Wavelet domain NMF image unmixing method based on adaptive local neighborhood constraints

Abstract

The present invention provides a wavelet domain NMF image unmixing method based on adaptive local neighborhood constraints, including: performing biorthogonal wavelet packet transform on a hyperspectral data matrix and an end-member data matrix respectively; obtaining the coefficient matrix at each node of a wavelet packet tree corresponding to the end-member data matrix, and finding the node with the lowest condition number; using the correlation matrix data corresponding to the node with the lowest condition number as an input of an NMF model based on adaptive local neighborhood weighted constraints, iteratively updating the abundance matrix and the end-member matrix until the model converges, and outputting the iteratively updated abundance matrix and the end-member matrix when converged; and reconstructing the end-members using the wavelet packet tree nodes at the lowest level of the condition number. The ill-conditioned matrix problem that occurs during the unmixing process is overcome, and the unmixing precision effect is further improved.

Description

Technical Field

[0001] The present invention relates to the technical field of hyperspectral unmixing, and in particular to a wavelet domain NMF image unmixing method based on adaptive local neighborhood constraints. Background Art

[0002] In recent years, hyperspectral remote sensing imaging technology has gradually become a hot topic among scholars. The processing and analysis of hyperspectral remote sensing images is still an important bottleneck restricting the application of hyperspectral remote sensing, and the research on hyperspectral remote sensing image unmixing is a new data processing problem accompanying the development of hyperspectral imaging technology and is one of the important tasks of hyperspectral data processing.

[0003] Due to the limitation of spatial resolution of hyperspectral remote sensing image information and the influence of complex objects, a large number of mixed pixels appear in the image, that is, one pixel contains the spectral information of several objects at the same time. If a pixel contains only one object, the pixel is called an endmember. Hyperspectral unmixing mainly includes endmember extraction and abundance estimation, that is, determining the types of objects that make up the mixed pixels and determining the proportion of each type.

[0004] The existing method of abundance estimation of hyperspectral remote sensing images mainly adopts the fully constrained least squares method. However, when this method processes noisy data, the error of abundance estimation is large and the accuracy of unmixing will be reduced. Alternatively, the non-negative matrix factorization (NMF) method can be used. In order to prevent the NMF algorithm from falling into the local optimal solution, scholars have proposed various constraints for NMF. Among them, the local neighborhood constraint using spatial information has achieved good unmixing effect in recent years. However, this algorithm is performed in the time domain, but due to the existence of ill-conditioned matrix problems, the accuracy of its unmixing is often affected. Summary of the invention

[0005] The present invention provides a wavelet domain NMF image unmixing method based on adaptive local neighborhood constraints, which is used to solve the problem of low unmixing accuracy caused by an ill-conditioned matrix introduced by the existing NMF constraints in the time domain.

[0006] The present invention provides a wavelet domain NMF image unmixing method based on adaptive local neighborhood constraints, comprising:

[0007] Step 1: Acquire hyperspectral remote sensing images;

[0008] Step 2: Obtain the hyperspectral data matrix X, endmember matrix A and abundance matrix S;

[0009] Step 3: Perform d-layer biorthogonal wavelet packet transform on the hyperspectral data matrix and the end metadata matrix respectively, and obtain the wavelet packet tree corresponding to the hyperspectral data matrix and the wavelet packet tree corresponding to the end metadata matrix respectively;

[0010] Step 4: Obtain the coefficient matrix at each node of the wavelet packet tree corresponding to the end metadata matrix, calculate the condition number of each coefficient matrix, and find the node with the lowest condition number, which is recorded as min Cond;

[0011] Step 5: using the coefficient matrix of the hyperspectral data matrix corresponding to the node min Cond of the minimum condition number, the coefficient matrix of the endmember data matrix corresponding to the node, and the abundance matrix as inputs to the NMF model based on adaptive local neighborhood weighted constraints, iteratively updating the abundance matrix and the endmember matrix until the model converges, and outputting the iteratively updated abundance matrix and endmember matrix when converged;

[0012] Step 6: taking the coefficient matrices of other nodes in the same layer as the minCond node and the iteratively updated endmember matrix as inputs of the reconstruction function, and outputting the reconstructed endmember matrix;

[0013] In step 5, the NMF model based on adaptive local neighborhood weighted constraints is:

[0014]

[0015]

[0016] Where λ is an adjustable parameter to balance the approximation error and the constraint term, w ij For a given pixel x i The local neighborhood pixel x j For pixel x i The contribution of weight, x i represents the i-th column of the hyperspectral data matrix, x j represents the jth column of the hyperspectral data matrix, and N(i) represents a fixed pixel x i The column set of local neighborhood pixels, j∈N(i); s i The i-th column of the abundance matrix S, s j The jth column of the abundance matrix S is represented by , P is the number of end members, and N is the total number of pixels;

[0017] In step 5, the abundance matrix S and the end member matrix A are iteratively updated.

