结合松弛变量的全约束丰度估计算法研究

发布时间：2018-04-04 07:03

本文选题：高光谱图像　切入点：松弛变量　出处：《大连海事大学》2017年硕士论文

【摘要】：高光谱遥感技术提供一种光谱解混的方法来分析混合像元中组成成分以及所占的比例。比较经典的算法是最小二乘算法,但该算法对丰度值没有任何约束,这是不符合实际物理意义的。全约束丰度估计算法同时满足非负性和和为一约束,具有实际物理意义。由于全约束丰度估计物理意义合理,近几年被广泛用于光谱解混算法中,但是端元数目过大时,该算法的工作效率降低,且当提取的端元数量不完全以及端元不理想时,解混误差也会变大。在提高算法的效率方面,已有部分改进工作,但是在提高解混精度方面的研究相对较少。本文基于传统的原始-对偶内点算法,考虑地物的丰度统计特征以及高光谱图像成像复杂、普遍存在噪声的特点,提出了两种新的对目标函数进行约束的原始-对偶内点算法。首先,本文在传统原始-对偶内点算法上进行改进,通过改进选择步长参数来使迭代出的点位于原始-对偶中心路径上,而不是通过路径跟踪法去计算中心路径。另外,在进行移动方向计算前,需要进行对偶间隙中参数的估计,这样可以保证原问题和对偶问题均趋于最优解。其次,因为高光谱图像存在空间分辨率低、噪声普遍、地物复杂、端元数量未知、可能不存在纯端元等问题,使丰度和为一约束不再满足。因此,本文通过加入松弛变量,来控制丰度和为一约束性。提出了结合松弛变量和改进选择步长参数的原始-对偶内点算法,即松弛原始-对偶内点算法。基于以上理论的研究,论文完成了对上述算法的理论和优化过程推导,分别在模拟高光谱图像和真实高光谱上对提出的算法进行实验,验证了所推出的算法在丰度估计准确度和重构误差上都得到了较原算法更好的精度,且在端元个数未知且端元不理想时,依然能够获得稳定的解混结果。
[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.
【学位授予单位】：大连海事大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP751

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