基于组稀疏表示和加权全变分的图像压缩感知重构

doi:10.3969/j.issn.1001-506X.2020.10.04

摘要/Abstract

摘要：

传统的基于组稀疏表示(group sparse representation, GSR)的压缩感知(compressd sensing, CS)重构算法利用信号的稀疏性和非局部相似性来重构图像信号,但没有充分考虑图像的局部平滑特性,影响了算法的重构性能。考虑信号的稀疏性、非局部相似性、平滑性3种先验信息,提出一种基于GSR和加权全变分(weighted total variation, WTV)的图像CS重构算法,并针对传统的WTV采用全局加权会引入错误的纹理以及边缘状伪影的问题,利用一种新的WTV策略,只对图像的高频分量设置权重来保证图像重构质量。此外，针对硬阈值迭代法忽略低频的主分量系数,采用硬阈值-模平方方法来更好地保护非主分量系数。实验表明,相同采样率下,所提算法的峰值信噪比比非局部正则化全变分和基于GSR的CS算法平均分别提高5.4 dB和0.62 dB,验证了所提算法有效保护图像的细节信息。

关键词: 压缩感知, 组稀疏表示, 加权全变分, 图像重构

Abstract:

The traditional compression sensing (CS) reconstruction algorithm based on group sparse representation (GSR) uses the sparsity and nonlocal similarity of the signal to reconstruct the image signal. However, the local smoothness of the image is not sufficiently consiclered, which affects the reconstruction performance of the algorithm. Considering the three prior informations of signal sparsity, nonlocal similarity and smoothness, an image CS reconstruction algorithm based on GSR and weighted total variation (WTV) is proposed. Aiming at the problem that global weighting will introduce wrong texture and edge artifacts for the traditional WTV, a new WTV strategy only sets the weight of high frequency cmponet of image is used to protect the image reconstruction quality. In addition, aiming at the problem that the hard threshold iteration ignores the low frequency principal component coefficient, the hard threshold modulus square method is used to better protect the non-principal component coefficient. Experimental results show that the peak signal to noise ratio of the proposed algorithm is improved 5.4 dB and 0.62 dB compared with the total variation nonlocal regularization and CS algorithm based on GSR at the same sampling rate respectively, which proves that the proposed algorithm effectively protects the details of the image.

Key words: compressed sensing (CS), group sparse representation, weighted total variation (WTV), image reconstruction

中图分类号:

TP391

赵辉, 方禄发, 张天骐, 李志伟, 徐先明. 基于组稀疏表示和加权全变分的图像压缩感知重构[J]. 系统工程与电子技术, 2020, 42(10): 2172-2180.

Hui ZHAO, Lufa FANG, Tianqi ZHANG, Zhiwei LI, Xianming XU. Image compressive sensing reconstruction via group sparse representation and weighted total variation[J]. Systems Engineering and Electronics, 2020, 42(10): 2172-2180.

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测试图像	采样率	PSNR/dB
测试图像	采样率	NLRTV	GSR	ALSB	GSR-NCR	GSR-WTV
House	0.1	29.68	33.76	32.52	32.01	34.00
	0.2	33.06	36.78	35.73	36.57	37.32
	0.3	35.53	38.93	38.15	39.38	39.52
	0.4	37.21	40.60	40.14	41.12	41.15
Barbara	0.1	22.48	29.99	29.09	27.99	30.16
	0.2	24.46	34.59	31.61	33.93	34.78
	0.3	25.62	36.92	34.73	37.19	37.31
	0.4	27.90	38.99	37.26	39.20	39.21
Monarch	0.1	24.12	25.29	24.12	23.72	26.02
	0.2	27.35	29.55	28.23	28.64	31.07
	0.3	29.84	33.17	31.48	33.53	34.16
	0.4	31.76	36.07	34.33	36.88	36.99
Starfish	0.1	22.81	23.60	23.23	22.87	24.41
	0.2	25.75	29.42	27.38	27.23	29.62
	0.3	27.96	33.00	30.26	31.75	32.90
	0.4	30.67	35.63	33.29	35.34	35.77
Average	0.1	24.77	28.16	27.24	26.64	28.64
	0.2	28.21	32.58	30.73	31.59	33.20
	0.3	29.73	35.49	33.66	35.46	36.00
	0.4	31.89	37.82	36.26	38.13	38.34

测试图像	采样率	SSIM
测试图像	采样率	NLRTV	GSR	ALSB	GSR-NCR	GSR-WTV
House	0.1	0.833 1	0.869 5	0.859 2	0.856 8	0.883 2
	0.2	0.881 2	0.913 6	0.914 3	0.913 9	0.932 5
	0.3	0.910 4	0.940 3	0.946 6	0.955 3	0.957 0
	0.4	0.930 8	0.958 2	0.962 5	0.968 0	0.968 7
Barbara	0.1	0.616 4	0.858 2	0.821 8	0.854 1	0.903 0
	0.2	0.741 8	0.938 3	0.927 5	0.942 7	0.957 5
	0.3	0.809 8	0.963 2	0.959 9	0.971 1	0.973 2
	0.4	0.880 5	0.975 1	0.973 3	0.980 3	0.980 9
Monarch	0.1	0.780 7	0.857 1	0.815 9	0.779 7	0.878 0
	0.2	0.882 7	0.929 2	0.908 0	0.904 5	0.944 6
	0.3	0.925 4	0.954 5	0.945 0	0.957 9	0.965 8
	0.4	0.945 6	0.968 8	0.967 0	0.975 1	0.977 0
Starfish	0.1	0.674 6	0.756 1	0.722 2	0.702 8	0.756 1
	0.2	0.802 3	0.869 5	0.843 9	0.837 5	0.892 0
	0.3	0.869 6	0.920 6	0.911 9	0.917 9	0.937 0
	0.4	0.918 9	0.947 9	0.947 6	0.953 9	0.961 7
Average	0.1	0.726 2	0.835 2	0.804 8	0.798 3	0.855 0
	0.2	0.827 0	0.912 6	0.898 4	0.899 6	0.931 6
	0.3	0.878 8	0.944 6	0.940 8	0.950 5	0.958 2
	0.4	0.918 9	0.962 5	0.962 6	0.969 3	0.972 0

图像	采样率	NLRTV	GSR	ALSB	GSR-NCR	GSR-WTV
House	0.1	142	396	414	831	430
	0.2	94	293	305	697	306
	0.3	72	237	266	585	287
	0.4	67	196	167	482	143
平均时间		94	281	288	649	291

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