基于结构组全变分模型的图像压缩感知重建

赵辉; 杨晓军; 张静; 孙超; 张天骐

doi:10.11999/JEIT190243

基于结构组全变分模型的图像压缩感知重建

doi: 10.11999/JEIT190243

1.
重庆邮电大学通信与信息工程学院重庆 400065
2.
重庆邮电大学信号与信息处理重庆市重点实验室重庆 400065

基金项目: 国家自然科学基金(61671095)

详细信息

作者简介:
赵辉：女，1980年生，教授，硕士生导师，研究方向为信号与图像处理

杨晓军：男，1994年生，硕士生，研究方向为信号与图像处理

张静：女，1992年生，硕士生，研究方向为信号与图像处理

孙超：男，1992年生，硕士生，研究方向为信号与图像处理

张天骐：男，1971年生，博士后，教授，研究方向为通信信号的调制解调、盲处理、语音信号处理

通讯作者:
赵辉　zhaohui@cqupt.edu.cn

中图分类号: TN911.73; TP391
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出版历程
- 收稿日期: 2019-04-11
- 修回日期: 2020-03-07
- 网络出版日期: 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: 针对基于传统全变分(TV)模型的图像压缩感知(CS)重建算法不能有效地恢复图像的细节和纹理，从而导致图像过平滑的问题，该文提出一种基于结构组全变分(SGTV)模型的图像压缩感知重建算法。该算法利用图像的非局部自相似性和结构稀疏特性，将图像的重建问题转化为由非局部自相似图像块构建的结构组全变分最小化问题。算法以结构组全变分模型为正则化约束项构建优化模型，利用分裂Bregman迭代将算法分离成多个子问题，并对每个子问题高效地求解。所提算法很好地利用了图像自身的信息和结构稀疏特性，保护了图像细节和纹理。实验结果表明，该文所提出的算法优于现有基于全变分模型的压缩感知重建算法，在PSNR和视觉效果方面取得了显著提升。
- 图像重建 /
- 压缩感知 /
- 非局部自相似 /
- 全变分
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

图 1 图像的结构组构造

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图 2 6幅标准测试图像

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图 3 Barbara仿真结果对比图

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图 4 Monarch仿真结果对比图

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图 5 相似块数目$c$取值不同时算法的性能比较

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图 6 采样率=0.3时，重叠块间距对算法重建性能的影响

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图 7 算法稳定性分析

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表 1 基于SGTV模型的图像CS重建算法(SGTV)的整体描述

　输入：随机投影测量矩阵${{H}}$和CS测量值${{y}}$

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

　　(1) 开始迭代：$t = 1,2, ··· ,N$

　　(2) 　根据式(10)计算得到${{{u}}^{(t + 1)}}$；

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

　　(4) 　根据块匹配法找到$n$个结构组；

　　(5) 　对于每一个结构组${{{r}}_{{G_i}}}$, $i = 1,2, ··· ,n$

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

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

　　(8) end for

　　(9) 根据式(11)计算得到${{{x}}^{(t + 1)}}$；

　　(10) 根据式(12)更新${{{b}}^{(t + 1)}}$；

　　(11) 达到最大迭代次数，算法结束

　　(12) 输出重建图像${{u}} = {{{u}}^{(t + 1)}}$

下载: 导出CSV

表 2 不同采样率下各图像CS重建算法重建图像的PSNR(dB)/FISM值比较

采样率	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

下载: 导出CSV

表 3 采样率为0.3时，各算法的实际运行处理时间(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

下载: 导出CSV

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