[0018] A←A·*(XS T ). / (ASS T )

[0019]

[0020] Where ·* represents the multiplication of corresponding matrix elements, . / represents the division of corresponding matrix elements, and the matrix χi Represents x i The sum of the local neighborhood weights, S w The i-th column of X f and A f are the augmented matrices of X and A respectively.

[0021] Compared with the prior art, the beneficial effects of the present invention are:

[0022] An adaptive local neighborhood constrained NMF model is proposed. According to the characteristics of the abundance matrix, the local neighborhood of a given pixel can be adaptively determined. The calculated weight fully utilizes the spatial information of the given pixel and the pixels in the neighborhood, making the unmixing accuracy higher.

[0023] Furthermore, unlike the traditional time-domain NMF unmixing image method, the adaptive local neighborhood constraint NMF model is combined with the biorthogonal wavelet packet transform to obtain a wavelet domain NMF image unmixing method based on adaptive local neighborhood constraint. The biorthogonal wavelet is used as the wavelet basis to represent the data. The characteristics of the wavelet basis linear phase and shorter support set can better compress the data and reduce the influence of noise on the unmixing results, further overcoming the ill-conditioned matrix problem that occurs in the unmixing process and further improving the unmixing accuracy effect;

[0024] At the same time, the calculation selects the node with the minimum condition number for subsequent calculation and reconstruction, which effectively reduces the amount of data to be processed and the image information is relatively completely preserved. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0026] Figure 1 A schematic diagram of a flow chart of a wavelet domain NMF image unmixing method based on adaptive local neighborhood constraints provided by the present invention;

[0027] Figure 2 A local area division diagram provided by the present invention; DETAILED DESCRIPTION

[0028] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] The existing gesture recognition and classification technologies generally have the problem that the multi-dimensional gesture feature extraction is not effective and convenient enough, and the accuracy of gesture classification is not high. Figure 1 The present invention describes the NMF unmixing method of hyperspectral remote sensing images based on adaptive local neighborhood constraints in wavelet domain. Figure 1 FIG. 4 is a flow chart of the wavelet domain NMF image unmixing method based on adaptive local neighborhood constraints of the present invention. Figure 1 As shown, the method includes:

[0030] Step 1: Acquire hyperspectral remote sensing images;

[0031] Specifically, a hyperspectral remote sensing image X of size N×M is obtained.

[0032] Step 2: Obtain hyperspectral data matrix, endmember matrix and abundance matrix;

[0033] Specifically, the VCA algorithm and FCLS algorithm are used to initialize the hyperspectral remote sensing image to obtain the endmember matrix A_init and the abundance matrix S_init. The purpose of initialization is to limit the endmember matrix A and the abundance matrix S to a certain range before starting to use the NMF algorithm for unmixing, so that when iterating, the algorithm convergence can be accelerated, the running time can be reduced, and the accuracy of the algorithm can be improved.

[0034] NMF is to realize non-negative decomposition of a large matrix under the condition that all elements of the matrix are non-negative, and obtain two non-negative low-rank matrices. Its mathematical model is:

[0035] V=WH (1)

[0036] Where: V is the original data; W is the basis matrix; H is the coefficient matrix. And W∈R n×r , H∈R r×m , where m, n, r are all constants representing the size of the matrix, and V, W, H are all non-negative matrices.

[0037] If the influence of noise is not considered, the linear mixed model and the NMF decomposition model have the same form. The remote sensing image X represents the matrix V in NMF, and the endmember spectrum matrix A represents the W in the NMF decomposition matrix. Then the abundance matrix S can be represented by H in NMF, and the "sum equals one" constraint is also added to H. In this way, using NMF to unmix remote sensing images can simultaneously obtain the endmembers and abundances in the mixed pixels.

