本文關鍵詞：非線性不光滑問題的鄰近修正Landweber迭代法研究　出處：《大連海事大學》2017年碩士論文　論文類型：學位論文

  更多相關文章： 非線性不光滑問題 鄰近修正Landweber迭代法 參數識別

【摘要】：本文主要研究了關于非線性不光滑問題的鄰近修正Landweber迭代法。在許多實際應用中都會涉及到反問題,反問題最大的特點就是不適定性。由于反問題的不適定性,所以需要用正則化方法來得到真實解的穩(wěn)定近似解。在大規(guī)模非線性反問題中,通常采用迭代正則化方法,我們采用的迭代正則化方法是修正Landweber迭代法。然而,L~2范數罰函數可能會引起解過度光滑,解的過度光滑會導致與實際情況出現(xiàn)較大的偏差,為了克服這一困難,我們引入了稀疏正則化方法,增加一項L~1范數罰項,但是,這樣會導致不光滑的情況。為了解決這一問題,我們引入了鄰近算子,將鄰近算子與修正Landweber迭代法相結合,用于解決非線性不光滑反問題。本文首先對鄰近算子和修正Landweber迭代法的定義及其相關性質進行了回顧。在此基礎上,將鄰近算子與修正Landweber迭代法相結合,得到了最終的鄰近修正Landweber迭代法。經過分析,我們證明了該算法的收斂性,并得到了相應的收斂率。最后,用該算法求解了參數識別問題,進行了一維、二維數值實驗,驗證了算法的有效性。理論分析和數值實驗的結果表明:鄰近修正Landweber迭代法可以有效地解決非線性不光滑參數識別問題。
[Abstract]:In this paper, the neighborhood modified Landweber iterative method for nonlinear nonsmooth problems is studied. The inverse problem is involved in many practical applications. The biggest characteristic of inverse problem is ill-posed. Due to the ill-posed of inverse problem, we need to use regularization method to obtain the stable approximate solution of real solution. In large-scale nonlinear inverse problem. The iterative regularization method is usually used, and the modified Landweber iterative method is used. However, the penalty function of Ln 2 norm may cause the solution to be excessively smooth. In order to overcome this difficulty, we introduce a sparse regularization method to add a penalty term of L ~ (1) norm, but in order to overcome the problem, the excessive smoothness of the solution will lead to a large deviation from the actual situation. In order to solve this problem, we introduce the adjacent operator and combine the adjacent operator with the modified Landweber iterative method. In this paper, the definitions of adjacent operators and modified Landweber iterative methods and their related properties are reviewed. By combining the adjacent operator with the modified Landweber iterative method, the final neighborhood modified Landweber iterative method is obtained. After analysis, we prove the convergence of the algorithm. The corresponding convergence rate is obtained. Finally, the algorithm is used to solve the parameter identification problem, and the one-dimensional and two-dimensional numerical experiments are carried out. The results of theoretical analysis and numerical experiments show that the neighborhood modified Landweber iteration method can effectively solve the problem of nonlinear nonsmooth parameter identification.
【學位授予單位】：大連海事大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O241.6

【參考文獻】

相關期刊論文 前5條

1 楊真真;楊震;李雷;;語音重構的DCT域加速Landweber迭代硬閾值算法[J];信號處理;2012年02期

2 柳建軍;賀國強;康傳剛;;Nonlinear implicit iterative method for solving nonlinear ill-posed problems[J];Applied Mathematics and Mechanics(English Edition);2009年09期

3 呂小紅;吳傳生;;圖像恢復的一種快速迭代正則化方法[J];數學雜志;2009年04期

4 陳至坤;趙波;王鴻雁;;基于正則化的LANDWEBER電容層析成像圖像重建算法研究[J];電子測量技術;2007年10期

5 劉力,吳曉鋒,印胤;正電子斷層掃描儀與PET圖像重建概述[J];CT理論與應用研究;2003年01期

，

本文編號：1364441