基于結(jié)構(gòu)組全變分模型的圖像壓縮感知重建

趙輝; 楊曉軍; 張靜; 孫超; 張?zhí)祢U

doi:10.11999/JEIT190243

基于結(jié)構(gòu)組全變分模型的圖像壓縮感知重建

doi: 10.11999/JEIT190243 cstr: 32379.14.JEIT190243

1.
重慶郵電大學(xué)通信與信息工程學(xué)院重慶 400065
2.
重慶郵電大學(xué)信號與信息處理重慶市重點實驗室重慶 400065

基金項目: 國家自然科學(xué)基金(61671095)

詳細(xì)信息

作者簡介:
趙輝：女，1980年生，教授，碩士生導(dǎo)師，研究方向為信號與圖像處理

楊曉軍：男，1994年生，碩士生，研究方向為信號與圖像處理

張靜：女，1992年生，碩士生，研究方向為信號與圖像處理

孫超：男，1992年生，碩士生，研究方向為信號與圖像處理

張?zhí)祢U：男，1971年生，博士后，教授，研究方向為通信信號的調(diào)制解調(diào)、盲處理、語音信號處理

通訊作者:
趙輝　zhaohui@cqupt.edu.cn

中圖分類號: TN911.73; TP391
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出版歷程
- 收稿日期: 2019-04-11
- 修回日期: 2020-03-07
- 網(wǎng)絡(luò)出版日期: 2020-04-09
- 刊出日期: 2020-11-16

Image Compressed Sensing Reconstruction Based on Structural Group Total Variation

1.
School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2.
Chongqing Key Laboratory of Signal and Information Processing, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Funds: The National Natural Science Foundation of China (61671095)

摘要

摘要: 針對基于傳統(tǒng)全變分(TV)模型的圖像壓縮感知(CS)重建算法不能有效地恢復(fù)圖像的細(xì)節(jié)和紋理，從而導(dǎo)致圖像過平滑的問題，該文提出一種基于結(jié)構(gòu)組全變分(SGTV)模型的圖像壓縮感知重建算法。該算法利用圖像的非局部自相似性和結(jié)構(gòu)稀疏特性，將圖像的重建問題轉(zhuǎn)化為由非局部自相似圖像塊構(gòu)建的結(jié)構(gòu)組全變分最小化問題。算法以結(jié)構(gòu)組全變分模型為正則化約束項構(gòu)建優(yōu)化模型，利用分裂Bregman迭代將算法分離成多個子問題，并對每個子問題高效地求解。所提算法很好地利用了圖像自身的信息和結(jié)構(gòu)稀疏特性，保護了圖像細(xì)節(jié)和紋理。實驗結(jié)果表明，該文所提出的算法優(yōu)于現(xiàn)有基于全變分模型的壓縮感知重建算法，在PSNR和視覺效果方面取得了顯著提升。
- 圖像重建 /
- 壓縮感知 /
- 非局部自相似 /
- 全變分
Abstract: To solve the problem that the traditional Compressed Sensing (CS) algorithm based on Total Variation (TV) model can not effectively restore details and texture of image, which leads to over-smoothing of reconstructed image, an image Compressed Sensing (CS) reconstruction algorithm based on Structural Group TV (SGTV) model is proposed. The proposed algorithm utilizes the non-local self-similarity and structural sparsity of image, and converts the CS recovery problem into the total variation minimization problem of the structural group constructed by non-local self-similar image blocks. In addition, the optimization model of the proposed algorithm is built with regularization constraint of the structural group total variation model, and it uses the split Bregman iterative algorithm to separate it into multiple sub-problems, and then solves them respectively. The proposed algorithm makes full use of the information and structural sparsity of image to protects the image details and texture. The experimental results demonstrate that the proposed algorithm achieves significant performance improvements over the state-of-the-art total variation based algorithm in both PSNR and visual perception.
- Image reconstruction /
- Compressed Sensing (CS) /
- Nonlocal self-similarity /
- Total Variation (TV)

HTML全文

圖 1 圖像的結(jié)構(gòu)組構(gòu)造

下載: 全尺寸圖片幻燈片

圖 2 6幅標(biāo)準(zhǔn)測試圖像

下載: 全尺寸圖片幻燈片

圖 3 Barbara仿真結(jié)果對比圖

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圖 4 Monarch仿真結(jié)果對比圖

下載: 全尺寸圖片幻燈片

圖 5 相似塊數(shù)目$c$取值不同時算法的性能比較

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圖 6 采樣率=0.3時，重疊塊間距對算法重建性能的影響

