基于分数阶变分问题的TV模型

TV model based on fractional variational problems

作为图像处理领域中的重要课题,图像去噪问题虽然已被研究多年,但将分数阶微积分应用于此,却还处于刚刚起步的阶段.本文采用频域分数阶化的技巧,引入了频域分数阶差分,并通过整数阶变分导出分数阶变分,再将其应用到分数阶TV模型中.仿真实验表明,频域分数阶差分能更好地保留图像的低频成分;而在图像去噪的研究中,相比整数阶差分,分数阶差分效果更优;并发现极大峰值信噪比的最优阶数和噪声方差有逆向联动关系.

This article is focus on image denoising which has always been a hot research topic in image processing area. Using fractional calculus to solve this issue still has a long way to go. This paper main- ly adopts fractional order difference in frequency domain and evolves fractional variational problem through general variational problem, then using it in fractional TV model and processing it with simula- tion approach. Simulation results show that fractional differentials can greatly preserve low frequency of signals, and the effect of fractional order is better than integer orde＇s in image denoising study and with the increase of white noise variance, the order of optimal conditions that the output of the system rea- ches the maximum of PSNR will decline.