Hybrid high-order nonlocal gradient sparsity regularization for Poisson image deconvolution

Tao He; Jie Hu; Haiqing Huang

doi:10.1364/AO.57.010243

Applied Optics
Vol. 57,
Issue 35,
pp. 10243-10256
(2018)
•https://doi.org/10.1364/AO.57.010243

Hybrid high-order nonlocal gradient sparsity regularization for Poisson image deconvolution

Tao He, Jie Hu, and Haiqing Huang

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Tao He, Jie Hu, and Haiqing Huang, "Hybrid high-order nonlocal gradient sparsity regularization for Poisson image deconvolution," Appl. Opt. 57, 10243-10256 (2018)

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Table of Contents Category
- Imaging Systems, Image Processing, and Displays
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About this Article
History
- Original Manuscript: August 29, 2018
- Revised Manuscript: October 25, 2018
- Manuscript Accepted: November 3, 2018
- Published: December 6, 2018

Abstract

Images obtained by photon-counting sensors are always contaminated with Poisson noise. Total variation (TV) has been extensively researched in image deconvolution because of its remarkable ability to preserve details. However, TV is based on the requirement that the global image gradient obeys a Laplacian distribution and can hardly maintain the information of each part of the image. We extended the global TV to nonlocal modeling and established an intensity-adaptive nonlocal regularization based on similar blocks. Meanwhile, to restrain the staircase effect caused by first-order regularization, we proposed a new hybrid nonlocal regularization by modeling the sparsity of the high-order derivative. An efficient alternating direction method of multipliers algorithm was employed to solve the proposed model, and the adaptive selection strategy of regularization parameters in the model was further studied and analyzed. The experimental results show that the proposed hybrid high-order nonlocal gradient sparsity regularization model achieves a substantial computational time improvement compared to another nonlocal restoration algorithm while producing a relatively clear recovery image.

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Image	$50 \leq γ \leq 100$
Image	Min (dB)	Max (dB)	Difference (dB)
Mandril	32.2481	32.6367	0.3886
Barbara	28.5364	28.7567	0.2203
Cameraman	30.0567	30.4891	0.4324
House	29.8436	30.0406	0.1970
Peppers	31.5478	31.8173	0.2695
Car	27.2522	27.6345	0.3823
Dog	32.3983	32.5169	0.1186
Cell	25.3725	25.6724	0.2999
Moon	27.3054	27.5242	0.2188
Organ	29.7354	30.0125	0.2711

Kernel Size	Motion Blur				Gaussian Blur				Average Blur
Method	TV	HOTV	NGS	HHONGS	TV	HOTV	NGS	HHONGS	TV	HOTV	NGS	HHONGS
Mandril	30.83	32.16	33.02	33.51	29.32	31.02	31.12	30.90	32.12	33.84	32.86	34.46
Barbara	24.67	26.03	25.67	28.19	25.61	27.34	27.65	28.05	32.15	34.53	26.24	28.61
Cameraman	30.78	32.11	31.18	31.83	26.72	29.02	28.22	30.95	33.52	36.14	35.94	36.85
House	28.94	32.19	29.45	32.04	28.38	29.04	29.32	29.43	29.67	30.61	30.59	31.12
Pepper	29.16	30.16	30.88	31.16	31.03	32.15	32.72	32.04	30.18	30.42	32.46	32.54
Car	28.19	29.26	28.54	29.80	25.32	26.54	26.15	26.89	24.58	27.69	27.15	26.14
Dog	29.90	31.13	29.19	31.36	30.94	32.11	31.28	32.51	29.86	31.18	33.47	34.67
Cell	22.94	23.58	24.11	24.32	22.08	24.58	24.12	25.67	26.04	26.37	26.98	28.35
Moon	24.96	25.69	24.63	26.35	23.57	24.38	26.14	27.52	25.69	27.16	27.35	29.99
Organ	25.33	26.89	26.17	29.38	26.38	29.54	29.34	30.01	28.67	30.38	31.95	33.63
Average	27.57	28.92	28.28	29.79	26.94	28.57	28.61	29.40	29.25	30.83	30.50	31.64

