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Efficient Convex Optimization Approaches to Variational Image Fusion

Published online by Cambridge University Press:  28 May 2015

Jing Yuan ,
Brandon Miles ,
Greg Garvin ,
Xue-Cheng Tai  and
Aaron Fenster
Jing Yuan*
Affiliation:
Medical Imaging Lab, Robarts Research Institute, University of Western Ontario, London ON, Canada N6A 5B7
Brandon Miles*
Affiliation:
Medical Imaging Lab, Robarts Research Institute, University of Western Ontario, London ON, Canada N6A 5B7
Greg Garvin*
Affiliation:
Department of Medical Imaging, St Jospeh’s HealthCare, London ON, Canada
Xue-Cheng Tai*
Affiliation:
Department of Mathematics, University of Bergen, Bergen, Norway
Aaron Fenster*
Affiliation:
Medical Imaging Lab, Robarts Research Institute, University of Western Ontario, London ON, Canada N6A 5B7 Department of Medical Imaging, St Jospeh’s HealthCare, London ON, Canada
*
Corresponding author.Email address:jyuan@robarts.ca
Corresponding author.Email address:bmiles@robarts.ca
Corresponding author.Email address:Greg.Garvin@lhsc.on.ca
Corresponding author.Email address:tai@mi.uib.no
Corresponding author.Email address:afenster@robarts.ca
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Abstract

Image fusion is an imaging technique to visualize information from multiple imaging sources in one single image, which is widely used in remote sensing, medical imaging etc. In this work, we study two variational approaches to image fusion which are closely related to the standard TV-L 2 and TV-L 1 image approximation methods. We investigate their convex optimization formulations, under the perspective of primal and dual, and propose their associated new image decomposition models. In addition, we consider the TV-L 1 based image fusion approach and study the specified problem of fusing two discrete-constrained images and where and are the sets of linearly-ordered discrete values. We prove that the TV-L 1 based image fusion actually gives rise to the exact convex relaxation to the corresponding nonconvex image fusion constrained by the discrete-valued set This extends the results for the global optimization of the discrete-constrained TV-L 1 image approximation [8, 36] to the case of image fusion. As a big numerical advantage of the two proposed dual models, we show both of them directly lead to new fast and reliable algorithms, based on modern convex optimization techniques. Experiments with medical images, remote sensing images and multi-focus images visibly show the qualitative differences between the two studied variational models of image fusion. We also apply the new variational approaches to fusing 3D medical images.

Keywords

68U1090CxxConvex optimizationprimal-dual programmingcombinatorial optimizationtotal-variation regularizationimage fusion

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 2 , May 2014 , pp. 234 - 250
Copyright
Copyright © Global Science Press Limited 2014

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