Non-Convex Low-Rank Approximation for Image Denoising and Deblurring

Yang LEI; Zhanjie SONG; Qiwei SONG

doi:10.1587/transinf.2015EDP7307

Non-Convex Low-Rank Approximation for Image Denoising and Deblurring

Yang LEI, Zhanjie SONG, Qiwei SONG

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Recovery of low-rank matrices has seen significant activity in many areas of science and engineering, motivated by theoretical results for exact reconstruction guarantees and interesting practical applications. Recently, numerous methods incorporated the nuclear norm to pursue the convexity of the optimization. However, this greatly restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings. This paper studies a generalized non-convex low-rank approximation, where the singular values are in l_p-heuristic. Then specific results are derived for image restoration, including denoising and deblurring. Extensive experimental results on natural images demonstrate the improvement of the proposed method over the recent image restoration methods.

Publication: IEICE TRANSACTIONS on Information Vol.E99-D No.5 pp.1364-1374

Publication Date: 2016/05/01

Publicized: 2016/02/04

Online ISSN: 1745-1361

DOI: 10.1587/transinf.2015EDP7307

Type of Manuscript: PAPER

Category: Image Processing and Video Processing

Authors

Yang LEI
  Tianjin University
Zhanjie SONG
  Tianjin University
Qiwei SONG
  Tianjin University

Keyword

low-rank approximation, nuclear norm, image restoration, non-convex optimization

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Yang LEI, Zhanjie SONG, Qiwei SONG, "Non-Convex Low-Rank Approximation for Image Denoising and Deblurring" in IEICE TRANSACTIONS on Information, vol. E99-D, no. 5, pp. 1364-1374, May 2016, doi: 10.1587/transinf.2015EDP7307.
Abstract: Recovery of low-rank matrices has seen significant activity in many areas of science and engineering, motivated by theoretical results for exact reconstruction guarantees and interesting practical applications. Recently, numerous methods incorporated the nuclear norm to pursue the convexity of the optimization. However, this greatly restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings. This paper studies a generalized non-convex low-rank approximation, where the singular values are in l_p-heuristic. Then specific results are derived for image restoration, including denoising and deblurring. Extensive experimental results on natural images demonstrate the improvement of the proposed method over the recent image restoration methods.
URL: https://globals.ieice.org/en_transactions/information/10.1587/transinf.2015EDP7307/_p

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@ARTICLE{e99-d_5_1364,
author={Yang LEI, Zhanjie SONG, Qiwei SONG, },
journal={IEICE TRANSACTIONS on Information},
title={Non-Convex Low-Rank Approximation for Image Denoising and Deblurring},
year={2016},
volume={E99-D},
number={5},
pages={1364-1374},
abstract={Recovery of low-rank matrices has seen significant activity in many areas of science and engineering, motivated by theoretical results for exact reconstruction guarantees and interesting practical applications. Recently, numerous methods incorporated the nuclear norm to pursue the convexity of the optimization. However, this greatly restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings. This paper studies a generalized non-convex low-rank approximation, where the singular values are in l_p-heuristic. Then specific results are derived for image restoration, including denoising and deblurring. Extensive experimental results on natural images demonstrate the improvement of the proposed method over the recent image restoration methods.},
keywords={},
doi={10.1587/transinf.2015EDP7307},
ISSN={1745-1361},
month={May},}

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TY - JOUR
TI - Non-Convex Low-Rank Approximation for Image Denoising and Deblurring
T2 - IEICE TRANSACTIONS on Information
SP - 1364
EP - 1374
AU - Yang LEI
AU - Zhanjie SONG
AU - Qiwei SONG
PY - 2016
DO - 10.1587/transinf.2015EDP7307
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E99-D
IS - 5
JA - IEICE TRANSACTIONS on Information
Y1 - May 2016
AB - Recovery of low-rank matrices has seen significant activity in many areas of science and engineering, motivated by theoretical results for exact reconstruction guarantees and interesting practical applications. Recently, numerous methods incorporated the nuclear norm to pursue the convexity of the optimization. However, this greatly restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings. This paper studies a generalized non-convex low-rank approximation, where the singular values are in l_p-heuristic. Then specific results are derived for image restoration, including denoising and deblurring. Extensive experimental results on natural images demonstrate the improvement of the proposed method over the recent image restoration methods.
ER -