Kernel Size	Motion Blur				Gaussian Blur				Average Blur
Method	TV	HOTV	NGS	HHONGS	TV	HOTV	NGS	HHONGS	TV	HOTV	NGS	HHONGS
Mandril	84.43	88.64	88.46	87.64	85.67	88.16	89.65	89.26	86.25	87.34	88.48	89.11
Barbara	87.64	85.39	89.24	90.87	86.37	88.94	88.12	88.30	88.26	90.27	88.68	89.07
Cameraman	84.64	90.01	89.37	90.24	87.64	86.34	89.13	89.54	89.35	90.57	91.68	88.28
House	86.42	86.24	84.21	88.34	85.13	86.14	84.62	86.61	88.34	86.61	88.39	88.53
Pepper	82.34	83.46	84.33	86.48	86.12	87.34	89.63	86.35	89.34	91.61	90.44	91.89
Car	85.24	90.36	91.23	92.64	84.25	85.14	87.53	88.67	88.64	90.56	90.47	91.46
Dog	87.72	89.37	89.43	90.72	83.14	84.35	83.35	85.13	90.42	90.63	90.54	91.22
Cell	85.65	86.38	86.98	88.02	84.96	86.35	85.83	86.96	87.69	89.35	89.34	90.69
Moon	84.33	85.69	86.66	87.39	86.39	87.93	87.37	89.32	88.36	89.78	90.36	91.22
Organ	87.92	88.96	88.31	89.63	86.17	87.39	87.69	89.67	87.38	88.61	89.46	90.96
Average	85.63	87.45	87.82	89.20	85.58	86.81	87.29	87.98	88.40	89.53	89.78	90.24

Kernel Size	Motion Blur				Gaussian Blur				Average Blur
Method	TV	HOTV	NGS	HHONGS	TV	HOTV	NGS	HHONGS	TV	HOTV	NGS	HHONGS
Mandril	54.09	39.72	32.48	29.11	76.18	61.72	58.42	52.88	40.02	27.03	33.84	23.36
Barbara	221.93	162.32	176.75	99.38	179.54	120.58	112.32	102.06	99.83	83.04	154.65	82.07
Cameraman	54.76	60.26	49.81	42.70	139.21	81.60	98.16	52.46	28.95	15.88	16.63	13.47
House	83.15	69.50	74.09	40.67	94.87	81.74	76.53	74.47	70.42	56.85	57.13	50.36
Pepper	79.01	63.09	53.35	49.98	51.66	39.93	34.85	40.83	62.70	59.10	36.93	36.45
Car	98.75	77.63	91.67	68.36	192.32	145.18	158.80	133.80	226.61	111.38	125.36	159.25
Dog	67.02	50.18	78.83	47.79	52.39	40.11	48.67	36.62	67.22	49.86	29.38	22.31
Cell	331.99	286.10	254.13	240.67	402.93	226.98	252.55	176.91	162.41	150.97	131.25	95.59
Moon	208.74	176.04	225.35	151.43	286.76	237.84	158.43	115.27	175.94	125.81	120.39	65.47
Organ	190.88	133.96	158.00	75.53	150.76	72.60	76.24	64.98	88.61	59.84	41.70	28.30
Average	139.03	111.88	119.45	84.56	162.66	110.83	107.50	85.03	102.27	73.98	74.73	57.66

Method	TV $λ = 200$	HOTV $λ^{0} = 1000, α^{0} = 0.4, γ = 50$	NGS $γ = 24, λ^{h} = λ^{v} = 8.5$	HHONGS $λ^{0} = 1000, γ = 54$
CPU time/s	1.42	11.05	4628.37	1624.77
Regularization	$‖ \nabla u ‖_{1}$	$α ‖ \nabla u ‖_{1} + (1 - α) ‖ \nabla^{2} u ‖_{1}$	$\frac{\sqrt{2}}{σ_{i}^{1}} ‖ \nabla_{i} u - m_{i}^{1} ‖_{1}$	$α (\frac{\sqrt{2}}{σ_{i}^{1}} ‖ \nabla_{i} (H u) - m_{i}^{1} ‖_{1}) + (1 - α) (\frac{\sqrt{2}}{σ_{i}^{2}} ‖ \nabla_{i}^{2} (H u) - m_{i}^{2} ‖_{1})$
Solver	ALM	ADMM	ALM	ADMM
Time for searching similar blocks/s	0	0	4627.36	1621.93
Time for deblurring/s	1.42	11.05	1.01	2.84
Number of iterations	5	23	4	12
Time per iteration/s	0.284	0.48	1157.09	0.24

Abstract

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Applied Optics