[0038] X=AS+E (2)

[0039] Step 3: Perform d-layer biorthogonal wavelet packet transform on the hyperspectral data matrix and the end metadata matrix respectively, and obtain the wavelet packet tree corresponding to the hyperspectral data matrix and the wavelet packet tree corresponding to the end metadata matrix respectively;

[0040] Hyperspectral image data is compressible in a suitable transform domain, such as Fourier, wavelet, etc. Fourier transform has good frequency localization characteristics, but poor spatial localization. In order to reach a compromise between spatial localization and frequency localization, wavelet transform is a convenient multi-resolution analysis tool. In addition, wavelet basis has better compressibility than Fourier. On the other hand, wavelet transform is more suitable for data compression related applications. Wavelet transform helps to solve the ill-posed problem of blind spectral decomposition by better constraining the solution space. Therefore, we can use wavelet basis and take advantage of its compact representation ability to represent hyperspectral data. In addition, in order to solve the incompatibility between symmetry and signal reconstruction, Biorthohonal (biorthogonal wavelet) is introduced. Biorthogonal wavelet solves the contradiction between linear phase and orthogonality requirements.

[0041] Wavelet packet analysis can provide a more sophisticated analysis method for signals. It divides the frequency band into multiple levels, further decomposes the high-frequency part that is not subdivided in the multi-resolution analysis, and can adaptively select the corresponding frequency band according to the characteristics of the analyzed signal to match it with the signal spectrum, thereby improving the time-frequency resolution.

[0042] Wavelet packet transform is developed on the basis of wavelet transform, which overcomes the disadvantage of low frequency domain resolution of wavelet transform in high frequency part. For any given time domain signal x(t), after j layers of wavelet packet decomposition, it can be written as:

[0043]

[0044] in:

[0045]

[0046] Wavelet packet coefficients for:

[0047]

[0048] Where: j,k,i (t) is a wavelet packet with scale index j, location index k and frequency index i. j,k,i (t) is a set of standard orthogonal bases, so when m≠n, we have:

[0049]

[0050] The total energy of the signal x(t) is:

[0051]

[0052] According to the orthogonality of wavelet packets, we can get:

[0053]

[0054] in:

[0055]

[0056] Where: is the wavelet packet node energy in the i-th frequency band, and the total wavelet packet node energy of the signal is equal to the sum of the signal node energies in each frequency band.

[0057] The wavelet packet basis used by the biorthogonal wavelet packet transform has orthogonality and can preserve the linear structure of the hyperspectral data. The hyperspectral data is moved to the wavelet domain. The wavelet packet transform of the hyperspectral data X is an inner product, which is defined as:

[0058] X W := <X,ψ a,b > (10)

[0059] Where X is the hyperspectral data, X W is the hyperspectral data after WPT transformation, ψ a,b is the wavelet packet basis, and <> is the inner product operator. From formula (10), we can get the transformation of the iterative rule in the wavelet domain:

[0060]

[0061] In the formula, X w represents a hyperspectral data matrix of size K×N, E W Represents a Gaussian noise matrix of size K×N. For e endmembers, the endmember matrix A in the wavelet domain W The size is K×e, S i Represents an abundance matrix of size e × N. Among them, K is the data dimension after wavelet packet decomposition, and the specific value is determined by the selection of decomposed nodes and wavelet packet basis.

[0062] The LMM model in the wavelet domain is applied to the NMF algorithm to achieve the combination of wavelet transform and NMF algorithm. Usually, the square expression of Euclidean distance is more intuitive and more widely used. On this basis, the optimization problem of NMF in the wavelet domain can be expressed as:

[0063]

[0064] Where S represents the abundance matrix.

[0065] Specifically, in this embodiment, X and A_init are respectively subjected to d-layer biorthogonal wavelet packet transforms to obtain the wavelet packet tree of X and the wavelet packet tree of A_init. The number of layers d of packet decomposition determines the degree of spectral band compression. The larger the value of d, the higher the degree of spectral band compression. However, in practical applications, with each additional layer of decomposition, the spectral band will be compressed to about 1 / 2 of the original (the specific value is affected by the selection of wavelet basis), so when taking the value of d, the size of the original data band should be considered. If the value of d is too small, the compression is insufficient, which is easy to cause data redundancy problems and cannot solve the ill-conditioned matrix problem well; if the value of d is too large, the spectral data compression is too serious, and the original high-dimensional data cannot be effectively expressed with low-dimensional data, resulting in a decrease in the accuracy of unmixing.

