A Variational Model for Joint Motion Estimation and Image Reconstruction

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Burger, Martin 
Dirks, Hendrik 
Schönlieb, Carola-Bibiane 

The aim of this paper is to derive and analyze a variational model for the joint estimation of motion and reconstruction of image sequences, which is based on a time-continuous Eulerian motion model. The model can be set up in terms of the continuity equation or the brightness constancy equation. The analysis in this paper focuses on the latter for robust motion estimation on sequences of twodimensional images. We rigorously prove the existence of a minimizer in a suitable function space setting. Moreover, we discuss the numerical solution of the model based on primal-dual algorithms and investigate several examples. Finally, the benefits of our model compared to existing techniques, such as sequential image reconstruction and motion estimation, are shown.

dynamic image reconstruction, motion estimation, image denoising, joint variational model, regularization, Eulerian motion model
Journal Title
SIAM Journal on Imaging Sciences
Conference Name
Journal ISSN
Volume Title
Society for Industrial and Applied Mathematics
Engineering and Physical Sciences Research Council (EP/H023348/1)
Royal Society (IE110314)
Engineering and Physical Sciences Research Council (EP/M00483X/1)
Leverhulme Trust (RPG-2015-250)
Engineering and Physical Sciences Research Council (EP/N014588/1)
European Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (691070)
Alan Turing Institute (unknown)
Engineering and Physical Sciences Research Council (EP/J009539/1)
The work of the first author was also supported by the German Science Foundation DFG via EXC 1003 Cells in Motion Cluster of Excellence, M¨unster, Germany