A fourth order dual method for staircase reduction in texture extraction and image restoration problems

Tony F. Chan; Selim Esedoglu; Frederick Park

doi:10.1109/ICIP.2010.5653199

A fourth order dual method for staircase reduction in texture extraction and image restoration problems

Tony F. Chan, Selim Esedoglu, Frederick Park

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

70 Scopus citations

Abstract

We propose a novel fourth order dual method for the minimization of the non-smooth semi-norm ∥Δ∥₁ when in amalgamation with a new staircase reducing texture decomposition model of image processing. The proposed model incorporating this high order energy is a variant of the Chambolle Lions denoising model that additionally utilizes a negative Sobolev norm. We claim that the dual method is faster and more stable than the current gradient descent time marching algorithms often used to minimize such energies. Moreover, a proof of convergence of the proposed method, in conjunction with the new model, will be provided. Lastly, we provide guidelines on how the new energy and proposed framework can be naturally incorporated into many popular texture extraction and restoration models of image processing.

Original language	English (US)
Title of host publication	2010 IEEE International Conference on Image Processing, ICIP 2010 - Proceedings
Pages	4137-4140
Number of pages	4
DOIs	https://doi.org/10.1109/ICIP.2010.5653199
State	Published - Dec 1 2010
Externally published	Yes
Event	2010 17th IEEE International Conference on Image Processing, ICIP 2010 - Hong Kong, Hong Kong Duration: Sep 26 2010 → Sep 29 2010

Conference

Conference	2010 17th IEEE International Conference on Image Processing, ICIP 2010
Country/Territory	Hong Kong
City	Hong Kong
Period	09/26/10 → 09/29/10

Keywords

Dual methods
Meyer norms
Staircase reduction
Texture removal
Total variation

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Signal Processing

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10.1109/ICIP.2010.5653199

Cite this

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title = "A fourth order dual method for staircase reduction in texture extraction and image restoration problems",

abstract = "We propose a novel fourth order dual method for the minimization of the non-smooth semi-norm ∥Δ∥1 when in amalgamation with a new staircase reducing texture decomposition model of image processing. The proposed model incorporating this high order energy is a variant of the Chambolle Lions denoising model that additionally utilizes a negative Sobolev norm. We claim that the dual method is faster and more stable than the current gradient descent time marching algorithms often used to minimize such energies. Moreover, a proof of convergence of the proposed method, in conjunction with the new model, will be provided. Lastly, we provide guidelines on how the new energy and proposed framework can be naturally incorporated into many popular texture extraction and restoration models of image processing.",

keywords = "Dual methods, Meyer norms, Staircase reduction, Texture removal, Total variation",

author = "Chan, {Tony F.} and Selim Esedoglu and Frederick Park",

year = "2010",

month = dec,

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doi = "10.1109/ICIP.2010.5653199",

language = "English (US)",

isbn = "9781424479948",

pages = "4137--4140",

booktitle = "2010 IEEE International Conference on Image Processing, ICIP 2010 - Proceedings",

note = "2010 17th IEEE International Conference on Image Processing, ICIP 2010 ; Conference date: 26-09-2010 Through 29-09-2010",

}

Chan, TF, Esedoglu, S & Park, F 2010, A fourth order dual method for staircase reduction in texture extraction and image restoration problems. in 2010 IEEE International Conference on Image Processing, ICIP 2010 - Proceedings., 5653199, pp. 4137-4140, 2010 17th IEEE International Conference on Image Processing, ICIP 2010, Hong Kong, Hong Kong, 09/26/10. https://doi.org/10.1109/ICIP.2010.5653199

TY - GEN

T1 - A fourth order dual method for staircase reduction in texture extraction and image restoration problems

AU - Chan, Tony F.

AU - Esedoglu, Selim

AU - Park, Frederick

PY - 2010/12/1

Y1 - 2010/12/1

N2 - We propose a novel fourth order dual method for the minimization of the non-smooth semi-norm ∥Δ∥1 when in amalgamation with a new staircase reducing texture decomposition model of image processing. The proposed model incorporating this high order energy is a variant of the Chambolle Lions denoising model that additionally utilizes a negative Sobolev norm. We claim that the dual method is faster and more stable than the current gradient descent time marching algorithms often used to minimize such energies. Moreover, a proof of convergence of the proposed method, in conjunction with the new model, will be provided. Lastly, we provide guidelines on how the new energy and proposed framework can be naturally incorporated into many popular texture extraction and restoration models of image processing.

AB - We propose a novel fourth order dual method for the minimization of the non-smooth semi-norm ∥Δ∥1 when in amalgamation with a new staircase reducing texture decomposition model of image processing. The proposed model incorporating this high order energy is a variant of the Chambolle Lions denoising model that additionally utilizes a negative Sobolev norm. We claim that the dual method is faster and more stable than the current gradient descent time marching algorithms often used to minimize such energies. Moreover, a proof of convergence of the proposed method, in conjunction with the new model, will be provided. Lastly, we provide guidelines on how the new energy and proposed framework can be naturally incorporated into many popular texture extraction and restoration models of image processing.

KW - Dual methods

KW - Meyer norms

KW - Staircase reduction

KW - Texture removal

KW - Total variation

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DO - 10.1109/ICIP.2010.5653199

M3 - Conference contribution

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SN - 9781424479948

SP - 4137

EP - 4140

BT - 2010 IEEE International Conference on Image Processing, ICIP 2010 - Proceedings

T2 - 2010 17th IEEE International Conference on Image Processing, ICIP 2010

Y2 - 26 September 2010 through 29 September 2010

ER -

A fourth order dual method for staircase reduction in texture extraction and image restoration problems

Abstract

Conference

Keywords

ASJC Scopus subject areas

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