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Iterative Constrained Minimization for Vectorial TV Image Deblurring

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Abstract

In this paper, we consider the problem of restoring blurred noisy vectorial images where the blurring model involves contributions from the different image channels (cross-channel blur). The proposed method restores the images by solving a sequence of quadratic constrained minimization problems where the constraint is automatically adapted to improve the quality of the restored images. In the present case, the constraint is the Total Variation extended to vectorial images, and the objective function is the \(\ell _2\) norm of the residual. After proving the convergence of the iterative method, we report the results obtained on a wide set of test images, showing that this approach is efficient for recovering nearly optimal results.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Centre for Mathematical Imaging Techniques (CMIT), The University of Liverpool, Liverpool, UK

    K. Chen

  2. Department of Mathematics, University of Bologna, Piazza di Porta S. Donato 5, 40126, Bologna, Italy

    E. Loli Piccolomini & F. Zama

Authors
  1. K. Chen
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  2. E. Loli Piccolomini
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  3. F. Zama
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Correspondence to E. Loli Piccolomini.

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Chen, K., Piccolomini, E.L. & Zama, F. Iterative Constrained Minimization for Vectorial TV Image Deblurring. J Math Imaging Vis 54, 240–255 (2016). https://doi.org/10.1007/s10851-015-0599-3

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  • DOI: https://doi.org/10.1007/s10851-015-0599-3

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