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An Adaptive Strategy for the Restoration of Textured Images Using Fractional Order Regularization

An Adaptive Strategy for the Restoration of Textured Images Using Fractional Order Regularization
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Year:    2013

Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 1 : pp. 276–296

Abstract

Total variation regularization has good performance in noise removal and edge preservation but lacks in texture restoration. Here we present a texture-preserving strategy to restore images contaminated by blur and noise. According to a texture detection strategy,  we apply spatially adaptive fractional order diffusion. A fast algorithm based on the half-quadratic technique is used to minimize the resulting objective function. Numerical results show the effectiveness of our strategy.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2013.mssvm15

Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 1 : pp. 276–296

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Ill-posed problem deblurring fractional order derivatives regularizing iterative method.

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  10. Variational Image Denoising Based on Autocorrelation Whiteness

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  11. Vector total fractional-order variation and its applications for color image denoising and decomposition

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    https://doi.org/10.1016/j.apm.2019.03.010 [Citations: 7]

  12. Symmetrized fractional total variation for signal and image analysis

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  13. A Total Fractional-Order Variation Model for Image Super-Resolution and Its SAV Algorithm

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  14. SPB-Net: A Deep Network for SAR Imaging and Despeckling With Downsampled Data

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  15. A fast adaptive reweighted residual-feedback iterative algorithm for fractional-order total variation regularized multiplicative noise removal of partly-textured images

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    https://doi.org/10.1016/j.sigpro.2013.12.009 [Citations: 44]

  16. Medical Image Enhancement Method Based on the Fractional Order Derivative and the Directional Derivative

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    https://doi.org/10.1142/S021800141857001X [Citations: 27]

  17. Some novel linear regularization methods for a deblurring problem

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    https://doi.org/10.3934/ipi.2017019 [Citations: 7]

  18. Hybrid Variational Model for Texture Image Restoration

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    https://doi.org/10.4208/eajam.090217.300617a [Citations: 4]

  19. Image restoration with Poisson–Gaussian mixed noise

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    https://doi.org/10.1080/21681163.2013.811039 [Citations: 11]

  20. Ultrasound speckle reduction based on fractional order differentiation

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  23. A Variational Pan-Sharpening Method Based on Spatial Fractional-Order Geometry and Spectral–Spatial Low-Rank Priors

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  24. A Total Fractional-Order Variation Model for Image Restoration with Nonhomogeneous Boundary Conditions and Its Numerical Solution

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  29. Statistical iterative reconstruction using adaptive fractional order regularization

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  30. Cartoon-texture composite regularization based non-blind deblurring method for partly-textured blurred images with Poisson noise

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  31. Bi-component decomposition based hybrid regularization method for partly-textured CS-MR image reconstruction

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  35. Fractional order variational pan-sharpening

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  36. Ultrasound speckle reduction based on fractional order differentiation

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  40. The Restoration of Textured Images Using Fractional‐Order Regularization

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  48. Keypoints from symmetries by wave propagation

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  49. Image denoising by a novel variable‐order total fractional variation model

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