基于结构加权低秩近似的泊松图像去模糊

吴庆波; 任文琦

doi:10.13700/j.bh.1001-5965.2020.0061

基于结构加权低秩近似的泊松图像去模糊

doi: 10.13700/j.bh.1001-5965.2020.0061

吴庆波^{1, 2},
任文琦^{1, 2, ,}

1.
中国科学院信息工程研究所信息安全国家重点实验室, 北京 100193
2.
中国科学院大学网络空间安全学院, 北京 100049

基金项目:

国家自然科学基金 U1605252

国家自然科学基金 U1803264

国家自然科学基金 61802403

国家重点研发计划 2019YFB1406500

北京市自然科学基金 L182057

北京市自然科学基金 KZ201910005007

北京市自然科学基金 L182057

详细信息

作者简介:
吴庆波男, 博士研究生。主要研究方向:图像处理

任文琦男, 博士, 副研究员。主要研究方向:图像处理和机器学习

通讯作者:
任文琦, E-mail: renwenqi@iie.ac.cn

中图分类号: TP391
计量
- 文章访问数: 485
- HTML全文浏览量: 117
- PDF下载量: 132
- 被引次数: 0
出版历程
- 收稿日期: 2020-03-02
- 录用日期: 2020-03-20
- 网络出版日期: 2020-09-20

Structural weighted low-rank approximation for Poisson image deblurring

WU Qingbo^{1, 2},
REN Wenqi^{1, 2
, ,}

1.
State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100193, China
2.
School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China

Funds:

National Natural Science Foundation of China U1605252

National Natural Science Foundation of China U1803264

National Natural Science Foundation of China 61802403

National Key R & D Program of China 2019YFB1406500

Beijing Natural Science Foundation L182057

Beijing Natural Science Foundation KZ201910005007

Beijing Natural Science Foundation L182057

More Information

Corresponding author: REN Wenqi, E-mail: renwenqi@iie.ac.cn

摘要

摘要:
针对由高斯模糊和泊松噪声引起的图像降质问题，提出了一种基于结构加权低秩近似的图像去模糊方法。首先，通过依次组合缩放、旋转、剪切和翻折等四种基本操作引入结构变换，以增加搜索空间内候选图像块的相似性。然后，构造新的目标函数，利用相似图像块的低秩性，在正则项中使用加权核范数（WNN）对结构变换后的图像块进行惩罚，以在去模糊的同时抑制泊松噪声。最后，基于半正定二次分裂（HQS）方法设计交替优化方案，用于求解目标函数，从泊松图像中去除模糊。实验结果表明：在多种泊松噪声强度下，所提方法取得的峰值信噪比（PSNR）和结构相似性（SSIM）都高于当前同类去模糊方法。
- 图像去模糊 /
- 泊松噪声 /
- 结构变换 /
- 加权低秩近似 /
- 半正定二次分裂(HQS)
Abstract:
To solve the problem of image quality degradation caused by Gaussian blur and Poisson noise, an image deblurring method based on structural weighted low-rank approximation is proposed. First, a structural transformation is introduced by subsequently combining the four basic operations of scaling, rotation, shearing, and flipping in order to boost the similarity of candidate patches in the searching space. Then, a novel objective function is proposed by carefully designing the regularization term. To this end, we perform structural transformation on image patches and then penalize the transformed results with Weighted Nuclear Norm (WNN) based on the assumption of low-rank among non-local similar patches, suppressing Poisson noise at the same time of deblurring. Finally, an alternating optimization algorithm is presented based on the Half-Quadratic Splitting (HQS) method to solve the proposed objective function for Poisson image deblurring. Experimental results demonstrate that, under multiple intensities of Poisson noise, the proposed algorithm achieves higher Peak Signal to Noise Ratio (PSNR) and Structural Similarity (SSIM) than the state-of-the-art deblurring methods.
- image deblurring /
- Poisson noise /
- structural transformation /
- weighted low-rank approximation /
- Half-Quadratic Splitting (HQS)

HTML全文

图 1 不同方法搜索相似图像块结果

Figure 1. Results of similar patches that are searched by different methods

下载: 全尺寸图片幻灯片

图 2 基于结构加权低秩近似泊松图像去模糊方法流程

Figure 2. Flowchart of structural weighted low-rank approximation method for Poisson image deblurring

下载: 全尺寸图片幻灯片

图 3 量化评估中的20张测试图像

Figure 3. Twenty test images for quantitative evaluation

下载: 全尺寸图片幻灯片

图 4 峰值信噪比随旋转角度间隔Δθ和超参数λ变化的曲线

Figure 4. Variation of PSNR with rotation interval Δθ and hyper-parameter λ

下载: 全尺寸图片幻灯片

图 5 本文方法对高斯模糊程度和泊松噪声水平的鲁棒性

Figure 5. Robustness of proposed method to levels of Gaussian blur and Poisson noise

下载: 全尺寸图片幻灯片

图 6 非盲图像去模糊中不同方法的比较

Figure 6. Comparison of different methods in non-blind image deblurring

下载: 全尺寸图片幻灯片

图 7 盲图像去模糊中不同方法的比较

Figure 7. Comparison of different methods in blind image deblurring

下载: 全尺寸图片幻灯片

图 8 结构变换的有效性

Figure 8. Effectiveness of structural transformation

下载: 全尺寸图片幻灯片

图 9 真实图像去模糊中不同方法的比较

Figure 9. Comparison of different methods on real-world image deblurring

下载: 全尺寸图片幻灯片

表 1 非盲图像去模糊中多种泊松噪声强度下不同方法恢复结果的平均峰值信噪比和结构相似性

Table 1. Mean PSNR and SSIM of results recovered by different methods on test images with various intensities of Poisson noise in non-blind image deblurring

图像	方法	mPSNR/dB			mSSIM
图像	方法	P_v=63	P_v=255	P_v=1 023	P_v=63	P_v=255	P_v=1 023
自然图像	PURE-LET^[8]	23.09	25.13	26.02	0.852 5	0.884 4	0.909 7
	TGV^[9]	24.35	26.16	28.86	0.859 0	0.893 9	0.918 8
	PDS^[7]	23.28	25.70	26.47	0.856 6	0.892 1	0.915 1
	Hess^[6]	25.15	27.63	29.75	0.873 4	0.901 1	0.920 6
	本文无结构变换	25.04	27.60	29.49	0.860 1	0.895 3	0.918 4
	本文方法	26.32	28.65	30.61	0.886 5	0.912 6	0.931 7
医学图像	PURE-LET^[8]	24.05	26.09	27.06	0.836 7	0.873 3	0.897 6
	TGV^[9]	24.96	27.17	29.75	0.843 8	0.880 6	0.904 3
	PDS^[7]	24.12	26.18	27.53	0.841 8	0.879 7	0.900 2
	Hess^[6]	26.10	28.59	30.63	0.857 5	0.889 1	0.907 8
	本文无结构变换	26.06	28.26	30.19	0.844 2	0.883 6	0.903 5
	本文方法	27.14	29.70	31.26	0.871 9	0.902 4	0.920 9

下载: 导出CSV

参考文献(30)

[1]	GUO Y F, CAO X C, ZHANG W, et al.Fake colorized image detection[J].IEEE Transactions on Information Forensics and Security, 2018, 13(8):1932-1944. doi: 10.1109/TIFS.2018.2806926
[2]	GUO Y F, AU O C, WANG R, et al.Half image watermarking by content aware double-sided embedding error diffusion[J].IEEE Transaction on Image Processing, 2018, 27(7):3387-3402. doi: 10.1109/TIP.2018.2815181
[3]	WANG R, LIANG D, ZHANG W, et al.MatchDR: Image correspondence by leveraging distance ratio constraint[C]//ACM International Conference on Multimedia.New York: ACM, 2016: 606-610.
[4]	GU R L, DOGANDZIC A.Blind X-ray CT image reconstruction from polychromatic Poisson measurements[J].IEEE Transactions on Computational Imaging, 2016, 2(2):150-165. doi: 10.1109/TCI.2016.2523431
[5]	LI J, LUISIER F, BLU T.PURE-LET deconvolution of 3D fluorescence microscopy images[C]//International Symposium on Biomedical Imaging.Piscataway: IEEE Press, 2017: 723-727.
[6]	LEFKIMMIATIS S, UNSER M.Poisson image reconstruction with Hessian Schatten-norm regularization[J].IEEE Transactions on Image Processing, 2013, 22(11):4314-4327. doi: 10.1109/TIP.2013.2271852
[7]	ONO S.Primal-dual plug-and-play image restoration[J].IEEE Signal Processing Letters, 2017, 24(8):1108-1112. doi: 10.1109/LSP.2017.2710233
[8]	LI J, LUISIER F, BLU T.PURE-LET image deconvolution[J].IEEE Transactions on Image Processing, 2018, 27(1):92-105. http://cn.bing.com/academic/profile?id=2cb1c3c6914cde459b7c6ac424e06c38&encoded=0&v=paper_preview&mkt=zh-cn
[9]	LIU X W.Total generalized variation and Shearlet transform based Poissonian image deconvolution[J].Multimedia Tools and Applications, 2019, 78:18855-18868. doi: 10.1007/s11042-019-7247-7
[10]	REN W Q, CAO X C, PAN J S, et al.Image deblurring via enhanced low rank prior[J].IEEE Transactions on Image Processing, 2016, 25(7):3426-3437. doi: 10.1109/TIP.2016.2571062
[11]	LE T, CHARTRAND R, ASAKI T J.A variational approach to reconstructing images corrupted by Poisson noise[J].Journal of Mathematical Imaging and Vision, 2007, 27(3):257-263. doi: 10.1007/s10851-007-0652-y
[12]	YAN Y Y, REN W Q, GUO Y F, et al.Image deblurring via extreme channels prior[C]//IEEE Conference on Computer Vision and Pattern Recognition.Piscataway: IEEE Press, 2017: 6978-6986.
[13]	HARMANY Z T, MARCIA R F, WILLETT R M.This is SPIRAL-TAP:Sparse Poisson intensity reconstruction algorithms-Theory and practice[J].IEEE Transactions on Image Processing, 2012, 21(3):1084-1096. http://dl.acm.org/citation.cfm?id=2334075
[14]	MA L, MOISAN L, YU J, et al.A dictionary learning approach for Poisson image deblurring[J].IEEE Transactions on Medical Imaging, 2013, 32(7):1277-1289. doi: 10.1109/TMI.2013.2255883
[15]	CHEN D Q.Regularized generalized inverse accelerating linearized alternating minimization algorithm for frame-based Poissonian image deblurring[J].SIAM Journal on Imaging Sciences, 2014, 7(2):716-739. doi: 10.1137/130932119
[16]	ROND A, GIRYES R, ELAD M.Poisson inverse problems by the plug-and-play scheme[J].Journal of Visual Communication and Image Representation, 2016, 41:96-108. doi: 10.1016/j.jvcir.2016.09.009
[17]	GETREUER P.Rudin-Osher-Fatemi total variation denoising using split Bregman[J/OL].Image Processing On Line, 2012, 2:74-95.(2012-05-19)[2020-03-01].https://doi.org/10.5201/ipol.2012.g-tvd.
[18]	ELAD M, AHARON M.Image denoising via sparse and redundant representations over learned dictionaries[J].IEEE Transactions on Image Processing, 2006, 15(12):3736-3745. doi: 10.1109/TIP.2006.881969
[19]	BUADES A, COLL B, MOREL J M.A non-local algorithm for image denoising[C]//IEEE Conference on Computer Vision and Pattern Recognition.Piscataway: IEEE Press, 2005, 2: 60-65.
[20]	GU S, ZHANG L, ZUO W M, et al.Weighted nuclear norm minimization with application to image denoising[C]//IEEE Conference on Computer Vision and Pattern Recognition.Piscataway: IEEE Press, 2014, 1: 2862-2869.
[21]	YAIR N, MICHAELI T.Multi-scale weighted nuclear norm image restoration[C]//IEEE Conference on Computer Vision and Pattern Recognition.Piscataway: IEEE Press, 2018, 1: 3165-3174.
[22]	HUANG J B, SINGH A, AHUJA N.Single image super-resolution from transformed self-exemplars[C]//IEEE Conference on Computer Vision and Pattern Recognition.Piscataway: IEEE Press, 2015, 1: 5197-5206.
[23]	BARNES C, SHECHTMAN E, GOLDMAN D B, et al.The generalized patchmatch correspondence algorithm[C]//European Conference on Computer Vision.Berlin: Springer, 2010, 6313(3): 29-43.
[24]	FEDOROV V, BALLESTER C.Affine non-local means image denoising[J].IEEE Transactions on Image Processing, 2017, 26(5):2137-2148. doi: 10.1109/TIP.2017.2681421
[25]	GU J J, LU H N, ZUO W M, et al.Blind super-resolution with iterative kernel correction[C]//IEEE Conference on Computer Vision and Pattern Recognition.Piscataway: IEEE Press, 2019: 1604-1613.
[26]	KAI Z, ZUO W M, ZHANG L.Learning a single convolutional super-resolution network for multiple degradations[C]//IEEE Conference on Computer Vision and Pattern Recognition.Piscataway: IEEE Press, 2018, 6: 3262-3271.
[27]	LEE J S.Refined filtering of image noise using local statistics[J].Computer Graphics and Image Processing, 1981, 15(4):380-389. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=gZq26tT1r6FtGYf5iDr+hXwC9TrsLGa2xK+7nJrj/IU=
[28]	ZHANG K, ZUO W M, CHEN Y, et al.Beyond a Gaussian denoiser:Residual learning of deep CNN for image denoising[J].IEEE Transactions on Image Processing, 2017, 26(7):3142-3155. doi: 10.1109/TIP.2017.2662206
[29]	GONG K, CATANA C, QI J Y, et al.PET image reconstruction using deep image prior[J].IEEE Transactions on Image Processing, 2019, 38(7):1655-1665. doi: 10.1109/TMI.2018.2888491
[30]	KRISHNAN D, TAY T, FERGUS R.Blind deconvolution using a normalized sparsity measure[C]//IEEE Conference on Computer Vision and Pattern Recognition.Piscataway: IEEE Press, 2011, 1: 233-240.