An Augmented Lagrangian Method for Solving a New Variational Model based on Gradients Similarity Measures and High Order Regularization for Multimodality Registration

Theljani, Anis and Chen, K ORCID: 0000-0002-6093-6623 (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.

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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.

Item Type:	Article
Uncontrolled Keywords:	Variational model, optimization, multi-modality images, similarity measures, mapping, high order regularisation, inverse problem, augmented lagrangian, multilevel
Depositing User:	Symplectic Admin
Date Deposited:	07 Nov 2018 08:52
Last Modified:	19 Jan 2023 01:13
DOI:	10.3934/ipi.2019016
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3028498