Orateur : Massimo Fornasier, RICAM
Titre : A comparison of joint sparsity and total variation minimization algorithms
in a real-life art restoration problem
Résumé : On March 11, 1944, the famous Eremitani Church in Padua (Italy) was
destroyed in an Allied bombing along with the inestimable frescoes by
Andrea Mantegna et al. contained in the Ovetari Chapel. In the last 60
years, several attempts have been made to restore the fresco fragments by
traditional methods, but without much success.
We contributed to the development of an efficient pattern recognition
algorithm to map the original position and orientation of the fragments,
based on comparisons with an old gray level image of the fresco prior to
the damage. This innovative technique allowed for the partial
reconstruction of the frescoes. Unfortunately, the surface covered
by the colored fragments is only 77 m2, while the original area was of
several hundreds.
This means that we can reconstruct only a fraction (less than 8%) of this
inestimable artwork. In particular, the original color of the blanks is
not known. This begs the question of whether it is possible to estimate
mathematically the original colors of the frescoes by making use of the
potential information given by the available fragments and the gray level
of the pictures taken before the damage. Moreover, is it possible to
estimate how faithful such a restoration is? In this talk we retrace the
development of the recovery of the frescoes as an inspiring and
challenging real-life problem for the development of new mathematical
methods. Then we review two models recently studied for the recovery of
vector valued functions from incomplete data, with applications to the
recolorization problem. The models are based on the minimization of
a functional which is formed by the discrepancy with respect to the data
and additional regularization constraints.
The latter refer to joint sparsity measures with respect to frame expansions,
in particular wavelet or curvelet expansions, for the first functional and
functional total variation for the second. We show numerical test on the
real-life problem of the A. Mantegna.s frescoes and we compare the results
due to the two methods.
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CMLA UMR 8536 |
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