摘要
图像分解是将图像的不同组成部分利用分解算法分别提取出来,而全变差方法是基于PDE方法进行图像处理问题的一种数学方法。在Meyer等思想的影响下,对现有基于BV(Ω)空间的全变差(TV)正则项进行分析研究后,提出了一种L1(Ω)空间上的改进的全变差正则模型。在改进的TV方法基础上,首先分别推荐了改进的TV-G和TV-H-1图像分解极小泛函模型;然后给出了相应的欧拉-拉格朗日方程以及对应的数值解;最后,对3类测试图像,包括纹理类图像、航空类图像、杂类图像分别进行了图像分解数值实验,同时也进行了信噪比和时间效率的对比分析。实验结果表明:改进的TV-H-1模型在针对纹理类图像分解时,分解效果优于TV-H-1模型,而改进的TV-G模型在针对上述3类图像分解时,大部分图像分解效果优于TV-G模型。
Image decomposition is to separate one image into some different components using decomposition algorithm. However,it is a mathematical method based total variation method for image processing problems. Inspired Meyer ’s ideas, they propose one new improved total variation regularization model after analyzing the current total variation( TV) regular terms. Based on the improved TV method,the improved TV-G and TV-H-1 image decomposition mini-functional models are firstly proposed, and then the corresponding Euler-Lagrange equations and corresponding numerical solutions are given. Finally, three kinds of test images, including texture images,aeronautical images,and miscellaneous images,are respectively subjected to image decomposition numerical experiments,and a comparative analysis of signal-to-noise ratio and time efficiency are also carried out. The experimental results show that the improved TV-H-model has better decomposition effect than the TV-H-1 model when decomposing for texture-like images,while the improved TV-G model is mostly for the above three types of image decomposition. The decomposition effect is better than the TV-G model.
作者
刘瑞华
谢挺
LIU Ruihua;XIE Ting(Liangjiang Artificial Intelligence College,Chongqing University of Technology,Chongqing 401135,China;School of Science,Chongqing University of Technology,Chongqing 400054,China)
出处
《重庆理工大学学报（自然科学）》
CAS
北大核心
2020年第7期156-161,共6页
Journal of Chongqing University of Technology：Natural Science
基金
重庆市自然科学基金项目(CSTC2019JCYJ-MSXMX0500)
重庆市教委科学技术基金项目(KJ1709207)。
关键词
图像分解
全变差
数值解
极小泛函
image decomposition
total variation
numerical solution
minimal functional
