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An Iterative Method with General Convex Fidelity Term for Image Restoration

  • Miyoun Jung
  • Elena Resmerita
  • Luminita Vese
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6311)

Abstract

We propose a convergent iterative regularization procedure based on the square of a dual norm for image restoration with general (quadratic or non-quadratic) convex fidelity terms. Convergent iterative regularization methods have been employed for image deblurring or denoising in the presence of Gaussian noise, which use L 2 [1] and L 1 [2] fidelity terms. Iusem-Resmerita [3] proposed a proximal point method using inexact Bregman distance for minimizing a general convex function defined on a general non-reflexive Banach space which is the dual of a separable Banach space. Based on this, we investigate several approaches for image restoration (denoising-deblurring) with different types of noise. We test the behavior of proposed algorithms on synthetic and real images. We compare the results with other state-of-the-art iterative procedures as well as the corresponding existing one-step gradient descent implementations. The numerical experiments indicate that the iterative procedure yields high quality reconstructions and superior results to those obtained by one-step gradient descent and similar with other iterative methods.

Keywords

Image Restoration General Convex Separable Banach Space Proximal Point Algorithm Proximal Point Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Miyoun Jung
    • 1
    • 2
  • Elena Resmerita
    • 1
    • 2
  • Luminita Vese
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesU.S.A.
  2. 2.Industrial Mathematics InstituteJohannes Kepler UniversityLinzAustria

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