基于广义交叉验证的正则参数选择在非凸非Lipschitzian图像恢复模型中的应用

发布时间：2018-04-15 09:39

本文选题：非凸非Lipschitzian + 病态问题　；参考：《北京交通大学》2017年硕士论文

【摘要】：病态问题的研究在优化理论、算法和应用中都占据非常重要的地位.许多应用都涉及到病态问题的参数估计问题,例如:图像恢复问题.目前已有多种估计正则参数的方法,常用的有L曲线法、交叉验证法和广义交叉验证法等.本论文主要研究基于广义交叉验证的正则参数估计方法在非凸非Lipschitzian图像恢复模型中的应用.我们采用非凸非Lipschitzian的Lp(0p1)正则项,从而有助于恢复清晰的轮廓.本文主要使用交替极小化算法框架、光滑最速下降算法及一维黄金分割搜索等来同时实现正则参数的调整及图像恢复.比较不同噪音水平下的图像恢复效果发现基于广义交叉验证来选择正则参数的非凸非Lipschitzian图像恢复模型能够得到比采用LTV、L1正则项的图像恢复模型均大的信噪比结果.
[Abstract]:The study of ill-posed problem plays an important role in optimization theory, algorithm and application.Many applications involve parameter estimation in ill-posed problems, such as image restoration.At present, there are many methods to estimate regular parameters, such as L curve method, cross validation method and generalized cross validation method.This paper mainly studies the application of regular parameter estimation method based on generalized cross validation in non-convex non- image restoration model.We use the non-convex non- LpP0p1) canonical term, which helps to restore the clear contour.This paper mainly uses the framework of alternating minimization algorithm, the smoothest descent algorithm and the one-dimensional golden section search to realize the regularization parameter adjustment and image restoration simultaneously.Comparing the effect of image restoration with different noise levels, it is found that the non-convex non- image restoration model based on generalized cross-validation can obtain more SNR results than the image restoration model with LTV-L1 canonical term.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O224

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