The Theory Of Non Negative Matrix Factorization And Its Application In The Highspectrual Unmixing

In fact, the hyperspectral remote sensing technology refers to obtain the electromagnetic spectrum band in the use of imaging spectrometer, and its spectral range can be extended by their infrared band to visible light band. The access of these bands are very narrow, but the datas which are included are very rich. They not only contain the spectral information on their own, but also can reflect the space and the surface’s radiometric information indrectly, it solves the difficult problems in the wide-band detection of the remote sensing successfully. Therefore, as a cutting-edge technology in the development of remote sensing and great advantages in the spectral resolution, hyperspectral remote sensing has poured the new vigor into the field of remote sensing and has been applied in more and more scientific researches.The “mixed pixel” refers to an image pixel, obtained by the romote sensing instruments, which is a mixture of substances,because of the fuzzy spatial resolution efficiency and the complex surface material. As its name implies, the mixed pixel’s spectrum is not pure. so, in order to improve the landmark’s identification, we need to obtain the sub-pixel’s spectral information from the remote sensing image, that is to get the corresponding matrixes about the end of the element and the abundance matrix.The method make the remote sensing data quantified, so it will play a far-reaching significance in hyperspectral application.In the field of remote sensing, more and more scholors are trying to explore and seek new ways which are more accurate and more quickly to decompose the mixed pixel in the hyperspectral remote sensing image with an unsupervised case. Among these,the theory and method of non-negative matrix factorization has attracted more and more people’s attention. The non-negative matrix factorization(NMF) method was originally developed by Lee and Seung in the famous Nature, it is a new and big breakthrough in the matrix decomposition and the main principle is to break down a non-negative matrix into two non-negative matrixs with some constraint conditions. Obviously, the decomposition model and mixed pixel decomposition have the same approaches, therefore, if the non-negative matrix factorization can be used in hyperspectral unmixing, it will bring a new revolution in the field of remote sensing, but the non-negative matrix may lead to the local minimum phenomenon in the process of decomposition. So, if we want to make the non-negative matrix factorization applied successfully in the hyperspectral unmixing, we must to improve and innovate the existing algorithms. Think about these problems, the paper make a lot of studies about the application of non-negative matrix factorization in hyperspectral unmixing on the basis of relevant literature and research, which providing a new way for understanding the synthesis and distribution of the space’s mixed pixel. The main research work of this paper:1.On the basis of the standard non negative matrix factorization algorithm, this paper join the volume、complexity and two mixed respectively to the non-negative matrix factorization, which forms the final CMVC-NMF. This method does not need to assume the existance of the pure pixel, but also considers the time prediction and spatial autocorrelation function among the abundance. Let the algorithm apply to the actual operation, we can test its effectiveness.2.The NMF algorithm itself has to meet the non-negative constraints, but the sparisty and smoothness can also be some important additional constraint conditions, so in the original method, we can add a penalty term to the objective function, add sparse or smooth constraint to the decomposition result to pursuit the best solutions. At last, we get the new algorithm, SNMFSC, which is constrained by the sparsity and smooth at the same time.3.Because of the non-convexity of the original NMF algorithm’s objective function, it often leads the decomposition result into a state which just satisfies the local optimal. Therefore, in order to reduce the occurrence of local optimization,we combine the genetic algorithm with the improved constrained non negative matrix factorization algorithm, It comes into being a new algorithm, GA-MCNMF. Through the experimental results, we can improve the operation efficiency and get the accurate result at the same time.