High-spectrum image demixing method based on end-member constraint non-negative matrix decomposition
A non-negative matrix decomposition, hyperspectral image technology, applied in image enhancement, image analysis, image data processing and other directions, can solve the problem of local minimum, affecting the acquisition of optimal solution, etc., to slow down mutation and improve unmixing. The effect of precision
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specific Embodiment approach 1
[0019] The hyperspectral image unmixing method based on endmember constrained non-negative matrix decomposition of this embodiment, combined with figure 1 As shown, the method is realized through the following steps:
[0020] Step 1. Set the pixel spectral vector X, the endmember spectral matrix S, the abundance matrix A of the N-dimensional vector, and the random noise N to establish a linear spectral mixing model:
[0021] X=SA+N(1)
[0022] Wherein, the endmembers refer to various substances contained in the pixels of the hyperspectral image presented by the spectral imager, and these pixels containing the endmembers are called mixed pixels;
[0023] Step 2, using the sum of the absolute values of the pairwise correlation coefficients between the spectra as a correlation function to measure the size of the endmember spectral correlation;
[0024] Step 3, adding the endmember spectrum difference constraint introduced by the natural logarithm function, so that the differe...
specific Embodiment approach 2
[0026] The difference from Embodiment 1 is that in the hyperspectral image unmixing method based on endmember-constrained non-negative matrix decomposition in this embodiment, in the linear spectral mixing model X=SA+N described in step 1, the endmember spectral matrix S= [s 1 ,s 2 ,...,s N ], the element s in the endmember spectral matrix S i Represents the endmember vector, i∈[1,N]; the abundance matrix A of N-dimensional vector=[a 1 ,a 2 ,...,a N ] T , each component element in the abundance matrix A of the N-dimensional vector represents the abundance of the corresponding end member, and
[0027] a i ≥0(2)
[0028] Σ i = 1 N a i = 1 , i ∈ [ 1 , N ] - - - ( 3 ) ...
specific Embodiment approach 3
[0030] The difference from the specific embodiment 1 or 2 is that in the hyperspectral image unmixing method based on endmember constrained non-negative matrix decomposition in this embodiment, as described in step 2, the sum of the absolute values of the pairwise correlation coefficients between the spectra is used as the correlation The process of measuring the magnitude of the endmember spectral correlation is,
[0031] Step 21. Perform non-negative matrix decomposition based on endmember constraints:
[0032] Using the NMF algorithm, by minimizing the Euclidean distance objective function, the optimal solution of S and A is obtained when X is known.
[0033] f ( S , A ) = 1 2 | | X - S A | | 2 - - - ...
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