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04/01/03 Colloquium
DR. THOMAS WUNDERLI
UNIVERSITY OF FLORIDA
UNIVERSITY OF FLORIDA
Adaptive Total Variation for Image Restoration in BV Space
Abstract: We study here the mathematical theory for an image restoration technique introduced by Chan and Strong, namely the minimization of the adaptive total variation functional. We prove the existence and uniqueness for the unconstrained variational problem in BV space. We also obtain the existence, uniqueness, and stability for the weak solution to the corresponding evolution equation, and show that the solution of the evolution equation weakly converges to the minimizer as t approaches infinity. Some numerical results are also presented.