An augmented Lagrangian method for solving a new variational model based on gradients similarity measures and high order regularization for multimodality registration

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Theljani, Anis and Chen, Ke (2019) An augmented Lagrangian method for solving a new variational model based on gradients similarity measures and high order regularization for multimodality registration. Inverse Problems and Imaging, 13 (2). pp. 309-335. ISSN 1930-8345 (https://doi.org/10.3934/ipi.2019016)

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Abstract

In this work we propose a variational model for multi-modal image registration. It minimizes a new functional based on using reformulated normalized gradients of the images as the fidelity term and higher-order derivatives as the regularizer. We first present a theoretical analysis of the proposed model. Then, to solve the model numerically, we use an augmented Lagrangian method (ALM) to reformulate it to a few more amenable subproblems (each giving rise to an Euler-Lagrange equation that is discretized by finite difference methods) and solve iteratively the main linear systems by the fast Fourier transform; a multilevel technique is employed to speed up the initialisation and avoid likely local minima of the underlying functional. Finally we show the convergence of the ALM solver and give numerical results of the new approach. Comparisons with some existing methods are presented to illustrate its effectiveness and advantages.

ORCID iDs

Theljani, Anis and Chen, Ke ORCID logoORCID: https://orcid.org/0000-0002-6093-6623;
  • Item type:Article
    ID code:87221
    Dates:
    Date
    Event
    1 April 2019
    Published
    1 October 2018
    Accepted
    Notes:Copyright © 2019 AIMS. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Inverse Problems and Imaging following peer review. The definitive publisher-authenticated version Theljani, A., & Chen, K. (2019). An augmented Lagrangian method for solving a new variational model based on gradients similarity measures and high order regularization for multimodality registration. Inverse Problems and Imaging, 13(2), 309-335. is available online at: https://doi.org/10.3934/ipi.2019016
    Subjects:UNSPECIFIED
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:08 Nov 2023 09:31
    Last modified:12 Dec 2024 15:04
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/87221
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