  Motion estimation across low-resolution frames and the reconstruction of
high-resolution images are two coupled subproblems of multi-frame
super-resolution. This paper introduces a new joint optimization approach for
motion estimation and image reconstruction to address this interdependence. Our
method is formulated via non-linear least squares optimization and combines two
principles of robust super-resolution. First, to enhance the robustness of the
joint estimation, we propose a confidence-aware energy minimization framework
augmented with sparse regularization. Second, we develop a tailor-made
Levenberg-Marquardt iteration scheme to jointly estimate motion parameters and
the high-resolution image along with the corresponding model confidence
parameters. Our experiments on simulated and real images confirm that the
proposed approach outperforms decoupled motion estimation and image
reconstruction as well as related state-of-the-art joint estimation algorithms.
