Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part II: Algorithm, Its Analysis and Numerical Tests

M. Hintermüller; C.N. Rautenberg; T. Wu; A. Langer

doi:10.1007/s10851-017-0736-2

Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part II: Algorithm, Its Analysis and Numerical Tests

M. Hintermüller, C.N. Rautenberg, T. Wu, A. Langer

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

Abstract

Based on the weighted total variation model and its analysis pursued in Hintermüller and Rautenberg 2016, in this paper a continuous, i.e., infinite dimensional, projected gradient algorithm and its convergence analysis are presented. The method computes a stationary point of a regularized bilevel optimization problem for simultaneously recovering the image as well as determining a spatially distributed regularization weight. Further, its numerical realization is discussed and results obtained for image denoising and deblurring as well as Fourier and wavelet inpainting are reported on.

Original language	English
Pages (from-to)	515-533
Number of pages	19
Journal	Journal of Mathematical Imaging and Vision
Volume	59
Issue number	3
Early online date	9 Jun 2017
DOIs	https://doi.org/10.1007/s10851-017-0736-2
Publication status	Published - Nov 2017
Externally published	Yes

Keywords

Image restoration
Spatially distributed regularization weight
Weighted total variation regularization
Fenchel predual
Bilevel optimization
Variance corridor
Projected gradient method
Convergence analysis

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10.1007/s10851-017-0736-2

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title = "Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part II: Algorithm, Its Analysis and Numerical Tests",

abstract = "Based on the weighted total variation model and its analysis pursued in Hinterm{\"u}ller and Rautenberg 2016, in this paper a continuous, i.e., infinite dimensional, projected gradient algorithm and its convergence analysis are presented. The method computes a stationary point of a regularized bilevel optimization problem for simultaneously recovering the image as well as determining a spatially distributed regularization weight. Further, its numerical realization is discussed and results obtained for image denoising and deblurring as well as Fourier and wavelet inpainting are reported on.",

keywords = "Image restoration, Spatially distributed regularization weight, Weighted total variation regularization, Fenchel predual, Bilevel optimization, Variance corridor, Projected gradient method, Convergence analysis",

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AU - Hintermüller, M.

AU - Rautenberg, C.N.

AU - Wu, T.

AU - Langer, A.

PY - 2017/11

Y1 - 2017/11

N2 - Based on the weighted total variation model and its analysis pursued in Hintermüller and Rautenberg 2016, in this paper a continuous, i.e., infinite dimensional, projected gradient algorithm and its convergence analysis are presented. The method computes a stationary point of a regularized bilevel optimization problem for simultaneously recovering the image as well as determining a spatially distributed regularization weight. Further, its numerical realization is discussed and results obtained for image denoising and deblurring as well as Fourier and wavelet inpainting are reported on.

AB - Based on the weighted total variation model and its analysis pursued in Hintermüller and Rautenberg 2016, in this paper a continuous, i.e., infinite dimensional, projected gradient algorithm and its convergence analysis are presented. The method computes a stationary point of a regularized bilevel optimization problem for simultaneously recovering the image as well as determining a spatially distributed regularization weight. Further, its numerical realization is discussed and results obtained for image denoising and deblurring as well as Fourier and wavelet inpainting are reported on.

KW - Image restoration

KW - Spatially distributed regularization weight

KW - Weighted total variation regularization

KW - Fenchel predual

KW - Bilevel optimization

KW - Variance corridor

KW - Projected gradient method

KW - Convergence analysis

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DO - 10.1007/s10851-017-0736-2

M3 - Article

SN - 1573-7683

VL - 59

SP - 515

EP - 533

JO - Journal of Mathematical Imaging and Vision

JF - Journal of Mathematical Imaging and Vision

IS - 3

ER -

Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part II: Algorithm, Its Analysis and Numerical Tests

Abstract

Keywords

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