下載: 全尺寸圖片幻燈片

圖 7 算法穩(wěn)定性分析

下載: 全尺寸圖片幻燈片

表 1 基于SGTV模型的圖像CS重建算法(SGTV)的整體描述

　輸入：隨機投影測量矩陣${{H}}$和CS測量值${{y}}$

　初始化：$t = 0$, ${{{u}}^{(0)}} = 0$, ${{}^{(0)}} = 0$, $B$, $c$, $\beta $, $\mu $；

　　(1) 開始迭代：$t = 1,2, ··· ,N$

　　(2) 　根據(jù)式(10)計算得到${{{u}}^{(t + 1)}}$；

　　(3) 　令${{{r}}^{(t + 1)}} = {{{u}}^{(t + 1)}} - {{}^{(t)}}$; ${{\mu = \left( {\lambda K} \right)}/{\left( {\beta N} \right)}}$；

　　(4) 　根據(jù)塊匹配法找到$n$個結(jié)構(gòu)組；

　　(5) 　對于每一個結(jié)構(gòu)組${{{r}}_{{G_i}}}$, $i = 1,2, ··· ,n$

　　(6) 　　　利用FISTA算法迭代更新得到${{{p}}^{m + 1}}$；

　　(7) 　　　根據(jù)式(3)算法迭代更新得到${{{\hat x}}_{{G_i}}}$；

　　(8) end for

　　(9) 根據(jù)式(11)計算得到${{{x}}^{(t + 1)}}$；

　　(10) 根據(jù)式(12)更新${{}^{(t + 1)}}$；

　　(11) 達(dá)到最大迭代次數(shù)，算法結(jié)束

　　(12) 輸出重建圖像${{u}} = {{{u}}^{(t + 1)}}$

下載: 導(dǎo)出CSV

表 2 不同采樣率下各圖像CS重建算法重建圖像的PSNR(dB)/FISM值比較

采樣率	算法	House	Barbara	Leaves	Monarch	Parrots	Vessels	Avg.
0.2	TV	31.54/0.9072	23.79/0.8190	22.66/0.8553	26.77/0.8862	26.51/0.9018	22.09/0.8356	25.56/0.8675
	NLTV	32.59/0.9199	25.01/0.8584	24.40/0.9012	27.07/0.8913	26.52/0.9247	23.54/0.8798	26.51/0.8959
	TVNLR	33.03/0.9230	25.68/0.8901	23.51/0.8834	27.42/0.9073	26.97/0.9225	23.34/0.8718	26.66/0.8997
	NGSR	33.60/0.9350	27.470.9175	24.79/0.9036	27.83/0.9090	27.43/0.9217	24.10/0.8874	27.54/0.9124
	SGTV	34.96/0.9519	29.27/0.9240	26.71/0.9249	28.59/0.9232	29.19/0.9386	25.16/0.9024	28.98/0.9275
0.3	TV	33.76/0.9382	25.16/0.8723	25.79/0.9090	29.94/0.9286	28.68/0.9309	25.27/0.8992	28.10/0.9130
	NLTV	34.96/0.9422	27.47/0.9157	27.57/0.9354	29.86/0.9278	29.02/0.9469	27.15/0.9352	29.31/0.9339
	TVNLR	35.23/0.9497	27.92/0.9153	26.67/0.9249	30.01/0.9374	28.96/0.9436	27.08/0.9321	29.31/0.9338
	NGSR	36.36/0.9679	29.54/0.9435	27.71/0.9359	30.92/0.9419	30.22/0.9526	27.26/0.9358	30.34/0.9463
	SGTV	37.08/0.9690	32.20/0.9558	29.91/0.9543	31.55/0.9508	31.17/0.9549	28.36/0.9446	31.73/0.9549
0.4	TV	35.41/0.9564	26.59/0.9095	28.76/0.9419	32.69/0.9520	30.46/0.9513	27.95/0.9441	30.31/0.9452
	NLTV	36.97/0.9603	30.01/0.9520	31.04/0.9682	32.66/0.9532	30.15/0.9619	29.70/0.9568	31.76/0.9587
	TVNLR	37.19/0.9664	30.27/0.9246	30.14/0.9546	32.95/0.9600	30.40/0.9576	29.35/0.9570	31.72/0.9534
	NGSR	37.25/0.9695	31.10/0.9602	31.08/0.9637	33.28/0.9590	31.37/0.9619	30.01/0.9609	32.35/0.9625
	SGTV	38.80/0.9775	34.33/0.9710	32.54/0.9702	34.20/0.9664	33.16/0.9666	31.25/0.9668	34.05/0.9698

下載: 導(dǎo)出CSV

表 3 采樣率為0.3時，各算法的實際運行處理時間(s)

	TV	NLTV	TVNLR	NGSR	SGTV
House (256×256)	5.27	75.26	99.57	110.52	132.85
Vessels(96×96)	1.29	36.75	49.09	63.12	73.96
平均	3.28	56.01	74.33	86.82	103.01

