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Seminario del 2014
2014
27 marzo
prof. Ke Chen
Seminario di analisi numerica
In recent years, the interdisciplinary field of imaging science
has been experiencing an explosive growth in active research and
applications.
In this talk I shall present some recent and new work of modeling
the inverse problem of removing noise and blur in a given and observed image.
Here we assume the Gaussian additive noise is present and the blur is
defined by some linear filters. Inverting the filtering process does not
lead to unique solutions without suitable regularization. There are several
cases to discuss:
Firstly I discuss the problem of how to select optimal coupling parameters,
given an accurate estimate of the noise level, in a total variation (TV)
optimisation model.
Secondly I show a new algorithm for imposing the positivity constraint for
the TV model for the case of a known blur.
Finally I show how to generalise the new idea to the blind deconvolution
where the blur operator is unknown and must be restored along with the image.
Again the TV regularisers are used. However with the splitting idea, our
work can be extended to include other high order regularizers such as
the mean curvature.
Once an observed image is improved, further tasks such as segmentation
and co-registration become feasible. There will be potentially ample
applications to follow up.
Joint work with B. Williams, J. P. Zhang, Y.Zheng, S. Harding (Liverpool)
and E. Piccolomini, F. Zama (Bologna). Other collaborators in imaging in general include T. F. Chan, R. H. Chan, B. Yu, N. Badshah, H. Ali, L. Rada, C. Brito, L. Sun, F. L. Yang, N. Chumchob, M. Hintermuller, Y. Q. Dong, X. C. Tai, etc.