Projected restarted framework for tomographic reconstruction

Abstract

Fluorescence molecular tomography (FMT) is an important molecular imaging modality developed to reveal the three-dimensional distribution of fluorescent targets using fluorescent measurements and appropriate image reconstruction methods. During the past years, many efforts have been devoted to the development of efficient inverse reconstruction methods for FMT. In this study, a projected restarted framework is proposed, using an inner–outer iteration scheme to compute the nonnegative solutions of the ill-posed non-square linear systems in FMT. In the inner iteration, conventional inverse reconstruction methods are employed to obtain a solution for the residual equation of the original linear system. In the outer iteration, the solution of the original linear system is updated using the results obtained in the inner iteration. Two kinds of projected restarted methods are obtained based on Tikhonov regularization (TR) and Generalized Minimal RESidual (GMRES). Both simulation and phantom studies are carried out to evaluate the performance of the proposed methods in the situation of limited projections, which is very helpful for reducing the acquisition time of fluorescent measurements and suitable for resolving fast biological processes in vivo . Compared with the conventional TR and GMRES needing 36 or even more projections, the projected restarted methods can maintain the image quality when limited projections (n≥4) are employed in the reconstruction. In addition, satisfactory reconstruction results based on the projected restarted methods can be obtained even when high noise level (SNR=20 dB) or closely adjacent targets (edge-to-edge distance between two targets is 0.4 cm) are encountered.