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基于改进的分数阶TV模型的图像修复算法

张桂梅,李艳兵(江西省图像处理与模式识别重点实验室南昌航空大学)

摘 要
目的 TV(total variation)模型能去除图像噪声,在图像修复领域得到了广泛的应用,但是TV模型的正则项是一阶导数,易导致纹理特征等具有弱导数性质的信息变得模糊。为了克服该缺陷,分数阶微分被引入到TV模型中,但存在的分数阶TV模型对具有弱导数性质的纹理和边缘细节等信息的保持仍然不够理想,并且没有充分利用已知的边缘和纹理等先验信息,修复精度仍有待提高。方法 针对这些问题,提出一种改进的分数阶TV模型,用于图像的修复。改进的模型在分数阶TV模型中求解梯度时引入极小值,此外改进的模型根据图像已知区域的先验信息确定待修复区域的纹理方向,充分利用图像的纹理信息。结果 一方面,在分数阶TV模型中求解梯度时引入极小值,从而增加模型的稳定性,并有效地保持了纹理特征的弱导数特性。另一方面,根据图像已知区域的先验信息确定待修复区域的纹理方向,以提高图像恢复的精度。结论 理论分析和实验结果均表明,提出的模型相对于原始的TV模型和分数阶TV模型,均能有效地提高图像修复的精度,适合于包含较多弱纹理和弱边缘信息的图像修复,该模型是TV模型的重要延伸和推广。
关键词
Research on TV model for image inpainting based on improved fractional-order differentiation

Zhang Guimei,Li Yanbing(Key Laboratory of Image Processing and Pattern Recognition,Nanchang Hangkong University,Jiangxi Nanchang,330063)

Abstract
Objective The TV (total variation) model can remove image noise and has been widely used in the field of image restoration. However, the regular term of the TV model is the first derivative, which tends to cause the information with weak derivative properties such as texture features to become blurred. In order to overcome this drawback, fractional differentials are introduced into the TV model, but the existence of fractional-order TV models is still not ideal for maintaining information such as texture and edge details with weak derivative properties, and does not make full use of known edges and textures. Waiting for prior information, the accuracy of repair still needs to be improved. Methods In response to these problems, an improved fractional-order TV model was proposed for image restoration. The improved model introduces a minimum value when solving the gradient in the fractional-order TV model. In addition, the improved model determines the texture direction of the area to be repaired based on the prior information of the known region of the image, and makes full use of the texture information of the image. Results On the one hand, the minimum value is introduced when solving the gradient in the fractional-order TV model, which increases the stability of the model and effectively maintains the weak derivative characteristics of the texture features. On the other hand, the texture direction of the area to be repaired is determined based on a priori information of the known area of ??the image to improve the accuracy of image restoration. Conclusion Both theoretical analysis and experimental results show that the proposed model can effectively improve the accuracy of image restoration compared with the original TV model and fractional-order TV model, and is suitable for image restoration with more weak texture and weak edge information. The model is an important extension and extension of the TV model.
Keywords
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