CN114297573A - Depth non-negative matrix image unmixing method and device based on local neighborhood constraint - Google Patents

Depth non-negative matrix image unmixing method and device based on local neighborhood constraint Download PDF

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CN114297573A
CN114297573A CN202111445170.7A CN202111445170A CN114297573A CN 114297573 A CN114297573 A CN 114297573A CN 202111445170 A CN202111445170 A CN 202111445170A CN 114297573 A CN114297573 A CN 114297573A
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刘钰龙
李杏梅
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China University of Geosciences
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Abstract

The invention provides a depth non-negative matrix image unmixing method and device based on local neighborhood constraint, wherein the depth non-negative matrix image unmixing method comprises the following steps: inputting raw data of an image to an NMF model; splitting original data into three layers, and initializing each layer of original data to obtain initialized data; pre-training the initialization data; inputting the pre-trained initialization data into the NMF model again for optimization iteration until convergence; and outputting the converged unmixing result. The method utilizes local neighborhood constraint to constrain the abundance matrix, and simultaneously expands a single-layer NMF model to a deep NMF model by means of the thought of deep learning, so that error accumulation is reduced.

Description

Depth non-negative matrix image unmixing method and device based on local neighborhood constraint
Technical Field
The invention relates to the technical field of image processing, in particular to a depth nonnegative matrix image unmixing method and device based on local neighborhood constraint.
Background
The hyperspectral unmixing technology is an important image processing technology and is widely applied to various fields of agriculture, mineral exploration, environmental monitoring and the like. Among them, the non-Negative Matrix Factorization (NMF) algorithm is the hot of research. Lee and Seung put forward a non-negative matrix decomposition method in the early stage, and in brief, we need to decompose an original remote sensing image into a form of multiplying end members by abundance, so that the proportion of each end member in each pixel can be obtained, and we turn the process into unmixing; the actual remote sensing image is actually a data set formed by stacking a plurality of images, wherein the pixel refers to a point in the image remote sensing image, and the point is called a mixed pixel as the point is formed by a plurality of stacked images; end members are understood to mean every kind of ground object, such as trees, stones, etc.; the abundance is the proportion corresponding to the ground object; both end members and abundance are expressed in the form of a matrix.
Because the NMF algorithm has obvious non-convexity and a plurality of local minimum values, researchers provide an improved NMF-based algorithm, and the NMF algorithm is subjected to sparse constraint when being used most before 2018; in recent years, local neighborhood constraint has been applied to remote sensing image unmixing, and spatial context information of the remote sensing image is fully mined.
However, although the spatial information of the image is better mined only by using the local neighborhood constraint, most algorithms are single-layer non-negative matrix decomposition, the fact that the original data contains the hierarchical features with hidden information is ignored, and for complex and highly mixed data, the unmixing performance is possibly not ideal; when weighting is performed on local neighborhood constraints, most of the methods are linear weighting, and in an actual image, due to factors such as complex terrain, the distance of each pixel cannot be simply represented by a Riemann distance or a Manhattan distance, which causes errors on the weights of local neighborhoods.
Disclosure of Invention
The invention solves the main problem that the existing hyperspectral unmixing method is not ideal in unmixing performance for complex and highly mixed data.
The invention provides a local neighborhood constraint-based depth non-negative matrix image unmixing method, which comprises the following steps:
inputting raw data of an image to an NMF model;
splitting the original data into three layers, and initializing each layer of the original data to obtain initialized data;
pre-training the initialization data;
inputting the pre-trained initialization data into the NMF model again for optimization iteration until convergence;
and outputting the converged unmixing result.
Further, initializing each layer of the raw data comprises:
and initializing an end member matrix of each layer of the original data by using a vertex component analysis method.
Further, initializing each layer of the raw data further comprises:
initializing an abundance matrix of the raw data of each layer by using a fully constrained least squares method.
Further, the pre-training of the initialization data comprises:
selecting a local neighborhood of an end member of the abundance matrix of the initialization data;
calculating a weight matrix of the local neighborhood;
adding the weight matrix to a first objective function;
and iterating the weight matrix added in the first objective function by using a gradient descent method.
Further, calculating the weight matrix of the local neighborhood includes:
the weight calculation formula of the local neighborhood to the central pixel element is as follows:
Figure BDA0003383906460000021
