Volume 2, Issue 3
A General Non-Lipschitz Joint Regularized Model for Multi-Channel/Modality Image Reconstruction

Yiming Gao & Chunlin Wu

CSIAM Trans. Appl. Math., 2 (2021), pp. 395-430.

Published online: 2021-08

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  • Abstract

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-preserving by sharing common edge features of individual images. We study the lower bound theory for the non-Lipschitz joint reconstruction model in two important cases with Gaussian 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 prove that the iterative sequence converges globally to a critical point of the original objective function. In a special case of single channel image restoration, the convergence result improves those in the literature. For numerical implementation, we adopt primal dual method to the inner subproblem. Numerical experiments in color image restoration and two-modality undersampled magnetic resonance imaging (MRI) reconstruction show that the proposed non-Lipschitz joint reconstruction method achieves considerable improvements in terms of edge preservation for piecewise constant images compared to existing methods.

  • Keywords

Joint reconstruction, multi-modality, multi-channel, variational method, non-Lipschitz, lower bound theory.

  • AMS Subject Headings

68U10, 65K10, 94A08, 90C26

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-2-395, author = {Gao , Yiming and Wu , Chunlin}, title = {A General Non-Lipschitz Joint Regularized Model for Multi-Channel/Modality Image Reconstruction}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2021}, volume = {2}, number = {3}, pages = {395--430}, abstract = {

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-preserving by sharing common edge features of individual images. We study the lower bound theory for the non-Lipschitz joint reconstruction model in two important cases with Gaussian 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 prove that the iterative sequence converges globally to a critical point of the original objective function. In a special case of single channel image restoration, the convergence result improves those in the literature. For numerical implementation, we adopt primal dual method to the inner subproblem. Numerical experiments in color image restoration and two-modality undersampled magnetic resonance imaging (MRI) reconstruction show that the proposed non-Lipschitz joint reconstruction method achieves considerable improvements in terms of edge preservation for piecewise constant images compared to existing methods.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0029}, url = {http://global-sci.org/intro/article_detail/csiam-am/19443.html} }
TY - JOUR T1 - A General Non-Lipschitz Joint Regularized Model for Multi-Channel/Modality Image Reconstruction AU - Gao , Yiming AU - Wu , Chunlin JO - CSIAM Transactions on Applied Mathematics VL - 3 SP - 395 EP - 430 PY - 2021 DA - 2021/08 SN - 2 DO - http://doi.org/10.4208/csiam-am.2020-0029 UR - https://global-sci.org/intro/article_detail/csiam-am/19443.html KW - Joint reconstruction, multi-modality, multi-channel, variational method, non-Lipschitz, lower bound theory. AB -

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-preserving by sharing common edge features of individual images. We study the lower bound theory for the non-Lipschitz joint reconstruction model in two important cases with Gaussian 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 prove that the iterative sequence converges globally to a critical point of the original objective function. In a special case of single channel image restoration, the convergence result improves those in the literature. For numerical implementation, we adopt primal dual method to the inner subproblem. Numerical experiments in color image restoration and two-modality undersampled magnetic resonance imaging (MRI) reconstruction show that the proposed non-Lipschitz joint reconstruction method achieves considerable improvements in terms of edge preservation for piecewise constant images compared to existing methods.

Yiming Gao & ChunlinWu. (2021). A General Non-Lipschitz Joint Regularized Model for Multi-Channel/Modality Image Reconstruction. CSIAM Transactions on Applied Mathematics. 2 (3). 395-430. doi:10.4208/csiam-am.2020-0029
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