本文關(guān)鍵詞： 遙感 端元提取 單形體體積增長算法 分塊矩陣 Cholesky分解　出處：《浙江大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：高光譜遙感數(shù)據(jù)以其波段多、光譜分辨率高、數(shù)據(jù)量大等特點(diǎn)而成為當(dāng)前遙感領(lǐng)域的前沿技術(shù),在各個(gè)領(lǐng)域發(fā)揮著越來越大的作用。但是由于地面物質(zhì)類型的復(fù)雜性以及成像系統(tǒng)空間分辨率的限制,高光譜圖像中普遍存在混合像元,因此光譜解混是遙感領(lǐng)域的重要研究方向。而端元提取作為光譜解混的關(guān)鍵步驟,如何有效而快速地進(jìn)行端元提取是高光譜遙感圖像處理的研究重點(diǎn)之一。本論文主要針對端元提取算法中比較常用的基于線性光譜混合模型的新的單形體體積增長算法NSGA中存在的主要問題進(jìn)行了一系列的改進(jìn),不僅將其擴(kuò)展至適用于非線性光譜混合模型,而且提出了兩種思路來解決其高計(jì)算復(fù)雜度的問題。 論文的主要工作如下： (1)針對NSGA只適用于線性光譜混合模型而無法應(yīng)用于非線性光譜混合模型的問題,本文利用核函數(shù)的方法實(shí)現(xiàn)該算法的非線性擴(kuò)展,提出適用于非線性光譜混合模型的算法KNSGA. (2)針對基于線性模型的NSGA和非線性模型的KNSGA兩算法中由重復(fù)體積計(jì)算而造成的高計(jì)算復(fù)雜度的問題,利用分塊矩陣的性質(zhì)提出了兩種快速實(shí)現(xiàn)算法FNSGA和FKNSGA.兩種快速算法主要通過利用分塊矩陣的性質(zhì),來簡化單形體體積公式行列式求解過程,從而減小時(shí)間及運(yùn)算復(fù)雜度,達(dá)到簡化算法,縮短算法運(yùn)行時(shí)間的目的。 (3)針對(2)中提到的NSGA和KNSGA中存在的高計(jì)算復(fù)雜度問題,利用改進(jìn)的Cholesky分解的方法提出了兩種相應(yīng)的快速實(shí)現(xiàn)算法FNSGACF和FKNSGACF。兩種快速算法主要利用改進(jìn)Cholesky分解方法,將求解最大單形體體積的計(jì)算轉(zhuǎn)化為尋找矩陣對角元素最大的過程,從而避免直接的體積計(jì)算,降低了計(jì)算復(fù)雜度,達(dá)到快速實(shí)現(xiàn)的目的。 在上述改進(jìn)思路的基礎(chǔ)上,本文采用仿真數(shù)據(jù)實(shí)驗(yàn)和真實(shí)高光譜圖像實(shí)驗(yàn)兩部分實(shí)驗(yàn)來對本文提出的改進(jìn)算法進(jìn)行實(shí)驗(yàn)驗(yàn)證,實(shí)驗(yàn)結(jié)果表明擴(kuò)展算法KNSGA能夠準(zhǔn)確有效地提取端元,并且四種快速算法也能在準(zhǔn)確提取端元的前提下縮短運(yùn)行時(shí)間,達(dá)到快速實(shí)現(xiàn)的目的。
[Abstract]:Hyperspectral remote sensing data has become the frontier technology in the field of remote sensing because of its many bands, high spectral resolution and large amount of data. However, due to the complexity of the type of material on the ground and the limitation of spatial resolution of imaging system, mixed pixels are widely used in hyperspectral images. Therefore, spectral demultiplexing is an important research direction in remote sensing field. End-element extraction is the key step of spectral unmixing. It is one of the key points in hyperspectral remote sensing image processing how to extract endcomponents efficiently and quickly. This paper mainly focuses on the new volume increase of single body based on linear spectral mixed model which is commonly used in End-component extraction algorithm. The main problems in the long algorithm NSGA are improved. It is not only extended to the nonlinear spectral mixing model, but also two ideas are proposed to solve the problem of high computational complexity. The main work of the thesis is as follows:. 1) aiming at the problem that NSGA can only be used in linear spectral mixing model but not in nonlinear spectral mixing model, the kernel function method is used to realize the nonlinear expansion of the algorithm, and a new algorithm, KNSGA, which is suitable for nonlinear spectral mixing model, is proposed in this paper. In order to solve the problem of high computational complexity caused by repeated volume calculation in NSGA algorithm based on linear model and KNSGA algorithm based on nonlinear model, Two fast algorithms, FNSGA and FKNSGA, are proposed by using the properties of block matrix. By using the properties of block matrix, the process of solving determinant of volume formula of single body is simplified, and the time and computational complexity are reduced. The purpose of simplifying the algorithm and shortening the running time of the algorithm is achieved. In order to solve the problem of high computational complexity in NSGA and KNSGA, two corresponding fast implementation algorithms, FNSGACF and FKNSGA CFS, are proposed by using the improved Cholesky decomposition method. The two fast algorithms mainly use the improved Cholesky decomposition method. The calculation of the maximum volume of a single body is transformed into the process of finding the largest diagonal element of the matrix, thus avoiding the direct volume calculation, reducing the computational complexity and achieving the goal of fast realization. On the basis of the above improved ideas, this paper uses two experiments, simulation data experiment and real hyperspectral image experiment, to verify the improved algorithm proposed in this paper. The experimental results show that the extended algorithm KNSGA can extract endelements accurately and effectively, and the four fast algorithms can shorten the running time and achieve the purpose of fast implementation.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TP751

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