wherein, sigma is a controllable parameter for controlling the weight of the Gaussian kernel function, alpha represents a space distance, beta represents similarity between pixels, and wijThe weighted value is j, the number of local neighborhood pixels is j, and i is the number of central pixels;
and obtaining a weight matrix of the local neighborhood based on the weight value calculated by the weight calculation formula.
Further, the first objective function is:
Figure BDA0003383906460000031
wherein, A end member matrix, S is abundance matrix, the first on the left of plus signOne item represents reconstruction error, the second item on the right of the plus sign represents local neighborhood constraint, N is the number of end members, N (i) is a local neighborhood set of a pixel point i, lambda is a regularization parameter, SlLayer I, S, representing the abundance matrixliThe l-th layer abundance matrix of the pixel point i, SliThe l-th layer abundance matrix of pixel point j, AlLayer I, S, representing an end-member matrix0Denotes X, wlijRepresenting the local neighborhood weight of the l-th layer.
Further, iterating the weight matrix added to the first objective function using a gradient descent method until convergence comprises:
and calculating partial derivatives of the abundance matrix and the end member matrix in the first objective function, and performing optimization iteration by using a gradient descent method until convergence.
According to another aspect of the present invention, there is also disclosed a depth non-negative matrix image unmixing device based on local neighborhood constraint, where the depth non-negative matrix image unmixing device is operable to implement the depth non-negative matrix image unmixing method based on local neighborhood constraint as described above, and the depth non-negative matrix image unmixing method includes:
the data processing module is used for inputting original data of an image, splitting the original data into a plurality of layers, and initializing each layer of the original data to obtain initialized data;
the training module is used for pre-training the initialization data;
and the fine tuning module is used for inputting the pre-trained initialization data into the NMF model again for optimization iteration until convergence and outputting a converged unmixing result.
The invention provides a depth nonnegative matrix factorization algorithm LNWC-DNMF based on local neighborhood constraint by using a depth Nonnegative Matrix Factorization (NMF) model to replace a traditional single-layer Nonnegative Matrix Factorization (NMF) model and using a Gaussian kernel function to replace the linear weighting of the distance in the traditional local neighborhood, and the information of a hidden layer of a remote sensing image can be mined while the spatial information is fully utilized. The validity of the algorithm is verified by simulating the data set.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description, serve to explain the principles of the invention.
FIG. 1 is a flowchart of a depth nonnegative matrix image unmixing algorithm based on local neighborhood constraint in an embodiment of the present invention.
Fig. 2 is a schematic diagram of a deep NMF unmixing model in an embodiment of the present invention.
FIG. 3 is a schematic diagram of synthesizing hyperspectral data in an embodiment of the invention.
FIG. 4 is a schematic diagram of the abundance of the end members of the simulation data in the embodiment of the present invention.
Detailed Description
Various exemplary embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be noted that: the relative arrangement of the components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless specifically stated otherwise.
Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description.
The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate.
In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
In the first embodiment, as shown in fig. 1, a flowchart of a depth nonnegative matrix image unmixing algorithm based on local neighborhood constraint in this embodiment is provided, where the algorithm specifically includes:
(1) raw data X of the image are input to the NMF model.
(2) Splitting the original data X into a plurality of layers, preferably three layers (the three layers can generally achieve the best unmixing effect), initializing an end member matrix of each layer of original data by using a vertex component analysis method, and initializing an abundance matrix of each layer of original data by using a fully constrained least square method.
(3) Pre-training the initialized original data, wherein the pre-training step comprises the following steps: taking the maximum point of each column in the abundance matrix, namely the local neighborhood of the main end member of the pixel; calculating a weight matrix of the local neighborhood; adding the weight matrix to a first objective function; and iterating the end members and the abundance of the weight matrix added in the first objective function by using a gradient descent method.
(4) And inputting the pre-trained initialization data into the NMF model for fine adjustment, and optimizing iteration until convergence.
(5) And outputting the converged unmixing result.
Specifically, in order to enable the final result to be close to the global optimal solution, after the original data are input into the depth NMF model in the step (1), the end member matrix is initialized through Vertex Component Analysis (VCA) in the step (2), and the abundance matrix is initialized through a Fully Constrained Least Squares (FCLS) method, so that the convergence rate of the subsequent iteration is improved.
