摘要
基于偏微分方程的变分模型是目前图像处理中最好的方法之一,然而,在解决图像去噪中的反问题时,传统的全变分模型存在"阶梯"效应这一固有缺陷。针对该不足,本文提出了一种基于平滑核的广义变分去噪模型(即u^=argminuJ(u)=∫Ω(u)dxdy+λ2∫Ωu-u0 2dxdy),该模型采用通用形式的平滑核函数作为图像的正则化项,选取一种鲁棒性好和边缘保持能力强的势函数,利用变分原理推导出与该模型相应的偏微分方程,最后给出了结合梯度加权最速下降法和半点格式的数值迭代算法(uni,+j1=uin,j+δt.(′(u u)uξξ+″(u)uηη)ni,j+(λ(u0-u))in,j)。大量实验仿真结果表明,该模型对高斯噪声图像具有良好的噪声滤除和细节保护能力,与传统全变分模型相比,无论是主观视觉效果,还是客观性能评价指标(PSNR)方面,都具有明显的优势。
Variarional model based on PDE is one of the best schemes for image processing.To improve the "staircase" effect of conventional total variational model in solving the inverse problem of image denoising,a generalized variational denoising model based on smooth kernel(u^=argminu{J(u)=∫Ω(|u1|)dxdy+λ2∫Ω|u-u012dxdy})is proposed.This model uses a smooth kernel function of general form as the regularized term of image,an edge preserving potential function was adopted,which had good bobustness to noises.Then the partial differential equation of the proposed model is deduced by variation approach.Finally a weighted gradient descent flow is developed for image denoising with an iterative algorithm based on semi-point scheme,that is un+1i,j=uni,j+δt·[(′(|u1)1|u1|uξξ+″(1|u1|)uηη)ni,j+(λ(u0-u))ni,j].Experimental results show that the proposed model has good performance in image denoising.It can suppress Gaussian noise very effectively and preserve image details very well,meanwhile,the restored images that are obtained by the proposed model have better objective quality(PSNR)and subjective vision effect than that by the conventional total variational model.
出处
《重庆师范大学学报(自然科学版)》
CAS
2010年第6期59-63,68,共6页
Journal of Chongqing Normal University:Natural Science
基金
四川省教育厅重点科研项目(No.09ZA104)
四川省教育厅青年基金项目(No.09ZB072)
2008年人工智能四川省重点实验室开放基金
四川文理学院2009年科研项目(No.2009B08Z)
关键词
图像去噪
平滑核
偏微分方程
全变分模型
边缘保持势函数
image denoising
smooth kernel
partial differential equation
total variational model
edge preserving potential function