L1/2 regularization method for multiple-target reconstruction in fluorescent molecular tomography

We present a method to accurately localize multiple small fluorescent objects within the tissue using fluorescence molecular tomography (FMT). The proposed method exploits the localized or sparse nature of the fluorophores in the tissue as a priori information to considerably improve the accuracy of the reconstruction of fluorophore distribution. This is accomplished by minimizing a cost function that includes the L_1/2 norm of the fluorophore distribution vector. To deal with the nonconvex penalty, the L_1/2 regularizer is transformed into a reweighted L₁-norm minimization problem and then it is efficiently solved by a homotopy-based algorithm. Simulation experiments on a 3D digital mouse atlas are performed to verify the feasibility of the proposed method, and the results demonstrate L_1/2 regularization is a promising approach for image reconstruction problem of FMT.