As shown in fig. 2, is a frame diagram of the depth NMF model. It can be seen that the structure is formed by stacking a plurality of single-layer NMF molds one on top of the other. For the l layer, the output S of the previous layer after non-negative matrix decompositionl-1As the input of the current NMF layer, decomposing to obtain the end member matrix A of the l layerlSum abundance matrixSL, and so on until the last L-th layer。
Based on the foregoing, the mathematical expression of the depth NMF model can be derived as:
X≈A1A2…AL-1ALSL (1)
wherein X is original data, A is an end member matrix, S is an abundance matrix, and L is the number of layers.
The deep NMF model algorithm flow in the invention mainly comprises two stages, namely a pre-training stage and a fine-tuning stage.
Specifically, in the pre-training stage in step (3), the objective function is as follows:
Figure BDA0003383906460000051
wherein, A end member matrix, S is abundance matrix, the first item on the left of plus sign represents reconstruction error, the second item on the right of plus sign represents local neighborhood constraint, N is end member number, N (i) is local neighborhood set of pixel point i, lambda is regularization parameter, S is normalization parameterlLayer I, S, representing the abundance matrixliThe l-th layer abundance matrix of the pixel point i, SliThe l-th layer abundance matrix of pixel point j, AlLayer I, S, representing an end-member matrix0Denotes X, wlijRepresenting the local neighborhood weight of the l-th layer.
In the hyperspectral image unmixing, in order to make the abundance matrix S satisfy the ASC constraint, the data set and the spectral feature matrix need to be redefined as follows:
Figure BDA0003383906460000061
wherein the content of the first and second substances,
Figure BDA0003383906460000062
for the spectral feature matrix, δ is a parameter that controls and is a constraint influence, which is usually set to 15, and vector 1 is a row vector of all 1's.
In the pre-training stage, the pre-training stageRespectively for Al，SlCalculating partial derivatives, selecting proper step length, and performing iteration by using a gradient descent method to obtain a multiplicative iteration rule of A and S as follows:
Al←Al.*Sl-1Sl T/AlSlSl T (4)
wherein S isl TIs SlThe transpose of "/is the corresponding matrix corresponding multiplication,/is the corresponding matrix division;
Figure BDA0003383906460000063
wherein, the lambda is a self-selection parameter,
Figure BDA0003383906460000064
is the first layer
Figure BDA0003383906460000065
The matrix of (a) is transposed,
Figure BDA0003383906460000066
is a complementary matrix of a and is,
Figure BDA0003383906460000067
is the l-1 st layer
Figure BDA0003383906460000068
The matrix of (a) is transposed,
Figure BDA0003383906460000069
a complementary matrix to the abundance matrix S, in particular S0＝X，
Figure BDA00033839064600000610
SwIs a local neighborhood weight matrix.
Based on the multiplicative iteration rules of (4) and (5), when the iteration is carried out for a certain number of times, the value of f (A, S) tends to be stable.
In this embodiment, the number of iterations in both the pre-training and fine-tuning stages is selected to be 1000, and the regularization parameter λ is selected from a finite set {0.0001, 0.0005, 0.001, 0.005, 0.01, 0.05, 0.1, 0.2 }.
Since pre-training can only guarantee that the NMF of each individual layer is convergent, the resulting unmixing results are a calculation of the whole, which may lead to accumulation of errors. In order to reduce the overall error of the deep NMF structure, each intermediate layer result needs to be individually fine-tuned by the optimization rule.
In the fine-tuning stage of step (4), rewriting | | X-AS | | | into a more detailed form, the specific expression is AS follows:
Figure BDA0003383906460000071
for ease of understanding and subsequent solution, two new variables need to be defined:
Figure BDA0003383906460000072
in the formula
Figure BDA0003383906460000073
Reconstructed abundance matrix representing the l-th layer for Ψl-1And, if and only if l is 1, represents one identity matrix. Thus, in the fine tuning phase, the objective function is as follows:
Figure BDA0003383906460000074
specifically, in the fine tuning stage, the objective functions f (A, S) of the fine tuning stage are respectively corresponding to Al，SlAnd (3) solving a partial derivative, selecting a proper step length, performing iteration by using a gradient descent method, and deducing a multiplicative iteration formula for obtaining a deep NMF fine adjustment l-th layer decomposition result, wherein the multiplicative iteration formula is as follows:
Figure BDA0003383906460000075
Figure BDA0003383906460000076
wherein the content of the first and second substances,
Figure BDA0003383906460000077
is ΨlThe completion matrix of (a) is,
Figure BDA0003383906460000078
is composed of
Figure BDA0003383906460000079
Matrix transposition of [ phi ], [ phi ]T l-1The identity matrix Ψ for the l-th layerT lIs transposed, SlwIs the local neighborhood weight matrix of the l-th layer.
As can be seen from equations (9) (10), unlike pre-training: the fine-tuning iteration process takes the result obtained by pre-training as an initial value, and uses the parameters of the whole depth NMF model, the update of the current layer parameters is not only related to all layers before the current layer, but also related to all layers after the current layer, so that the decomposition result after each iteration update is estimated based on the whole error, and the accumulation of the error is reduced.
The effect of the aforementioned algorithm model is verified experimentally below.
