A General Non-Lipschitz Joint Regularized Model for Multi-Channel/Modality Image Reconstruction (CSIAM Transactions on Applied Mathematics, 2021)
Multi-channel/modality image joint reconstruction has gained much research interest in recent years. In this paper, we propose to use a nonconvex and non-Lipschitz joint regularizer in a general variational model for joint reconstruction under additive measurement noise. This framework has good ability in edge-preservingby sharing common edge features of individual images. We study the lower boundtheory for the non-Lipschitz joint reconstruction model in two important cases withGaussian and impulsive measurement noise, respectively. In addition, we extend previous works to propose an inexact iterative support shrinking algorithm with proximal linearization for multi-channel image reconstruction (InISSAPL-MC) and provethat the iterative sequence converges globally to a critical point of the original objectivefunction. In a special case of single channel image restoration, the convergence resultimproves those in the literature. For numerical implementation, we adopt primal dualmethod to the inner subproblem. Numerical experiments in color image restorationand two-modality undersampled magnetic resonance imaging (MRI) reconstructionshow that the proposed non-Lipschitz joint reconstruction method achieves considerable improvements in terms of edge preservation for piecewise constant images compared to existing methods.