【计算机论文全套栏目提醒】:网学会员为广大网友收集整理了,基于同伦延拓的全变分图像去噪 - 会议论文,希望对大家有所帮助!
人连理工大学硕士学位论文 摘 要 本文主要研究了全变分图像去噪问题.全变分图像去噪是目前图像去嗓的主要方法之一,它的解属于有界变差函数类,允许有不连续点,因此用全变分去噪模型恢复图像能够有效的保持边界,有利于图像的后期处理.,但是求解它比较困难,主要是因为Tv.范数在IV“l=0处不可微,不能用诸如牛顿法之类的方法将其线性化:且Euler-Lagrange方程含有一个高度非线性的项,牛顿法只有局部收敛性,对于高度非线性问题它的收敛域很小,因此难以保证所取的初始点在它的收敛域内,故一般不用牛顿法直接求解.本文对传统的时间依赖方法,不动点迭代法,原始对偶方法,Zhou,Zhou和Chain提出的牛顿法与延拓法相结合的方法进行了比较分析.然后基于上述方法的局限性,提出了一种克服牛顿法局部收敛性缺陷的方法一同伦方法.它的主要思想是将Euler-Lagrange方程中TV.范数做一个足够大的扰动,得到一个能用以观测图像z为初值的牛顿法求解的辅助方程,通过构造同伦方程将辅助方程和Euler-Lagrange方程联系起来.以辅助方程的解为起点跟踪同伦方程的解曲线.在路径跟踪过程中我们采用割线预估,因为路径的正则性,当同伦参数f增加的时候,解路径从不转回.因此预估后,在f保持不变的超平面上校正.并初步对算法加以实现,结果表明同伦延拓法去噪效果比较好.关键词:全变分去噪;同伦延拓法;Euler-Lagrange方程;牛顿法 基丁同伦延拓的全变分图去噪法 Total Variation Image Denoising Bases on Homotopy Continuation Abstract We mainly study the total variation image denoising using homotopy continuation in thispaper.Total variation image denoising is regarded as one of the main methods for imagedenoising.Its solution belongs to variation function,SO it allows to have discontinuities in thesolution.Therefore,we can keep edges well if we use this model for image restoring,and it isalso benefit for the postprocessing.But it is a hard task to solve this equation,one reason istllat the TV-norm is nondifferentiable when IVuI=0,s0 we Call’t apply a linearizationtechnique such as the Newton method.The other reason is that the Euler-Lagrange equationhas a highly nonlinear term.The Newton method for such equation is known to have a verysmall domain of convergence,and it is very difficult to make sure that the initial value such asthe observed image belongs to this domain.So the Newton method is not an ideal method forsolving this equation.We analyse and compare the traditiona