A Two-Stage Algorithm for Joint Multimodal Image Reconstruction

Abstract

We propose a new two-stage joint image reconstruction method by recovering edge directly from observed data and then assembling image using the recovered edges. More specifically, we reformulate joint image reconstruction with vectorial total-variation regularization as an l 1 minimization problem of the Jacobian of the underlying multi-modality or multi-contrast images. We provide detailed derivation of data fidelity for Jacobian in Radon and Fourier transform domains. The new minimization problem yields an optimal convergence rate higher than that of existing primal-dual 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 multi-contrast CT and MR image datasets, which demonstrate that the proposed method significantly improves reconstruction efficiency and accuracy compared to the state-ofthe-arts joint image reconstruction methods.

A General Non-Lipschitz Joint Regularized Model for Multi-Channel/Modality Image Reconstruction

“…The JTV favors sparsity in the magnitude of the 'joint gradient', i.e., ∇u = (∇u 1 ,••• ,∇u M ). It has been successfully used in color image restoration [9,52,54], multimodality MRI reconstruction [15,32] and PET-MRI joint reconstruction [21,39]. Also, there are some other vectorial TVs defined with respect to geometric structure; see, for instance, [27,36].…”