Infinite Dimensional Optimization Models and PDEs for Dejittering

  • Guozhi Dong
  • Aniello Raffaele Patrone
  • Otmar Scherzer
  • Ozan Öktem
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9087)

Abstract

In this paper we do a systematic investigation of continuous methods for pixel, line pixel and line dejittering. The basis for these investigations are the discrete line dejittering algorithm of Nikolova and the partial differential equation of Lenzen et al for pixel dejittering. To put these two different worlds in perspective we find infinite dimensional optimization algorithms linking to the finite dimensional optimization problems and formal flows associated with the infinite dimensional optimization problems. Two different kinds of optimization problems will be considered: Dejittering algorithms for determining the displacement and displacement error correction formulations, which correct the jittered image, without estimating the jitter. As a by-product we find novel variational methods for displacement error regularization and unify them into one family. The second novelty is a comprehensive comparison of the different models for different types of jitter, in terms of efficiency of reconstruction and numerical complexity.

Keywords

Dejittering Variational methods Nonlinear evolution PDEs 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Guozhi Dong
    • 1
  • Aniello Raffaele Patrone
    • 1
  • Otmar Scherzer
    • 1
    • 2
  • Ozan Öktem
    • 3
  1. 1.Computational Science CenterUniversity of ViennaWienAustria
  2. 2.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria
  3. 3.Department of MathematicsKTH - Royal Institute of TechnologyStockholmSweden

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