Journal ArticleA Two-Stage Algorithm for Joint Multimodal Image ReconstructionChen, Yunmei; Li, Bin; Ye, XiaojingWe propose a new two-stage joint image reconstruction method by recovering edges directly from observed data and then assembling an image using the recovered edges. More specifically, we reformulate joint image reconstruction with vectorial total-variation regularization as an l1 minimization problem of the Jacobian of the underlying multimodality or multicontrast images. We provide detailed derivation of data fidelity for the Jacobian in Radon and Fourier transform domains. The new minimization problem yields an optimal convergence rate higher than that of existing primaldual based reconstruction algorithms, and the per-iteration cost remains low by using closed-form matrix-valued shrinkages. We conducted numerical tests on a number of multicontrast CT and MR image datasets, which demonstrate that the proposed method significantly improves reconstruction efficiency and accuracy compared to the state-of-the-art joint image reconstruction methods.2019-08-0110189024SIAM journal on imaging sciences1231425--14631936-4954https://doi.org/10.1137/18M12108731719932National Science Foundation