A study on convex optimization approaches to image fusion

Abstract

Image fusion is an imaging technique to visualize information from multiple images 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 models under the perspective of primal and dual and propose the associated new image decompositions. In addition, we consider the TV-L 1 based image fusion approach and study the problem of fusing two discrete-constrained images f 1(x) ∈ L 1 and f 2(x) ∈ L 2, where L 1 and L 2 are the sets of linearly-ordered discrete values. We prove that the TV-L 1 based image fusion actually gives rise to an exact convex relaxation to the corresponding nonconvex image fusion given the discrete-valued constraint u(x) ∈ L 1 ∪ L 2. This extends the results for the global optimization of the discrete-constrained TV-L 1 image approximation [7,30] to the case of image fusion. The proposed dual models also lead to new fast and reliable algorithms in numerics, based on modern convex optimization techniques. Experiments of medical imaging, remote sensing and multi-focusing visibly show the qualitive differences between the two studied variational models of image fusion. © 2012 Springer-Verlag.