Image Enhancement Algorithm with Histogram Equalization Based on Saturation-Value Total Generalized Variation

Yihui Zhu; Xiaoya Guo; Zhengmeng Jin; Qinxia Wang

doi:10.3788/LOP242061

Laser & Optoelectronics Progress, Volume. 62, Issue 12, 1237006(2025)

Image Enhancement Algorithm with Histogram Equalization Based on Saturation-Value Total Generalized Variation

Yihui Zhu¹, Xiaoya Guo^1、*, Zhengmeng Jin¹, and Qinxia Wang²

Author Affiliations

¹College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, Jiangsu , China

²Artificial Intelligence Research Institute, China University of Mining and Technology, Xuzhou 221116, Jiangsu , China

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Abstract Get PDF(in Chinese)

Figures & Tables(11)

Fig. 1. Image enhancement effects of different methods. (a) Damaged images; (b) SV-TV-HE; (c) SV-TV-HE only with adaptive brightness weight function; (d) SV-TV-HE only with SV-TGV regularization term; (e) proposed method; (f) ground truth images

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Fig. 2. PSNR values corresponding to different $α_{0}$ values

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Fig. 3. Visual comparison of the enhancement effects on synthetic images using different methods

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Fig. 4. Enlarged views of the green box (region ①) from the enhanced results of synthetic images

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Fig. 5. Enlarged views of the red box (region ②) from the enhanced results of synthetic images

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Fig. 6. Visual comparison of the enhancement effects on real images using different methods

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Fig. 7. Enlarged views of green box (region ①) from the enhanced results of real images

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Fig. 8. Enlarged views of red box (region ②) from the enhanced results of real images

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Table 0. [in Chinese]

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Table 0. [in Chinese]

算法1

1）初始化 $q^{(0)} = \tilde{f}$ ， $γ_{1}^{(0)} = γ_{2}^{(0)}$ ， $λ_{1} > 0$ ， $λ_{2} > 0$ ；

2）未满足迭代停止条件时，反复执行以下步骤：

• 固定 $q^{(k)}$ 、 $z^{(k)}$ 、 $t^{(k)}$ 、 $γ_{1}^{(k)}$ 、 $γ_{2}^{(k)}$ ，更新迭代 $r^{(k)}$ ：

$r^{(k + 1)} = \underset{r}{a r g m i n} L (q^{(k)}, r, z^{(k)}, t^{(k)}, γ_{1}^{(k)}, γ_{2}^{(k)})$ （10）

• 固定 $q^{(k)}$ 、 $r^{(k + 1)}$ 、 $γ_{1}^{(k)}$ 、 $γ_{2}^{(k)}$ ，更新迭代 $z^{(k + 1)}$ 、 $t^{(k + 1)}$ ：

$(z^{(k + 1)}, t^{(k + 1)}) = \underset{z, t}{a r g m i n} L (q^{(k)}, r^{(k + 1)}, z, t, γ_{1}^{(k)}, γ_{2}^{(k)})$ （11）

• 固定 $r^{(k + 1)}$ 、 $z^{(k + 1)}$ 、 $t^{(k + 1)}$ 、 $γ_{1}^{(k)}$ 、 $γ_{2}^{(k)}$ ，更新迭代 $q^{(k + 1)}$ ：

$q^{(k + 1)} = \underset{q}{a r g m i n} L (q^{(k)}, r^{(k + 1)}, z^{(k + 1)}, t^{(k + 1)}, γ_{1}^{(k)}, γ_{2}^{(k)})$ （12）

• 固定 $r^{(k + 1)}$ 、 $z^{(k + 1)}$ 、 $t^{(k + 1)}$ 、 $q^{(k + 1)}$ ，更新迭代 $γ_{1}^{(k + 1)}$ 、 $γ_{2}^{(k + 1)}$ ：

$\begin{array}{l} γ_{1}^{(k + 1)} = γ_{1}^{(k)} + λ_{1} (q^{(k + 1)} - r^{(k + 1)}) \\ γ_{2}^{(k + 1)} = γ_{2}^{(k)} + λ_{2} (q^{(k + 1)} - z^{(k + 1)}) \end{array}$

