Robust TruncatedL1-L2Total Variation Sparse Restoration Models

doi:10.12141/j.issn.1000-565X.220485

Abstract

Abstract:

In addition to Gaussian noise, there is sparse noise with impulsive properties in the signal acquisition process. The common robust sparse signal recovery models can recover the original sparse signal under sparse noise environment. However, in many practical applications, the structural sparsity of the original signal, for example, gradient sparsity needs to be considered. In order to recover the sparse structure of the original high-dimensional signal from the coexistence of sparse noise and Gaussian noise, this paper proposed two nonconvex and nonsmooth optimization models based on truncated L₁-L₂ total variation (TV) and 3D truncated L₁-L₂ TV, respectively. These optimization models were solved by the proximal alternating linearized minimization algorithm with extrapolation, and the sub-problems involved were solved by the proximal convex difference algorithm with extrapolation. Under the assumption that the potential function has Kurdyka-Lojasiewicz (KL) property, the convergence analysis of these algorithms was given. The numerical experiments test grey images with Gaussian noise, color images with mixed noise, grey video with mixed noise and so on. The peak signal-to-noise ratio (PSNR) was used as the evaluation criterion for recovered quality. The experimental results show that the new models can correctly recover the original structured sparse signal, and have better PSNR values in the same noisy environment.

Key words: robust compressed sensing, truncated total variation, nonconvex and nonsmooth optimization, sparse noise, structural sparse

CLC Number:

TP391.41

HAN Le, JIANG Yihua. Robust TruncatedL1-L2Total Variation Sparse Restoration Models[J]. Journal of South China University of Technology(Natural Science Edition), 2023, 51(5): 45-53.

Figures/Tables 9

Fig.1

Table 1

PSNR， SSIM and running time of recovering grey images with Gaussian noise"

图像序号	PSNR/dB			SSIM/dB			运行时间/s
图像序号	$L 1 / 2$	TVT0	TVT1	$L 1 / 2$	TVT0	TVT1	$L 1 / 2$	TVT0	TVT1
1	26.82	25.62	27.16	0.760 0	0.506 9	0.802 8	0.02	0.01	45.25
2	28.10	26.72	30.19	0.760 0	0.438 4	0.818 0	0.02	0.01	43.30
3	26.84	26.96	29.08	0.800 0	0.508 9	0.880 7	0.02	0.01	44.01
4	28.90	27.68	31.21	0.820 0	0.692 1	0.896 1	0.02	0.01	46.86
5	26.92	26.51	29.38	0.860 0	0.807 3	0.910 0	0.10	0.05	282.85
6	23.98	24.90	24.90	0.860 0	0.806 7	0.834 0	0.10	0.05	733.15

Table 1

Fig.2

Table 2

Table 3

Fig.3

Table 4

Table 5

Fig.4

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图像序号	含稀疏噪声的PSNR/dB			含混合噪声的PSNR/dB
图像序号	TRPCA	TVT0	TVT1	TRPCA	TVT0		TVT1
1	23.28	24.38	24.71	19.18	21.48	21.74
2	24.49	24.67	24.98	19.21	21.40	21.40
3	27.70	28.00	27.50	20.68	23.22	22.71
4	24.43	24.62	24.40	19.52	21.36	21.08
5	29.73	30.11	29.87	21.79	21.79	23.73
6	31.52	31.89	29.83	20.63	21.12	20.75

图像序号	噪声	每次迭代的平均运行时间/s			总迭代次数
图像序号	噪声	TRPCA	TVT0	TVT1	TRPCA	TVT0	TVT1
1	稀疏噪声	0.002	0.993	4.956	43	150	150
2		0.001	0.960	3.815	42	150	150
3		0.001	1.025	3.962	43	84	113
4		0.002	1.043	3.909	43	127	150
5		0.001	0.970	4.029	44	89	143
6		0.001	1.020	3.720	43	116	101
1	混合噪声	0.001	1.149	3.474	40	150	1
2		0.002	1.127	3.087	40	150	1
3		0.001	1.099	3.071	40	150	1
4		0.002	1.056	3.140	40	150	1
5		0.001	1.119	3.092	41	150	1
6		0.001	1.108	3.257	40	150	150

帧数	PSNR/dB
帧数	TRPCA	中值滤波	TVT0	TVT1
1	23.38	24.85	25.67	25.64
7	21.03	22.52	23.44	23.48
13	20.77	21.93	22.92	22.92
18	20.65	21.74	22.53	22.45
24	20.47	21.51	22.34	22.26
30	20.60	21.44	22.10	22.10
36	20.61	21.32	22.09	22.12
42	19.31	20.55	20.86	20.84
48	21.29	22.88	23.93	23.86

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