Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Multisensor image fusion using the wavelet transform
Graphical Models and Image Processing
Convex analysis and variational problems
Convex analysis and variational problems
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection
International Journal of Computer Vision
Remote Sensing, Third Edition: Models and Methods for Image Processing
Remote Sensing, Third Edition: Models and Methods for Image Processing
Image Fusion for Enhanced Visualization: A Variational Approach
International Journal of Computer Vision
A continuous max-flow approach to potts model
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part VI
Exploiting redundancy for aerial image fusion using convex optimization
Proceedings of the 32nd DAGM conference on Pattern recognition
Exact optimization for Markov random fields with convex priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
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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-L2 and TV-L1 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-L1 based image fusion approach and study the problem of fusing two discrete-constrained images $f_1(x) \in \mathcal{L}_1$ and $f_2(x) \in \mathcal{L}_2$ , where $\mathcal{L}_1$ and $\mathcal{L}_2$ are the sets of linearly-ordered discrete values. We prove that the TV-L1 based image fusion actually gives rise to an exact convex relaxation to the corresponding nonconvex image fusion given the discrete-valued constraint $u(x) \in \mathcal{L}_1 \cup \mathcal{L}_2$ . This extends the results for the global optimization of the discrete-constrained TV-L1 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.