A mixed pixel may contain a variety of ground objects, so determining the number of endmembers is the premise of spectral linear decomposition and an essential link in the whole spectral linear unmixing technology. The common method of multispectral data is to determine the number of endmembers according to the covariance of principal component analysis, but its analysis method is rough. For hyperspectral remote sensing images with hundreds of narrow bands, PCA can easily classify subtle spectral information into noise parts (Chang C, 2007). Therefore, the common method to determine the number of endmembers in hyperspectral remote sensing images is characteristic threshold analysis based on Neyman-Pearson detection theory (Harsanyi et al., 1994), which is abbreviated as HFC(Harsanyi, Farrand, Chang). This chapter also uses this method to determine the number of endmembers.
The principle of HFC is to get the correlation matrix Rm×n and covariance matrix Km×n and their eigenvalues by calculating the correlation matrix of the image, and record the eigenvalues as.
If the signal energy of the image is positive, it exists.
Information extraction technology of hyperspectral remote sensing image
Where: n is the number of endmembers; M is the number of bands of hyperspectral images.
Even if principal component analysis is not used, some weak signals will inevitably be excluded as noise signals. Therefore, in order to minimize this phenomenon, it is best to whiten before calculating the number of endmembers (Gruninger et al., 2004).
3. 1.3.2 Endmember Extraction
At present, people have deeply studied the methods of endmember extraction from hyperspectral images, and researchers have put forward many practical extraction methods from different angles. Among them, pure pixel index (PPI), internal maximum volume method (N-FindR), vertex component analysis (VCA), simplex projection method (SPM), sequential maximum convex cone (SMACC), iterative error analysis (IEA), wrapped simplex contraction (SSWA), minimum volume simplex analysis (MVSA) and convex cone analysis (MVSA) are commonly used. Automatic morphology (AMEE), maximum distance method (MaxD), maximum volume method (MaxV), maximum zero-space projection distance method (NSP), quantitative independent component analysis (ICA), etc. (Zhang Bing et al, 20 1 1). In this chapter, the method of endmember extraction is SMACC, which provides a faster and more automatic method to obtain endmember spectrum, but its results are high in approximation and low in accuracy. Because the purpose of this chapter is an improved linear decomposition method, rather than focusing on the study of endmember selection, SMACC is not the best algorithm, but it can achieve the purpose of this chapter's experiment.
SMACC algorithm (Gruninger et al., 2004) can get the results of abundance inversion while extracting endmembers. Its basic principle is to obtain endmembers through iteration. After many iterations, the proportion of each end member in the mixed pixel is continuously calculated and adjusted, and the interaction between the end members is eliminated by projection transformation. Among them, the most critical step is to judge whether there are endmembers in the pixel and whether oblique projection (or orthogonal projection) is needed. The specific algorithm is as follows:
Let the original pixel set be expressed as, the pixel set before the j-th iteration is, the endmember set before the j-th iteration is, wj is the projection direction of each iteration, and XJ- 1 is the longest spectral vector, then the projection coefficient of XJ- 1 in the wj direction is
Information extraction technology of hyperspectral remote sensing image
The ej proportional coefficient of xi is
Information extraction technology of hyperspectral remote sensing image
Where: βij is the adjustment coefficient; When β ij = 1, it is an orthogonal projection; Otherwise it is oblique projection. After many iterations, the proportional coefficient of Xi EJ can be finally obtained.
The projection result of the pixel is
Information extraction technology of hyperspectral remote sensing image
Among them, the principle of adjusting the coefficient βij is: when Oij≤0, β ij = 0, that is, there is no such end member; Otherwise, according to
Information extraction technology of hyperspectral remote sensing image
The minimum value is obtained by calculating vk and recorded as vmin. When vmin > 1, β ij = 1, which is an orthographic projection; Otherwise it is oblique projection, β ij = vmin.
3. 1.3.3 Extraction and classification of mixed pixel feature information
By decomposing the matrix constructed by the spectral curves of mixed pixels, the abundance value fj (j = 1, 2, ... n), but the classification of hyperspectral images or the extraction of ground object information are all divided by pixels, that is to say, it is impossible to paint a pixel with different colors in classification or ground object extraction. Therefore, in order to facilitate classification,