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A Truncated Lagrange Method for Total Variation-Based Image Restoration

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Abstract

In the last years, Total Variation minimization has become a popular and valuable technique for the restoration of noisy and blurred images. In this paper, we present a new technique for image restoration based on Total Variation minimization and the discrepancy principle. The new approach replaces the original image restoration problem with an equality constrained minimization problem. An inexact Newton method is applied to the first-order conditions of the constrained problem. The stopping criterium is derived from the discrepancy principle. Numerical results of image denoising and image deblurring test problems are presented to illustrate the effectiveness of the new approach.

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Authors and Affiliations

  1. Department of Mathematics, University of Bologna, Piazza Porta San Donato, 5, 40126, Bologna, Italy

    G. Landi

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  1. G. Landi
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Correspondence to G. Landi.

Additional information

This work was supported by the Italian FIRB Project “Parallel Algorithms and Nonlinear Numerical Optimization” RBAU01JYPN.

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Landi, G. A Truncated Lagrange Method for Total Variation-Based Image Restoration. J Math Imaging Vis 28, 113–123 (2007). https://doi.org/10.1007/s10851-007-0016-7

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