewise Weighted Tikhonov Regularization for Reconstructing Fluorophore Distribution in Tissue using Mesoscopic Epifluorescence Tomography

Tuo ZHOU, Takehiro ANDO, Hongen LIAO, Etsuko KOBAYASHI, Ichiro SAKUMA
Vol. 2 (2013) p. 84-94

The technique of mesoscopic epifluorescence tomography (MEFT) has been reported previously. Although it allows three-dimensional (3D) imaging of the concentration distribution of fluorophore reporters embedded in tissue in reflectance geometry with a resolution of hundreds of micrometers, reconstruction accuracy is unsatisfactory. In this study, a novel regularization method is proposed to improve the accuracy. The proposed method is a derivation of Tikhonov regularization but inherits the iterative reweighted nature of sparsity regularization. First, Tikhonov regularization is utilized to generate an initial estimation. Then, a weight matrix is generated on the initial estimation and then coupled to the regularization objective function for a new estimation. The new estimation leads to a new weight matrix that begins iteration. The weight is decided in a piecewise manner : a high but constant weight is set to the region of interest (ROI) where the fluorophore is highly likely to exist, while lower weights are set to background regions. The values in the ROI are thus enhanced to a similar degree in each iteration while those in the background regions are suppressed. We constructed a MEFT system and conducted a series of numerical simulations and phantom experiments to evaluate the performance of the proposed method in comparison with several general regularization methods. Our results showed that application of our method produced reconstructed distribution with more accurate values (concentrations) and a clearer boundary compared with Tikhonov regularization and LSQR algorithm (used in previous report). Moreover, due to the constant weight set for the ROI, our proposed method preserves local smoothness and completeness of actual fluorophore distribution, for which sparsity regularization is inadequate.

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