基于组稀疏非负矩阵分解的高光谱图像去噪方法研究

发布时间：2018-10-13 12:31

【摘要】：高光谱遥感图像包含同一空间位置较大数量的连续窄波段图像,是由二维空间信息和一维光谱信息组成的三维数据,在环境监测、地质调查等领域有着广泛的应用。噪声在高光谱图像获取的过程中不可避免地被引入,降低了图像质量并影响着之后图像处理应用的性能。因此,高光谱图像去噪是非常重要的图像预处理工作。最近,基于低秩近似和稀疏表达的高光谱图像去噪方法吸引了很多的关注。在高光谱图像中,全波段图像块(包含同一局部区域不同波段图像的子立方体)中的光谱向量间存在着较大的联系,同时相邻波段间也具有较大的相关性。这样的特点揭示着在纯净全波段图像块中的光谱向量可以被一小部分基元线性表示。非局部相似性,即一个图像块在图像空间范围内存在着与其相似的若干图像块,在高光谱图像中也同样存在。对于高光谱图像中非局部相似的全波段图像块联合进行去噪可以利用图像在空间维的自相似性带来的额外结构信息,有机会带来更好的去噪效果。需要注意的是,非局部相似的全波段图像块由于来自不同的空间位置,它们之间在存在着相似结构的同时也存在着一些差异性。基于这样的考虑,本文提出了一个全新的基于组稀疏非负矩阵分解的高光谱图像去噪方法用于同时反映这样的相似性和差异性。在本文提出的方法中,全波段图像块中的光谱向量假设可以被较小数目的基元线性表示,且表示系数是稀疏的。每个全波段图像块对应分解中的一组,由于组稀疏正则化项的使用,同一个全波段图像块中的光谱向量在重构中共享完全相同的基元子集,体现出高光谱图像中的强局部相关性。同时,不同全波段图像块的光谱向量部分共享一些基元,即每一个全波段图像块在分解中可能持有自己特有的基元,对应高光谱图像中的非局部相似性和差异性。由此,通过组稀疏非负矩阵分解,高光谱图像中共享+特有的结构同时得以体现。本文首先建立高光谱图像噪声模型,包括高斯噪声模型和泊松高斯混合噪声模型。对于泊松高斯混合噪声的情况,使用方差稳定化变换将其转换为高斯噪声的近似。然后,基于对高光谱结构特性的分析,给出基于组稀疏非负矩阵分解的高光谱图像去噪方法的思想和详细过程。对于模型优化,本文给出了三种优化算法的理论推导和优化步骤,并通过实验对算法的运行效率进行对比。最后,通过在高光谱数据集上的仿真实验和真实实验,把本文提出的去噪方法与相关方法进行对比,验证了本文提出方法的有效性。
[Abstract]:Hyperspectral remote sensing images contain a large number of continuous narrow band images in the same spatial position. They are three-dimensional data composed of two-dimensional spatial information and one-dimensional spectral information. They are widely used in environmental monitoring geological survey and other fields. Noise is inevitably introduced in the process of hyperspectral image acquisition, which reduces the image quality and affects the performance of subsequent image processing applications. Therefore, hyperspectral image denoising is a very important work of image preprocessing. Recently, hyperspectral image denoising based on low rank approximation and sparse representation has attracted much attention. In hyperspectral images, the spectral vectors in the whole band image blocks (including sub-cubes of different waveband images in the same local region) are closely related, and there is also a great correlation between adjacent bands. This feature reveals that spectral vectors in a pure full band image block can be linearly represented by a small number of primitives. Non-local similarity, that is, there are several image blocks similar to them in the image space, and the same exists in hyperspectral images. For hyperspectral images with non-locally similar full-band image blocks de-noising can take advantage of the spatial dimension of the image self-similarity to bring additional structural information which has the opportunity to bring better denoising effect. It is important to note that there are some differences between the non-local similar full-band image blocks due to their different spatial positions. Based on this consideration, a novel hyperspectral image denoising method based on group sparse nonnegative matrix decomposition is proposed to reflect the similarity and difference simultaneously. In the proposed method, the spectral vectors in a full-band image block are assumed to be linearly represented by a small number of primitives, and the representation coefficients are sparse. Each full band image block corresponds to a set of decomposed images. Due to the use of sparse regularization terms, the spectral vectors in the same full band image block share exactly the same fundamental subsets in the reconstruction. It reflects the strong local correlation in hyperspectral images. At the same time, the spectral vectors of different full band image blocks share some elements, that is, each full band image block may hold its own unique elements in decomposition, corresponding to the non-local similarity and difference in hyperspectral images. Therefore, by sparse nonnegative matrix decomposition, the shared unique structure in hyperspectral images can be realized simultaneously. In this paper, the noise models of hyperspectral images are established, including Gao Si noise model and Poisson Gao Si mixed noise model. In the case of Poisson Gao Si mixed noise, the variance stabilization transformation is used to transform it into an approximation of Gao Si noise. Then, based on the analysis of the characteristics of hyperspectral structure, the idea and detailed process of hyperspectral image denoising method based on sparse nonnegative matrix decomposition are presented. For model optimization, the theoretical derivation and optimization steps of three optimization algorithms are given, and the efficiency of the algorithm is compared through experiments. Finally, the effectiveness of the proposed method is verified by comparing the proposed denoising method with the related methods through the simulation and real experiments on the hyperspectral data set.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP751

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