Variational Deconvolution of Multi-channel Images with Inequality Constraints

  • Authors:
  • Martin Welk;James G. Nagy

  • Affiliations:
  • Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Bldg. E1 1, Saarland University, 66041 Saarbrücken, Germany;Department of Mathematics and Computer Science, Emory University, 400 Dowman Drive, Suite W401, Atlanta, Georgia 30322, USA

  • Venue:
  • IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part I
  • Year:
  • 2007

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Abstract

A constrained variational deconvolution approach for multi-channel images is presented. Constraints are enforced through a reparametrisation which allows a differential geometric reinterpretation. This view point is used to show that the deconvolution problem can be formulated as a standard gradient descent problem with an underlying metric that depends on the imposed constraints. Examples are given for bound constrained colour image deblurring, and for diffusion tensor magnetic resonance imaging with positive definiteness constraint. Numerical results illustrate the effectiveness of the methods.