14/07/2017, 16:00 — 17:00 — Amphitheatre Pa1, Mathematics Building
Rita Ferreira, KAUST
A chromaticity-brightness model for color images denoising
In this talk, we address an imaging processing problem aimed at denoising colored images using a “$u+v$” model as in [Me] coupled with a chromaticity-brightness decomposition approach as in [KaMa]. It amounts to solve a minimization problem associated with energy integral functionals depending on a small parameter $\varepsilon \gt 0$. The asymptotic behavior as $\varepsilon \to 0^+$ is characterized, and convergence of infima, almost minimizers, and energies are established. In particular, an integral representation of the lower semicontinuous envelope, with respect to the $L^1$-norm, of functionals with linear growth and defined for maps taking values on a certain manifold is provided. This study escapes the realm of previous results since the underlying manifold has boundary, and the integrand and its recession function fail to satisfy hypotheses commonly assumed in the literature. This is a joint work with Irene Fonseca (Carnegie Mellon University, Pittsburgh, USA) and M. Luísa Mascarenhas (Faculdade de Ciências e Tecnologia - UNL, Lisbon, Portugal).
- [KaMa] S.H. Kang and R. March, Variational Models for Image Colorization via Chromaticity and Brightness Decomposition, IEEE Trans. Image Process. 16 (9), 2251-2261 (2007).
- [Me] Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolutions Equations. The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures, University Lecture Series, Vol. 22, Amer. Math. Soc., 2001.
See also
RF_s.pdf
