發(fā)布時(shí)間：2018-04-11 01:16

  本文選題：數(shù)字圖像處理 + 全變分��； 參考：《昆明理工大學(xué)》2017年碩士論文

【摘要】：在數(shù)字圖像去噪處理中,基于變分法的思想是根據(jù)泛函知識進(jìn)行排除圖像噪聲的慣用思想。由此思想發(fā)展的方法中最典型的模型是全變分(Total Variation:TV)模型,它的最大優(yōu)點(diǎn)在于去除圖像噪聲的同時(shí)保持圖像的周圍邊界。但由于TV模型的正則項(xiàng)是不可微項(xiàng)的,導(dǎo)致整個(gè)模型是不可微優(yōu)化(非光滑優(yōu)化)的,傳統(tǒng)的基于微分定義的優(yōu)化方法不再適用。推廣經(jīng)典的微分定義,建立廣義微分定義和對應(yīng)的優(yōu)化理論和算法就成為非光滑優(yōu)化的研究重點(diǎn)。研究者們在鉆研過程中提出了半光滑牛頓法,之后迅速成為非光滑優(yōu)化方法中熱門的研究方向之一。本文繼續(xù)發(fā)展半光滑牛頓法消除噪聲,恢復(fù)圖像,提高圖像的質(zhì)量和視覺效果,以TV模型為數(shù)學(xué)模型,以一維信號問題、二維逆源問題、二維圖像問題為研究對象,研究數(shù)值優(yōu)化算法。本文開展的主要工作有:(1)綜述了數(shù)字圖像處理理論中的一些去噪基礎(chǔ)知識,概述了近年來國內(nèi)外關(guān)于圖像去噪的研究現(xiàn)狀及圖像去噪在工程等應(yīng)用中的實(shí)際意義。(2)敘述了最優(yōu)化的基本理論和全變分模型,根據(jù)優(yōu)化理論將其轉(zhuǎn)變?yōu)樽顑?yōu)化問題。闡述目前廣泛用于求解TV問題的原對偶算法和交替迭代法。(3)介紹了帶約束條件的最小二乘問題,將有約束條件的優(yōu)化問題通過投影轉(zhuǎn)化為沒有約束條件的優(yōu)化問題的整個(gè)過程,并提出了基于投影的梯度下降法。(4)研究了非線性非光滑方程組和半光滑牛頓法的相關(guān)定義,提出一種新算法:結(jié)合定點(diǎn)迭代法的半光滑牛頓法,并敘述它的局部超線性收斂性。(5)將論文中描述過的算法在Matlab中寫出對應(yīng)代碼做數(shù)值模擬實(shí)驗(yàn),通過對實(shí)驗(yàn)現(xiàn)象和結(jié)果作對比分析得出實(shí)驗(yàn)結(jié)論:在同級噪聲和相同參數(shù)的情況下,所提新算法優(yōu)于其他三種算法。
[Abstract]:In digital image denoising, the idea based on variational method is to eliminate image noise according to functional knowledge.The most typical model developed from this idea is the Total variation: (TTV) model, which has the greatest advantage of removing image noise while preserving the peripheral boundaries of the image.However, because the regular term of TV model is non-differentiable, the whole model is non-differentiable (non-smooth optimization), so the traditional optimization method based on differential definition is no longer applicable.Generalizing the classical differential definition and establishing the generalized differential definition and corresponding optimization theory and algorithm becomes the research focus of non-smooth optimization.Researchers put forward semi-smooth Newton method in the process of research, and then became one of the hot research directions in non-smooth optimization methods.In this paper, we continue to develop a semi-smooth Newton method to eliminate noise, restore images, improve image quality and visual effect, take TV model as mathematical model, take one-dimensional signal problem, two-dimensional inverse source problem and two-dimensional image problem as research object.Numerical optimization algorithm is studied.The main work carried out in this paper is to summarize some basic knowledge of denoising in the theory of digital image processing.The research status of image denoising at home and abroad in recent years and the practical significance of image denoising in engineering and other applications are summarized. The basic theory of optimization and total variational model are described. According to the optimization theory, the optimization problem is transformed into an optimization problem.In this paper, the primal dual algorithm and alternating iteration method, which are widely used to solve TV problem at present, are introduced. The constrained least squares problem is introduced. The whole process of transforming the constrained optimization problem into an optimization problem without constraints by projection is introduced.A gradient descent method based on projection is proposed. (4) the definitions of nonlinear nonsmooth equations and semi-smooth Newton method are studied, and a new algorithm is proposed: a semi-smooth Newton method based on fixed-point iterative method.Its local superlinear convergence. 5) the algorithm described in this paper is written out in Matlab for numerical simulation.The experimental results show that the proposed algorithm is superior to the other three algorithms in the case of the same level noise and the same parameters.
【學(xué)位授予單位】：昆明理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP391.41

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本文編號：1733784