本文選題：高光譜圖像　切入點(diǎn)：松弛變量　出處：《大連海事大學(xué)》2017年碩士論文

【摘要】：高光譜遙感技術(shù)提供一種光譜解混的方法來(lái)分析混合像元中組成成分以及所占的比例。比較經(jīng)典的算法是最小二乘算法,但該算法對(duì)豐度值沒(méi)有任何約束,這是不符合實(shí)際物理意義的。全約束豐度估計(jì)算法同時(shí)滿(mǎn)足非負(fù)性和和為一約束,具有實(shí)際物理意義。由于全約束豐度估計(jì)物理意義合理,近幾年被廣泛用于光譜解混算法中,但是端元數(shù)目過(guò)大時(shí),該算法的工作效率降低,且當(dāng)提取的端元數(shù)量不完全以及端元不理想時(shí),解混誤差也會(huì)變大。在提高算法的效率方面,已有部分改進(jìn)工作,但是在提高解混精度方面的研究相對(duì)較少。本文基于傳統(tǒng)的原始-對(duì)偶內(nèi)點(diǎn)算法,考慮地物的豐度統(tǒng)計(jì)特征以及高光譜圖像成像復(fù)雜、普遍存在噪聲的特點(diǎn),提出了兩種新的對(duì)目標(biāo)函數(shù)進(jìn)行約束的原始-對(duì)偶內(nèi)點(diǎn)算法。首先,本文在傳統(tǒng)原始-對(duì)偶內(nèi)點(diǎn)算法上進(jìn)行改進(jìn),通過(guò)改進(jìn)選擇步長(zhǎng)參數(shù)來(lái)使迭代出的點(diǎn)位于原始-對(duì)偶中心路徑上,而不是通過(guò)路徑跟蹤法去計(jì)算中心路徑。另外,在進(jìn)行移動(dòng)方向計(jì)算前,需要進(jìn)行對(duì)偶間隙中參數(shù)的估計(jì),這樣可以保證原問(wèn)題和對(duì)偶問(wèn)題均趨于最優(yōu)解。其次,因?yàn)楦吖庾V圖像存在空間分辨率低、噪聲普遍、地物復(fù)雜、端元數(shù)量未知、可能不存在純端元等問(wèn)題,使豐度和為一約束不再滿(mǎn)足。因此,本文通過(guò)加入松弛變量,來(lái)控制豐度和為一約束性。提出了結(jié)合松弛變量和改進(jìn)選擇步長(zhǎng)參數(shù)的原始-對(duì)偶內(nèi)點(diǎn)算法,即松弛原始-對(duì)偶內(nèi)點(diǎn)算法。基于以上理論的研究,論文完成了對(duì)上述算法的理論和優(yōu)化過(guò)程推導(dǎo),分別在模擬高光譜圖像和真實(shí)高光譜上對(duì)提出的算法進(jìn)行實(shí)驗(yàn),驗(yàn)證了所推出的算法在豐度估計(jì)準(zhǔn)確度和重構(gòu)誤差上都得到了較原算法更好的精度,且在端元個(gè)數(shù)未知且端元不理想時(shí),依然能夠獲得穩(wěn)定的解混結(jié)果。
[Abstract]:Hyperspectral remote sensing provides a spectral demultiplexing method to analyze the composition and proportion of the mixed pixel.The classical algorithm is the least square algorithm, but the algorithm has no restriction on the abundance value, which is not in line with the actual physical meaning.The full constraint abundance estimation algorithm satisfies the sum of nonnegative sum and is a constraint, which is of practical physical significance.Due to the reasonable physical meaning of the fully constrained abundance estimation, it has been widely used in the spectral demultiplexing algorithm in recent years. However, when the number of endmembers is too large, the efficiency of the algorithm is reduced, and when the number of the extracted endmembers is incomplete and the endmembers are not ideal,The unmixing error also increases.In the aspect of improving the efficiency of the algorithm, some improvements have been done, but the research on improving the resolution of the algorithm is relatively few.Based on the traditional primal-dual interior point algorithm and considering the statistical feature of the abundance of the ground object and the complexity of hyperspectral image imaging and the ubiquitous noise, two new primal-dual interior point algorithms are proposed to constrain the objective function.Firstly, this paper improves the traditional primal-dual interior point algorithm. By improving the step size parameter, the iterative point is located on the primal-dual center path, rather than the path tracking method to calculate the central path.In addition, it is necessary to estimate the parameters in the duality gap before calculating the moving direction, which can ensure that both the original problem and the dual problem tend to the optimal solution.Secondly, because of the problems of low spatial resolution, universal noise, complex objects and unknown number of endmembers in hyperspectral images, there may be no pure endpoints, so that the sum of abundance is no longer satisfied with a constraint.Therefore, the abundance sum is controlled by the addition of relaxation variables.A primal-dual interior point algorithm, a relaxation primal-dual interior point algorithm, is proposed, which combines relaxation variables with improved selection of step size parameters.Based on the above theoretical research, this paper has completed the theoretical and optimization process derivation of the above algorithm, respectively in the simulation of hyperspectral images and real hyperspectral experiments on the proposed algorithm.It is verified that the proposed algorithm has better accuracy than the original algorithm in terms of accuracy of abundance estimation and reconstruction error, and can still obtain stable unmixing results when the number of endmembers is unknown and the endmembers are not ideal.
【學(xué)位授予單位】：大連海事大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：TP751

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