@Article{NMTMA-7-234,
author = {Jing Yuan, Brandon Miles, Greg Garvin, Xue-Cheng Tai and Aaron Fenster},
title = {Efficient Convex Optimization Approaches to Variational Image Fusion},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2014},
volume = {7},
number = {2},
pages = {234--250},
abstract = {<p style="text-align: justify;">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 $f_1(x) ∈&nbsp;\mathcal{L}_1$ and $f_2(x) ∈&nbsp;\mathcal{L}_2$, where&nbsp;$\mathcal{L}_1$ and&nbsp;$\mathcal{L}_2$ 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 $u(x) ∈&nbsp;\mathcal{L}_1 ∪&nbsp;\mathcal{L}_2$. 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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2014.ssvm10},
url = {http://global-sci.org/intro/article_detail/nmtma/5873.html}
}