[0066] Step 4: Obtain the coefficient matrix at each node of the wavelet packet tree corresponding to the end metadata matrix, calculate the condition number of each coefficient matrix, and find the node with the lowest condition number, which is recorded as min Cond;

[0067] For the linear model X = AS, the condition number of the matrix A is used to measure the sensitivity of the output of the matrix multiplication or inversion to the input error. The larger the condition number, the worse the sensitivity. For a general matrix A, there exists an inverse matrix A of A -1 (i.e. A is a non-singular matrix), then its condition number is:

[0068] cond(A)=‖A‖·‖A -1 ‖ (13)

[0069] In the formula, cond(A) represents the condition number of matrix A, and ‖·‖ represents the norm of the matrix. According to the definition, any matrix norm can be used to define the condition number. Then the corresponding 2-norm condition number is:

[0070] cond 2 (A)=‖A‖ 2 ·‖A -1 ‖ 2 (14)

[0071] It has also been proved that ||A|| 2 =σ max ,||A-1 || 2 =1 / σ min , so the condition number of the 2-norm can be calculated by the singular value decomposition of the matrix:

[0072]

[0073] In the formula, cond 2 (A) represents the bi-norm condition number of matrix A, σ max represents the largest singular value of the matrix, σ min Represents the smallest singular value of the matrix.

[0074] There is a certain similarity between pixels in homogeneous areas. However, when considering the similarity between pixels, it is inconvenient to judge the similarity between the central pixel and all other pixels due to the amount of calculation of the algorithm. Therefore, we need to use the idea of ​​local neighborhood to solve this problem. i When similarity is considered, only x i The pixel in the local neighborhood N(i) of i Represents the hyperspectral data matrix Y∈R L×N The i-th column of .

[0075] There are many ways to select the local neighborhood N(i). Common local neighborhood structures include square and circular structures. These structures are easy to operate and cannot make good use of spatial information when dealing with transition areas and boundary areas. Combined with the characteristics of abundance data, this algorithm proposes a local neighborhood determination algorithm that can make full use of spatial information.

[0076] The principle of this method is to divide the entire hyperspectral image into multiple different similar regions, each of which is closer to a ground feature, that is, an end member. Figure 2 It is a division map of a local area of ​​the hyperspectral image. Assuming that the ground object in area 1 is closer to endmember K, then the proportion of endmember K in area 1 is relatively large, and the abundance values ​​of other endmembers in area 1 are relatively small. Therefore, by comparing the abundance values ​​of different abundance maps at the same position, the endmembers close to the pixel at that position can be determined. Subsequently, the local neighborhood is determined using the points in similar areas where the abundance values ​​of the corresponding endmembers are relatively close.

[0077] First, determine the spatial coordinates of each pixel. Assume that the hyperspectral image is arranged on an r×c grid, and r×c=N. Each position on the grid corresponds to an L-dimensional pixel vector, that is, a pixel. L×N The N pixels of y are arranged in the grid from left to right and from top to bottom. In this way, the pixel y i The relationship between its spatial position (p, q)

[0078] i=(p-1)*r+q (16)

[0079] i=(q-1)*c+p (17)

[0080] Secondly, change the representation of abundance data to obtain the similarity between pixels. Let each row of the abundance matrix S be sorted into a corresponding matrix according to the spatial position of its pixel. Q ∈R 1×N For example, suppose it is sorted into S Q ∈R r×c , where r and c represent the number of rows and columns of the matrix respectively. The abundances of p rows corresponding to p end members are sorted into The elements in are represented as The magnitude of the element value is equal to the abundance value.

[0081] Then, before determining the local neighborhood of a given pixel with spatial coordinates (i, j), it is necessary to determine which end member the pixel is close to. By comparing the abundance values ​​corresponding to each abundance matrix with spatial coordinates (i, j) of size, find the largest It can be judged that the pixel is relatively close to the end member K.

[0082] Finally, according to the characteristics that the corresponding abundance values ​​of similar regions are relatively close, the abundance matrix corresponding to the end member K is In As the center, find all abundance values ​​in the 3×3 window. The positions within the range are taken as the local neighborhood N(i), and τ is a controllable parameter. The local neighborhood area of ​​each pixel can be obtained by traversing each pixel.

[0083] In order to determine the local neighborhood pixel x j (j∈N(i)) for a given pixel x j To determine the contribution of the local neighborhood pixels, two factors need to be considered: spatial distance and the similarity of local neighborhood pixels. Because the abundances of pixels in the local neighborhood are very close, the similarity of pixels can be judged by the similarity of abundances.

[0084] Based on the above analysis, the local neighborhood pixel x j x i The contribution of the weight can be defined as:

[0085]

[0086] Among them, α represents the spatial distance between pixels, β represents the similarity between pixels, The value range of and β is (0,1], which is the same order of magnitude. Assuming that the spatial coordinates of the i-th pixel and the j-th pixel are (r,s) and (k,l) respectively, we simply define α and β as:

[0087] α=|rk|+|sl| (19)

[0088] β= i ·s j > (20)

[0089] where |·| represents the absolute value, <·> represents the inner product, and α represents the pixel x i and x j The Manhattan distance between them, β represents the abundance s i and j The similarity of i represents the i-th column of the abundance matrix S. When the distance is close and the abundance similarity is high, the j-th pixel has a greater impact on the i-th pixel. Obviously, w ij The contribution of the j-th pixel to the i-th pixel in terms of spatial distance and similarity can be measured.

[0090] For a given pixel x i , the influence of all pixels in the local neighborhood on it can be expressed as χ i ,x i By calculating each neighborhood pixel x j (j∈N(i)) for x i Contribution and expression:

[0091] χ i =∑ j∈N(i) w ij ,i=1,2,…,N (21)

[0092] Specifically, in this embodiment, in the wavelet packet tree of A, (2 d+1 -2) nodes, calculate the 2-norm condition number of each node coefficient matrix, and find the node with the lowest condition number, recorded as min Cond.

[0093] Step 5: using the coefficient matrix of the hyperspectral data matrix corresponding to the node min Cond of the minimum condition number, the coefficient matrix of the endmember data matrix corresponding to the node, and the abundance matrix as inputs to the NMF model based on adaptive local neighborhood weighted constraints, iteratively updating the abundance matrix and the endmember matrix until the model converges, and outputting the iteratively updated abundance matrix and endmember matrix when converged;

[0094] ​Due to the non-convexity of the objective function of the NMF model, there will be local minima problems when the NMF algorithm is directly used for hyperspectral image unmixing. To better estimate the endmember A and abundance S, some auxiliary constraints must be added to the NMF model. Based on the fact that the abundance of a given pixel is similar to the abundance of pixels in the local neighborhood, the prior information of the local neighborhood abundance is used as a constraint and weighted, which fully utilizes the spatial information of the hyperspectral image and the similarity of the local neighborhood pixels to improve the accuracy of unmixing.

[0095] The NMF model based on adaptive local neighborhood weighted constraints is

[0096]

[0097] Where λ is an adjustable parameter to balance the approximation error and the constraint term, w ij For a given pixel x i The local neighborhood pixel x j For pixel x i The contribution of weight, x i represents the i-th column of the hyperspectral data matrix, x j represents the jth column of the hyperspectral data matrix, and N(i) represents a fixed pixel x i The column set of local neighborhood pixels, j∈N(i); s i The i-th column of the abundance matrix S, s j The jth column of the abundance matrix S is represented by , P is the number of end members, and N is the total number of pixels;

[0098] After derivation, the update rules of end members A and S are obtained:

[0099] A←A·*(XS T ). / (ASS T ) (twenty three)

[0100]

[0101] Where .* means multiplying corresponding elements of the matrix, and . / means dividing corresponding elements of the matrix. χ i Represents x i The sum of the local neighborhood weights, S w The i-th column of

[0102] X f and A f is an augmented matrix, as shown in formula (25):

[0103]

[0104] Where δ is a positive constant used to adjust the abundance sum to 1. The larger the constraint of δ, the closer the sum of each column of S is to 1.

[0105] Specifically, in this embodiment, the coefficient matrix at the min Cond node in the wavelet packet tree of X, the coefficient matrix at the min Cond node in the wavelet packet tree of A_init, and the initialized abundance matrix S_init are used as the input of the NMF unmixing algorithm based on adaptive local neighborhood constraints, and the abundance matrix S and the end member matrix A in the wavelet domain are iteratively solved. W .

[0106] Step 6: Use the coefficient matrices of other nodes in the same layer as the minCond node and the iteratively updated endmember matrix as inputs of the reconstruction function, and output the reconstructed endmember matrix, that is, reconstruct the endmembers using the wavelet packet tree nodes at the lowest layer of the condition number.

[0107] The key points of the embodiments of the present invention are: 1. An adaptive local neighborhood constrained NMF model is proposed. According to the characteristics of the abundance matrix, the local neighborhood of a given pixel can be adaptively determined. The calculated weight fully utilizes the spatial information of the given pixel and the pixels in the neighborhood, so that the unmixing accuracy is higher; 2. Secondly, different from the traditional time-domain NMF unmixing image method, the adaptive local neighborhood constrained NMF model is combined with the biorthogonal wavelet packet transform to obtain an adaptive local neighborhood constrained NMF unmixing method for hyperspectral remote sensing images in the wavelet domain. The biorthogonal wavelet is used as the wavelet basis to represent the data. The characteristics of the linear phase and the shorter support set of the wavelet basis can better compress the data and reduce the influence of noise on the unmixing result, further overcome the ill-conditioned matrix problem that occurs in the unmixing process, and further improve the unmixing accuracy effect; 3. Not all nodes are selected to input the adaptive local neighborhood constrained NMF model and participate in the reconstruction of the end member matrix, but the minimum condition number node is selected. The calculation selection application of this node effectively reduces the amount of data processing, and the image information is relatively completely preserved, that is, the integrity of the image information is taken into account, the calculation amount is small and efficient.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A wavelet domain NMF image unmixing method based on adaptive local neighborhood constraints, characterized in that: include: Step 1: Acquire hyperspectral remote sensing images; Step 2: Obtain the hyperspectral data matrix X, endmember matrix A and abundance matrix S; Step 3: Perform d-layer biorthogonal wavelet packet transform on the hyperspectral data matrix and the end metadata matrix respectively, and obtain the wavelet packet tree corresponding to the hyperspectral data matrix and the wavelet packet tree corresponding to the end metadata matrix respectively; Step 4: Obtain the coefficient matrix at each node of the wavelet packet tree corresponding to the end metadata matrix, calculate the condition number of each coefficient matrix, and find the node with the lowest condition number, which is recorded as min Cond; Step 5: using the coefficient matrix of the hyperspectral data matrix corresponding to the node min Cond of the minimum condition number, the coefficient matrix of the endmember data matrix corresponding to the node, and the abundance matrix as inputs to the NMF model based on adaptive local neighborhood weighted constraints, iteratively updating the abundance matrix and the endmember matrix until the model converges, and outputting the iteratively updated abundance matrix and endmember matrix when converged; Step 6: taking the coefficient matrices of other nodes in the same layer as the minCond node and the iteratively updated endmember matrix as inputs of the reconstruction function, and outputting the reconstructed endmember matrix; In step 5, the NMF model based on adaptive local neighborhood weighted constraints is: Where λ is an adjustable parameter to balance the approximation error and the constraint term, w ij For a given pixel x i The local neighborhood pixel x j For pixel x i The contribution of weight, x i represents the i-th column of the hyperspectral data matrix, x j represents the jth column of the hyperspectral data matrix, and N(i) represents the given pixel x i The column set of local neighborhood pixels, j∈N(i); s i The i-th column of the abundance matrix S, s j The jth column of the abundance matrix S is represented by , P is the number of end members, and N is the total number of pixels; In step 5, the abundance matrix S and the end member matrix A are iteratively updated. A←A.*(XS T ). / (ASS T ) Where ·* represents the multiplication of corresponding matrix elements, . / represents the division of corresponding matrix elements, and the matrix χ i Represents x i The sum of the local neighborhood weights, S w The i-th column of X f and A f are the augmented matrices of X and A respectively.

2. The wavelet domain NMF image unmixing method based on adaptive local neighborhood constraints according to claim 1 is characterized in that: The step 4 also includes obtaining (2 d+1 -2) nodes, calculate the 2-norm condition number of the coefficient matrix of each node, and find the node with the lowest condition number.

3. The wavelet domain NMF image unmixing method based on adaptive local neighborhood constraints according to claim 1 is characterized in that: The w ij It is related to the spatial distance between pixels and the similarity between pixels. The higher the similarity between the abundance of a given pixel and the abundance of local neighboring pixels, the higher the corresponding weight w ij Also bigger.

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