V O R T R A G
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Oesterreichisches Forschungsinstitut fuer Artificial Intelligence(OFAI)
Freyung 6/6, A-1010 Wien
Tel.: +43-1-533611-17, Fax: +43-1-5336112-77, Email: sec@ofai.at
Dipl.-Ing. Dr. Thomas Pock
Institute for Computer Graphics and Vision, Graz University of Technology
"A first-order primal-dual algorithm with applications to convex
optimization problems in computer vision"
Variational methods have proven to be particularly useful to solve a number of
ill-posed inverse imaging problems. In particular variational methods
incorporating total variation regularization have become very popular for a
number of applications. Unfortunately, these methods are difficult to minimize
due to the non-smoothness of the total variation. The aim of this work is
therefore to provide a flexible algorithm which is particularly suitable for
non-smooth convex optimization problems in imaging. In particular, we study a
first-order primal-dual algorithm for non-smooth convex optimization problems
with known saddle-point structure. We prove convergence to a saddle-point with
rate O(1/N) in finite dimensions for the complete class of problems. We
further show accelerations of the proposed algorithm to yield improved rates
on problems with some degree of smoothness. Indeed, we show that we can
achieve O(1/N2) convergence on problems, where the primal or the dual
objective is uniformly convex, and we can show linear convergence on smooth
problems. The wide applicability of the proposed algorithm is demonstrated on
several imaging problems such as image denoising, image deconvolution, image
inpainting, motion estimation and multi-label image segmentation.
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Time: Monday, 4th April 2011, 6.30 p.m. sharp
Location: Oesterreichisches Forschungsinstitut
fuer Artificial Intelligence, OFAI
Freyung 6, Stiege 6, 1010 Wien.
OESTERREICHISCHES FORSCHUNGSINSTITUT
FUER ARTIFICIAL INTELLIGENCE
Univ.-Prof. Ing. Dr. Robert Trappl
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