3）迭代终止条件为 $\frac{‖q^{(k + 1)} - q^{(k)}‖}{‖q^{(k)}‖} \leq ε$ ，其中 $ε$ 为控制迭代终止条件的参数，当满足该条件时停止迭代，输出 $u$ ， $u = P^{- 1} q$ 。

Table 1. PSNR and SSIM values of enhanced results for synthetic images by different methods

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Table 1. PSNR and SSIM values of enhanced results for synthetic images by different methods

Method	PSNR /dB					SSIM
Method	Ⅰ	Ⅱ	Ⅲ	Ⅳ	Ⅴ	Ⅰ	Ⅱ	Ⅲ	Ⅳ	Ⅴ
FCCE	22.91	17.83	19.06	20.62	19.20	0.95	0.79	0.91	0.93	0.89
JED	16.87	17.54	16.26	16.00	14.38	0.86	0.90	0.90	0.90	0.87
RGF	17.77	22.30	20.23	20.98	21.75	0.81	0.80	0.79	0.88	0.91
NLW-AGC	22.78	19.85	21.76	19.95	19.95	0.84	0.79	0.83	0.80	0.80
PCA	18.62	17.89	22.07	20.14	18.79	0.88	0.85	0.93	0.90	0.89
SV-TV-HE	22.58	21.94	22.57	23.63	22.54	0.90	0.90	0.93	0.92	0.94
Proposed	24.42	22.96	24.43	25.01	23.00	0.96	0.94	0.97	0.96	0.94

Table 2. NIQE, Entropy, and BRISQUE values of enhanced results for real images by different methods

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Table 2. NIQE, Entropy, and BRISQUE values of enhanced results for real images by different methods

Indicator	Image	FCCE	JED	RGF	NLW-AGC	PCA	SV-TV-HE	Proposed
NIQE	Ⅰ	2.9404	3.0650	3.8429	3.0415	3.3856	3.2092	3.0032
	Ⅱ	2.3631	4.0927	3.2587	3.5119	3.2287	4.0572	2.3136
	Ⅲ	2.4123	3.0407	3.2959	3.1694	2.8914	2.7771	2.2758
	Ⅳ	2.5541	3.1175	3.7423	3.1884	3.5793	3.9506	2.7940
	Ⅴ	2.6586	2.6586	3.8396	2.8419	3.9718	2.9096	2.5300
	Average	2.5857	3.1949	3.5959	3.1506	3.4114	3.3807	2.5833
Entropy	Ⅰ	7.0717	5.9034	6.8075	6.7897	7.0076	7.3586	7.4090
	Ⅱ	7.4396	6.2831	7.1718	7.2168	6.9346	7.7407	7.7596
	Ⅲ	7.0983	7.0523	7.1761	6.5121	7.4815	7.4983	7.5530
	Ⅳ	7.5413	7.0838	7.1639	7.5905	7.4721	7.7210	7.7704
	Ⅴ	7.7724	7.7724	7.6108	7.3925	7.8459	7.7299	7.7895
	Average	7.3847	6.8190	7.1860	7.1003	7.3483	7.6097	7.6563
BRISQUE	Ⅰ	6.7599	15.8494	8.4590	10.4936	19.5048	10.9270	6.6956
	Ⅱ	23.6796	18.8463	22.5548	10.9342	6.9271	27.8012	6.8929
	Ⅲ	15.6629	15.5776	12.3588	15.3465	17.3604	28.2877	13.1346
	Ⅳ	8.4203	18.4244	15.2185	0.7372	5.0546	14.6222	1.4954
	Ⅴ	15.8930	15.8930	21.9241	12.6438	14.0522	29.1868	8.6312
	Average	14.0831	16.9181	16.1030	10.0311	12.5798	22.1650	7.3699

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Yihui Zhu, Xiaoya Guo, Zhengmeng Jin, Qinxia Wang. Image Enhancement Algorithm with Histogram Equalization Based on Saturation-Value Total Generalized Variation[J]. Laser & Optoelectronics Progress, 2025, 62(12): 1237006

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Paper Information

Category: Digital Image Processing

Received: Sep. 30, 2024

Accepted: Dec. 19, 2024

Published Online: Jun. 6, 2025

The Author Email: Xiaoya Guo (guoxy@njupt.edu.cn)

DOI:10.3788/LOP242061

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology