Low rank matrix recovery via augmented lagrange multiplier with nonconvex minimization

Jieun Lee, Yoonsik Choe

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

In recovery problem, nuclear norm as a convex envelope of rank function is widely used. However, nuclear norm minimization problem tends not to identify optimal solution, so recently, other heuristic surrogate functions such as nonconvex logdet are utilized to recover sparser signal. In this paper, to handle nonconvex optimation problem, a modified Augmented Lagrange Multiplier Method (ALMM) is developed using weighted nuclear norm instead of nuclear norm which conventional ALMM treats for convex optimization. We experiment on real images in Matrix Completion problem with diverse nonconvex, and show that instead of solving a simple convex problem, nonconvex optimization problem can reconstruct a low rank matrix more accurately and the convergence rate is faster with having higher average PSNR.

Original languageEnglish
Title of host publication2016 IEEE 12th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781509019298
DOIs
Publication statusPublished - 2016 Aug 1
Event12th IEEE Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2016 - Bordeaux, France
Duration: 2016 Jul 112016 Jul 12

Other

Other12th IEEE Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2016
CountryFrance
CityBordeaux
Period16/7/1116/7/12

Fingerprint

Lagrange multipliers
Recovery
Convex optimization
Experiments

All Science Journal Classification (ASJC) codes

  • Media Technology
  • Signal Processing

Cite this

Lee, J., & Choe, Y. (2016). Low rank matrix recovery via augmented lagrange multiplier with nonconvex minimization. In 2016 IEEE 12th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2016 [7528217] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/IVMSPW.2016.7528217
Lee, Jieun ; Choe, Yoonsik. / Low rank matrix recovery via augmented lagrange multiplier with nonconvex minimization. 2016 IEEE 12th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2016. Institute of Electrical and Electronics Engineers Inc., 2016.
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Lee, J & Choe, Y 2016, Low rank matrix recovery via augmented lagrange multiplier with nonconvex minimization. in 2016 IEEE 12th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2016., 7528217, Institute of Electrical and Electronics Engineers Inc., 12th IEEE Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2016, Bordeaux, France, 16/7/11. https://doi.org/10.1109/IVMSPW.2016.7528217

Low rank matrix recovery via augmented lagrange multiplier with nonconvex minimization. / Lee, Jieun; Choe, Yoonsik.

2016 IEEE 12th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2016. Institute of Electrical and Electronics Engineers Inc., 2016. 7528217.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - In recovery problem, nuclear norm as a convex envelope of rank function is widely used. However, nuclear norm minimization problem tends not to identify optimal solution, so recently, other heuristic surrogate functions such as nonconvex logdet are utilized to recover sparser signal. In this paper, to handle nonconvex optimation problem, a modified Augmented Lagrange Multiplier Method (ALMM) is developed using weighted nuclear norm instead of nuclear norm which conventional ALMM treats for convex optimization. We experiment on real images in Matrix Completion problem with diverse nonconvex, and show that instead of solving a simple convex problem, nonconvex optimization problem can reconstruct a low rank matrix more accurately and the convergence rate is faster with having higher average PSNR.

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Lee J, Choe Y. Low rank matrix recovery via augmented lagrange multiplier with nonconvex minimization. In 2016 IEEE 12th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2016. Institute of Electrical and Electronics Engineers Inc. 2016. 7528217 https://doi.org/10.1109/IVMSPW.2016.7528217