Multiplicative updates algorithm to minimize the generalized Total Variation functional with a non-negativity constraint

Rodríguez Paul

doi:10.1109/ICIP.2010.5654074

Multiplicative updates algorithm to minimize the generalized Total Variation functional with a non-negativity constraint

Rodríguez Paul

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

6 Scopus citations

Abstract

We propose an efficient algorithm to solve the generalized Total Variation (TV) functional with a non-negativity constraint. This algorithm, which does not involve the solution of a linear system, but rather multiplicative updates only, can be used to solve the denoising and deconvolution problems. The derivation of our method is straightforward once the generalized TV functional is cast as a Non-negative Quadratic Programming (NQP) problem. The proposed algorithm offers a fair computational performance to solve the ℓ2-TV and ℓ1-TV denoising and deconvolution problems and it is the fastest algorithm of which we are aware for general inverse problems involving a nontrivial forward linear operator and a non-negativity constraint.

Original language	English
Title of host publication	2010 IEEE International Conference on Image Processing, ICIP 2010 - Proceedings
Pages	2509-2512
Number of pages	4
DOIs	https://doi.org/10.1109/ICIP.2010.5654074
State	Published - 2010
Event	2010 17th IEEE International Conference on Image Processing, ICIP 2010 - Hong Kong, Hong Kong Duration: 26 Sep 2010 → 29 Sep 2010

Publication series

Name	Proceedings - International Conference on Image Processing, ICIP
ISSN (Print)	1522-4880

Conference

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

Keywords

Non-negative quadratic programming
Total Variation

Access to Document

10.1109/ICIP.2010.5654074

Cite this

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title = "Multiplicative updates algorithm to minimize the generalized Total Variation functional with a non-negativity constraint",

abstract = "We propose an efficient algorithm to solve the generalized Total Variation (TV) functional with a non-negativity constraint. This algorithm, which does not involve the solution of a linear system, but rather multiplicative updates only, can be used to solve the denoising and deconvolution problems. The derivation of our method is straightforward once the generalized TV functional is cast as a Non-negative Quadratic Programming (NQP) problem. The proposed algorithm offers a fair computational performance to solve the ℓ2-TV and ℓ1-TV denoising and deconvolution problems and it is the fastest algorithm of which we are aware for general inverse problems involving a nontrivial forward linear operator and a non-negativity constraint.",

keywords = "Non-negative quadratic programming, Total Variation",

author = "Rodr{\'i}guez Paul",

year = "2010",

doi = "10.1109/ICIP.2010.5654074",

language = "English",

isbn = "9781424479948",

series = "Proceedings - International Conference on Image Processing, ICIP",

pages = "2509--2512",

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",

}

Paul, R 2010, Multiplicative updates algorithm to minimize the generalized Total Variation functional with a non-negativity constraint. in 2010 IEEE International Conference on Image Processing, ICIP 2010 - Proceedings., 5654074, Proceedings - International Conference on Image Processing, ICIP, pp. 2509-2512, 2010 17th IEEE International Conference on Image Processing, ICIP 2010, Hong Kong, Hong Kong, 26/09/10. https://doi.org/10.1109/ICIP.2010.5654074

Multiplicative updates algorithm to minimize the generalized Total Variation functional with a non-negativity constraint. / Paul, Rodríguez.
2010 IEEE International Conference on Image Processing, ICIP 2010 - Proceedings. 2010. p. 2509-2512 5654074 (Proceedings - International Conference on Image Processing, ICIP).

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

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N2 - We propose an efficient algorithm to solve the generalized Total Variation (TV) functional with a non-negativity constraint. This algorithm, which does not involve the solution of a linear system, but rather multiplicative updates only, can be used to solve the denoising and deconvolution problems. The derivation of our method is straightforward once the generalized TV functional is cast as a Non-negative Quadratic Programming (NQP) problem. The proposed algorithm offers a fair computational performance to solve the ℓ2-TV and ℓ1-TV denoising and deconvolution problems and it is the fastest algorithm of which we are aware for general inverse problems involving a nontrivial forward linear operator and a non-negativity constraint.

AB - We propose an efficient algorithm to solve the generalized Total Variation (TV) functional with a non-negativity constraint. This algorithm, which does not involve the solution of a linear system, but rather multiplicative updates only, can be used to solve the denoising and deconvolution problems. The derivation of our method is straightforward once the generalized TV functional is cast as a Non-negative Quadratic Programming (NQP) problem. The proposed algorithm offers a fair computational performance to solve the ℓ2-TV and ℓ1-TV denoising and deconvolution problems and it is the fastest algorithm of which we are aware for general inverse problems involving a nontrivial forward linear operator and a non-negativity constraint.

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KW - Total Variation

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

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Y2 - 26 September 2010 through 29 September 2010

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Multiplicative updates algorithm to minimize the generalized Total Variation functional with a non-negativity constraint

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