Half-quadratic regularization, preconditioning and applications

Michael Ng

doi:10.1109/ISIMP.2001.925323

Half-quadratic regularization, preconditioning and applications

Michael Ng^*

^*Corresponding author for this work

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

1 Citation (Scopus)

Abstract

In this paper, we address a wide class of image deconvolution or reconstruction situations where a sought image is recovered from degraded observed image. The sought solution is defined to be the minimizer of an objective function combining a data-fidelity term and a edge-preserving, convex regularization term. Our objective is to speed up the calculation of the solution in a wide range of situations. We propose a method applying pertinent preconditioning to an adapted half-quadratic equivalent form of the objective function. The optimal solution is then found using an alternating minimization (AM) scheme. We focus specifically on Huber regularization. We exhibit the possibility get very fast calculations while preserving the edges in the solution. Preliminary numerical results are reported to illustrate the effectiveness of our method.

Original language	English
Title of host publication	Proceedings of 2001 International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP 2001
Publisher	IEEE
Pages	32-35
Number of pages	4
ISBN (Print)	9628576623, 9789628576623
DOIs	https://doi.org/10.1109/ISIMP.2001.925323
Publication status	Published - May 2001
Event	2001 International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP 2001 - , Hong Kong, China Duration: 2 May 2001 → 4 May 2001 https://ieeexplore.ieee.org/xpl/conhome/7375/proceeding (Conference Proceedings)

Publication series

Name	Proceedings of International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP

Conference

Conference	2001 International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP 2001
Country/Territory	Hong Kong, China
Period	2/05/01 → 4/05/01
Internet address	https://ieeexplore.ieee.org/xpl/conhome/7375/proceeding (Conference Proceedings)

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 9 Industry, Innovation, and Infrastructure

Access to Document

10.1109/ISIMP.2001.925323

Cite this

@inproceedings{73f4f9ef88014e188140cf2e88606306,

title = "Half-quadratic regularization, preconditioning and applications",

abstract = "In this paper, we address a wide class of image deconvolution or reconstruction situations where a sought image is recovered from degraded observed image. The sought solution is defined to be the minimizer of an objective function combining a data-fidelity term and a edge-preserving, convex regularization term. Our objective is to speed up the calculation of the solution in a wide range of situations. We propose a method applying pertinent preconditioning to an adapted half-quadratic equivalent form of the objective function. The optimal solution is then found using an alternating minimization (AM) scheme. We focus specifically on Huber regularization. We exhibit the possibility get very fast calculations while preserving the edges in the solution. Preliminary numerical results are reported to illustrate the effectiveness of our method.",

author = "Michael Ng",

note = "Publisher Copyright: {\textcopyright} Centre for Multimedia Signal Processing, Department of Electronic and Information Engineering; The Hong Kong Polytechnic University 2001 and IEEE Hong Kong Chapter of Signal Processing. Funding Information: Research supported in part by Hong Kong Research Grants Council Grant Nos. HKU 7 147/99P and HKU 7 132/00P, and HKU CRCG Grant Nos. 10203408 and 10203501.; 2001 International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP 2001 ; Conference date: 02-05-2001 Through 04-05-2001",

year = "2001",

month = may,

doi = "10.1109/ISIMP.2001.925323",

language = "English",

isbn = "9628576623",

series = "Proceedings of International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP",

publisher = "IEEE",

pages = "32--35",

booktitle = "Proceedings of 2001 International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP 2001",

address = "United States",

url = "https://ieeexplore.ieee.org/xpl/conhome/7375/proceeding",

}

Ng, M 2001, Half-quadratic regularization, preconditioning and applications. in Proceedings of 2001 International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP 2001. Proceedings of International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP, IEEE, pp. 32-35, 2001 International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP 2001, Hong Kong, China, 2/05/01. https://doi.org/10.1109/ISIMP.2001.925323

Half-quadratic regularization, preconditioning and applications. / Ng, Michael.
Proceedings of 2001 International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP 2001. IEEE, 2001. p. 32-35 (Proceedings of International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

TY - GEN

T1 - Half-quadratic regularization, preconditioning and applications

AU - Ng, Michael

N1 - Publisher Copyright: © Centre for Multimedia Signal Processing, Department of Electronic and Information Engineering; The Hong Kong Polytechnic University 2001 and IEEE Hong Kong Chapter of Signal Processing. Funding Information: Research supported in part by Hong Kong Research Grants Council Grant Nos. HKU 7 147/99P and HKU 7 132/00P, and HKU CRCG Grant Nos. 10203408 and 10203501.

PY - 2001/5

Y1 - 2001/5

N2 - In this paper, we address a wide class of image deconvolution or reconstruction situations where a sought image is recovered from degraded observed image. The sought solution is defined to be the minimizer of an objective function combining a data-fidelity term and a edge-preserving, convex regularization term. Our objective is to speed up the calculation of the solution in a wide range of situations. We propose a method applying pertinent preconditioning to an adapted half-quadratic equivalent form of the objective function. The optimal solution is then found using an alternating minimization (AM) scheme. We focus specifically on Huber regularization. We exhibit the possibility get very fast calculations while preserving the edges in the solution. Preliminary numerical results are reported to illustrate the effectiveness of our method.

AB - In this paper, we address a wide class of image deconvolution or reconstruction situations where a sought image is recovered from degraded observed image. The sought solution is defined to be the minimizer of an objective function combining a data-fidelity term and a edge-preserving, convex regularization term. Our objective is to speed up the calculation of the solution in a wide range of situations. We propose a method applying pertinent preconditioning to an adapted half-quadratic equivalent form of the objective function. The optimal solution is then found using an alternating minimization (AM) scheme. We focus specifically on Huber regularization. We exhibit the possibility get very fast calculations while preserving the edges in the solution. Preliminary numerical results are reported to illustrate the effectiveness of our method.

UR - https://www.scopus.com/pages/publications/51849116219

U2 - 10.1109/ISIMP.2001.925323

DO - 10.1109/ISIMP.2001.925323

M3 - Conference proceeding

AN - SCOPUS:51849116219

SN - 9628576623

SN - 9789628576623

T3 - Proceedings of International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP

SP - 32

EP - 35

BT - Proceedings of 2001 International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP 2001

PB - IEEE

T2 - 2001 International Symposium on Intelligent Multimedia, Video and Speech Processing, ISIMP 2001

Y2 - 2 May 2001 through 4 May 2001

ER -

Half-quadratic regularization, preconditioning and applications

Abstract

Publication series

Conference

UN SDGs

Access to Document

Other files and links

Fingerprint

Cite this