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

Michael Hintermüller; Carlos N. Rautenberg; Tao Wu; Andreas 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

Michael Hintermüller, Carlos N. Rautenberg, Tao Wu, Andreas Langer

Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

Sammanfattning

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.

Originalspråk	engelska
Sidor (från-till)	515-533
Antal sidor	19
Tidskrift	Journal of Mathematical Imaging and Vision
Volym	59
Nummer	3
DOI	https://doi.org/10.1007/s10851-017-0736-2
Status	Published - 2017 nov. 1
Externt publicerad	Ja

Bibliografisk information

Funding Information:
This research was carried out in the framework of Matheon supported by the Einstein Foundation Berlin within the ECMath projects OT1, SE5 and SE15 as well as by the DFG under Grant No.?HI 1466/7-1 ?Free Boundary Problems and Level Set Methods?.

Funding Information:
This research was carried out in the framework of Matheon supported by the Einstein Foundation Berlin within the ECMath projects OT1, SE5 and SE15 as well as by the DFG under Grant No. HI 1466/7-1 “Free Boundary Problems and Level Set Methods”.

Publisher Copyright:
© 2017, Springer Science+Business Media New York.

Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

Ämnesklassifikation (UKÄ)

Beräkningsmatematik
Datorgrafik och datorseende

Tillgång till dokument

10.1007/s10851-017-0736-2

Citera det här

@article{5a8042dbe26c47d4b35d432d88edc40f,

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

author = "Michael Hinterm{\"u}ller and Rautenberg, {Carlos N.} and Tao Wu and Andreas Langer",

note = "Funding Information: This research was carried out in the framework of Matheon supported by the Einstein Foundation Berlin within the ECMath projects OT1, SE5 and SE15 as well as by the DFG under Grant No.?HI 1466/7-1 ?Free Boundary Problems and Level Set Methods?. Funding Information: This research was carried out in the framework of Matheon supported by the Einstein Foundation Berlin within the ECMath projects OT1, SE5 and SE15 as well as by the DFG under Grant No. HI 1466/7-1 “Free Boundary Problems and Level Set Methods”. Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media New York. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",

year = "2017",

month = nov,

day = "1",

doi = "10.1007/s10851-017-0736-2",

language = "English",

volume = "59",

pages = "515--533",

journal = "Journal of Mathematical Imaging and Vision",

issn = "0924-9907",

publisher = "Springer",

number = "3",

}

Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part II: Algorithm, Its Analysis and Numerical Tests. / Hintermüller, Michael; Rautenberg, Carlos N.; Wu, Tao et al.
I: Journal of Mathematical Imaging and Vision, Vol. 59, Nr. 3, 01.11.2017, s. 515-533.

Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

TY - JOUR

T1 - Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part II

T2 - Algorithm, Its Analysis and Numerical Tests

AU - Hintermüller, Michael

AU - Rautenberg, Carlos N.

AU - Wu, Tao

AU - Langer, Andreas

N1 - Funding Information: This research was carried out in the framework of Matheon supported by the Einstein Foundation Berlin within the ECMath projects OT1, SE5 and SE15 as well as by the DFG under Grant No.?HI 1466/7-1 ?Free Boundary Problems and Level Set Methods?. Funding Information: This research was carried out in the framework of Matheon supported by the Einstein Foundation Berlin within the ECMath projects OT1, SE5 and SE15 as well as by the DFG under Grant No. HI 1466/7-1 “Free Boundary Problems and Level Set Methods”. Publisher Copyright: © 2017, Springer Science+Business Media New York. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017/11/1

Y1 - 2017/11/1

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 - Bilevel optimization

KW - Convergence analysis

KW - Fenchel predual

KW - Image restoration

KW - Projected gradient method

KW - Spatially distributed regularization weight

KW - Variance corridor

KW - Weighted total variation regularization

U2 - 10.1007/s10851-017-0736-2

DO - 10.1007/s10851-017-0736-2

M3 - Article

AN - SCOPUS:85020658187

SN - 0924-9907

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

Sammanfattning

Bibliografisk information

Ämnesklassifikation (UKÄ)

Tillgång till dokument

Fingeravtryck

Citera det här