一种应用博弈和L0约束的盲图像修复方法

doi:10.19665/j.issn1001-2400.2021.04.014

摘要/Abstract

摘要：

图像修复是利用原始图像的先验信息从缺失像素的观察图像出发恢复原始图像的过程。大多数图像修复模型假定图像缺失区域是已知的,但在实际应用中,这些缺失区域的信息很难直接获得。为了解决这类问题,利用L₀范数的稀疏性先验和博弈理论,建立了新的图像修复模型。新模型适用于图像缺失区域已知和未知两种情况。根据目标函数的结构,提出了有效的临近交替方向乘子法和基于博弈的交替框架来解决相应的最小化问题,分析了文中模型在一定的条件下的收敛性。与现有的修复模型进行了对比,数值实验表明,所提出的模型和算法在主观和客观质量评价上比现有修复模型具有更好的结果和稳健性。

关键词: 图像修复, L₀范数, 交替方向乘子法, 峰值信噪比, 博弈

Abstract:

Image inpainting is the process of restoring the original image from the observed image with missing pixels using the prior information on the original image.Most image inpainting models assume that the missing areas of the image are known.However,inpractical applications,the information on these missing areas is difficult to obtain directly.In order to solve this problem,a new image inpainting model is established by using the sparse priori of L₀ norm and game theory.The new model is suitable for the two cases of known and unknown image missing areas.According to the structure of the objective function,an effective proximal alternating direction method of multipliers and a game-based alternating framework are proposed to solve the corresponding minimization problem,and the convergence of the model under certain conditions is analyzed.Compared with the existing inpainting models,numerical experiments show that the models and algorithms proposed can lead to better results and robustness insubjective and objective quality evaluation than the image inpainting methods available.

Key words: image inpainting, L₀ norm, alternating direction method of multipliers, peak signal to noise ratio, game

中图分类号:

TP391

冯象初,王萍,何瑞强. 一种应用博弈和L0约束的盲图像修复方法[J]. 西安电子科技大学学报, 2021, 48(4): 103-112.

FENG Xiangchu,WANG Ping,HE Ruiqiang. Method for inpainting blind images using the game and L0 constraint[J]. Journal of Xidian University, 2021, 48(4): 103-112.

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缺失比例/%	观测图像的峰值信噪比	恢复图像的峰值信噪比
缺失比例/%	观测图像的峰值信噪比	O已知(算法2)	O未知(算法3)
10	17.261 0	44.434 7	44.423 5
20	14.278 0	40.868 6	40.859 9
30	12.512 6	38.538 6	38.529 6
40	11.263 2	36.488 3	36.483 6
50	10.289 6	34.618 1	34.616 5

缺失比例/%	观测图像的峰值信噪比	恢复图像的峰值信噪比
缺失比例/%	观测图像的峰值信噪比	O已知(算法2)	O未知(算法3)
10	17.248 8	45.832 2	45.773 7
20	14.272 6	42.371 3	42.347 3
30	12.509 4	40.062 7	40.050 4
40	11.261 1	38.093 5	38.087 4
50	10.288 3	36.262 1	36.249 1

缺失比例/%	观测图像的峰值信噪比	恢复图像的峰值信噪比
缺失比例/%	观测图像的峰值信噪比	L1TV_SBM	L0TV_PDA	文中模型(算法2)
10	15.586 0	33.585 0	42.439 3	46.495 8
20	12.582 6	31.428 9	39.355 2	42.386 5
30	10.812 3	28.748 6	36.873 6	39.508 8
40	9.570 6	24.711 2	34.415 1	36.899 2
50	8.600 9	19.162 4	32.165 9	34.573 2

缺失比例/%	观测图像的峰值信噪比	恢复图像的峰值信噪比
缺失比例/%	观测图像的峰值信噪比	L1TV_SBM	L0TV_PDA	文中模型(算法2)
10	15.581 2	33.627 6	47.955 5	49.735 6
20	12.580 4	31.895 0	43.551 7	45.306 3
30	10.811 0	28.766 9	40.339 4	42.338 0
40	9.569 7	24.907 7	37.252 7	39.652 6
50	8.600 4	19.128 0	34.385 9	37.271 6

缺失比例/%	观测图像的峰值信噪比	恢复图像的峰值信噪比
缺失比例/%	观测图像的峰值信噪比	L02TV_AOP	文中模型(算法3)
10	15.586 0	41.760 9	44.737 8
20	12.582 6	38.148 8	41.478 4
30	10.812 3	35.397 7	38.985 5
40	9.570 6	31.029 9	36.551 5
50	8.600 9	19.817 0	34.311 4