下載: 導(dǎo)出CSV

參考文獻(xiàn)(20)

DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289–1306. doi: 10.1109/TIT.2006.871582

TSAIG Y and DONOHO D L. Extensions of compressed sensing[J]. Signal Processing, 2006, 86(3): 549–571. doi: 10.1016/j.sigpro.2005.05.029

AHARON M, ELAD M, and BRUCKSTEIN A. K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation[J]. IEEE Transactions on Signal Processing, 2006, 54(11): 4311–4322. doi: 10.1109/TSP.2006.881199

SHEN Yangmei, XIONG Hongkai, and DAI Wenrui. Multiscale dictionary learning for hierarchical sparse representation[C]. 2017 IEEE International Conference on Multimedia and Expo, Hong Kong, China, 2017: 1332–1337.

ZHANG Jian, ZHAO Chen, ZHAO Debin, et al. Image compressive sensing recovery using adaptively learned sparsifying basis via L0 minimization[J]. Signal Processing, 2014, 103: 114–126. doi: 10.1016/j.sigpro.2013.09.025

LI Chengbo, YIN Wotao, and ZHANG Yin. TVAL3: TV minimization by augmented lagrangian and alternating direction algorithms[EB/OL]. http://www.caam.rice.edu/~optimization/L1/TVAL3/, 2013.

HE Wei, ZHANG Hongyan, and ZHANG Liangpei. Total variation regularized reweighted sparse nonnegative matrix factorization for hyperspectral unmixing[J]. IEEE Transactions on Geoscience and Remote Sensing, 2017, 55(7): 3909–3921. doi: 10.1109/tgrs.2017.2683719

WAHID A and LEE H J. Image denoising method based on directional total variation filtering[C]. The 8th International Conference on Information and Communication Technology Convergence, Jeju, South Korea, 2017: 798–802.

BUADES A, COLL B, and MOREL J M. A non-local algorithm for image denoising[C]. 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, USA, 2005: 60–65.

LIU Hangfan, XIONG Ruiqin, ZHANG Xinfeng, et al. Nonlocal gradient sparsity regularization for image restoration[J]. IEEE Transactions on Circuits and Systems for Video Technology, 2017, 27(9): 1909–1921. doi: 10.1109/TCSVT.2016.2556498

ZHANG Jian, ZHAO Debin, and GAO Wen. Group-based sparse representation for image restoration[J]. IEEE Transactions on Image Processing, 2014, 23(8): 3336–3351. doi: 10.1109/TIP.2014.2323127

CAO Wenfei, CHANG Yi, HAN Guodong, et al. Destriping remote sensing image via low-rank approximation and nonlocal total variation[J]. IEEE Geoscience and Remote Sensing Letters, 2018, 15(6): 848–852. doi: 10.1109/LGRS.2018.2811468

SHEN Yan, LIU Qing, LOU Shuqin, et al. Wavelet-based total variation and nonlocal similarity model for image denoising[J]. IEEE Signal Processing Letters, 2017, 24(6): 877–881. doi: 10.1109/LSP.2017.2688707

TU Bing, HUANG Siyuan, FANG Leyuan, et al. Hyperspectral image classification via weighted joint nearest neighbor and sparse representation[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2018, 11(11): 4063–4075. doi: 10.1109/JSTARS.2018.2869376

XU Jin, QIAO Yuansong, FU Zhizhong, et al. Image block compressive sensing reconstruction via group-based sparse representation and nonlocal total variation[J]. Circuits, Systems, and Signal Processing, 2019, 38(1): 304–328. doi: 10.1007/s00034-018-0859-8

ZHANG Xiaoqun, BURGER M, BRESSON X, et al. Bregmanized nonlocal regularization for deconvolution and sparse reconstruction[J]. SIAM Journal on Imaging Sciences, 2010, 3(3): 253–276. doi: 10.1137/090746379

ZHANG Jian, LIU Shaohui, XIONG Ruiqin, et al. Improved total variation based image compressive sensing recovery by nonlocal regularization[C]. 2013 IEEE International Symposium on Circuits and Systems, Beijing, China, 2013: 2836–2839.

GOLDSTEIN T and OSHER S. The split Bregman method for L1-regularized problems[J]. SIAM Journal on Imaging Sciences, 2009, 2(2): 323–343. doi: 10.1137/080725891

ZHANG Lin, ZHANG Lei, MOU Xuanqin, et al. FSIM: A feature similarity index for image quality assessment[J]. IEEE Transactions on Image Processing, 2011, 20(8): 2378–2386. doi: 10.1109/TIP.2011.2109730

BECK A and TEBOULLE M. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems[J]. IEEE Transactions on Image Processing, 2009, 18(11): 2419–2434. doi: 10.1109/TIP.2009.2028250

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