The synthetic image of the simulated data is shown in FIG. 3: the composite image contains 48 × 48 pixels, each pixel containing 188 bands. The abundance image of the synthesized image satisfies ANC and ASC, wherein the 1 st row is pure pixels, the 2 nd to 4 th rows are respectively the mixture of 2, 3 and 4 end members, and the background pixels around the square are also the mixture of the same 4 end members in different proportions.
For the evaluation of the unmixing effect of the simulation data, since the prior information such as the spectral characteristics and abundance coefficients of the end members included in the simulation data is known, the accuracy of the extracted end members and abundance can be quantitatively evaluated by using the Spectral Angular Distance (SAD) and the Root Mean Square Error (RMSE), which are specifically defined as follows:
(1) spectral angular distance SAD: measuring original end member spectral characteristic A and its estimated value
Figure BDA0003383906460000081
The difference between them, the formula is as follows:
Figure BDA0003383906460000082
the spectral angular distance is used for evaluating the similarity of the end member spectral matrix obtained by the experiment and a reference value.
From the above definitions it follows that: the smaller the SAD value, the more similar to the reference result, the better the experimental result.
(2) Root mean square error RMSE: measurement abundance truth value SijAnd abundance estimate
Figure BDA0003383906460000083
The difference between them, the formula is as follows:
Figure BDA0003383906460000084
wherein N is the total number of the hyperspectral image pixels;
the root mean square error is used to evaluate the proximity of the experimentally obtained abundance matrix to a reference value.
From the above definitions it follows that: the smaller the RMSE value, the more similar the reference results, the better the experimental results.
The evaluation of the unmixing effect of the real data is generally performed by a qualitative method.
Specifically, the quality of the unmixing result is visually evaluated, whether the physical significance of the abundance of the extracted end member is clear or not, whether obvious deviation exists in the abundance composition or not and whether the spectral characteristic curve obtained by unmixing accords with the characteristics of a certain ground object or not are observed.
In the experiment, the validity of the LNWC-DNMF algorithm is verified by using a synthetic data set, and the validity is matched with the ALNWC-NMF algorithm and the L1/2-NMF algorithmA comparison is made.
All results in the experiment were averaged over 20 replicates.
As shown in FIG. 4, 4 end members of the composite data pass through L1/2Comparison of the unmixed abundance maps of the three algorithms-NMF, ALNWC-NMF and LNWC-DNMF with the reference abundance map. The light and dark colors in the abundance map of the end members respectively indicate the proportion of the corresponding end members contained in the region, namely the size of the abundance value, the darker color indicates that the proportion of the contained end members is less (the abundance value is small), the darker color indicates that the end members are not contained, and the yellow color (the bright color) indicates that the region is all the end members and does not contain other end members. As can be taken from fig. 4, the unmixing effect of the LNWC-DNMF algorithm is the best.
Table 1 shows the SAD and RMSE values for the four algorithm unmixing results. From the experimental results, two evaluation indexes of the LNWC-DNMF algorithm are basically superior to L1/2-NMF algorithm, DNMF algorithm and ALNWC-NMF algorithm.
TABLE 1 SAD and RMSE values in simulation data for four NMF unmixing algorithms
Figure BDA0003383906460000091
The above description is only exemplary of the present invention and should not be taken as limiting the invention, as any modification, equivalent replacement, or improvement made within the spirit and scope of the present invention should be included in the present invention.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in the process, method, article, or apparatus that comprises the element.

Claims (6)

1. A depth non-negative matrix image unmixing method based on local neighborhood constraint is characterized by comprising the following steps:
inputting raw data of an image to an NMF model;
splitting the original data into a plurality of layers;
initializing an end member matrix of the original data of each layer by using a vertex component analysis method, and initializing an abundance matrix of the original data of each layer by using a fully constrained least square method to obtain initialized data;
pre-training the initialization data;
inputting the pre-trained initialization data into the NMF model again for optimization iteration until convergence;
and outputting the converged unmixing result.
2. The method of claim 1, wherein the step of pre-training the initialization data comprises:
selecting a local neighborhood of an end member of the abundance matrix of the initialization data;
calculating a weight matrix of the local neighborhood;
adding the weight matrix to a first objective function;
and iterating the weight matrix added in the first objective function by using a gradient descent method.
3. The method of claim 2, wherein computing the weight matrix of the local neighborhood comprises:
the weight calculation formula of the local neighborhood to the central pixel element is as follows:
Figure FDA0003383906450000011
wherein, sigma is a controllable parameter for controlling the weight of the Gaussian kernel function, a represents the space distance, beta represents the similarity between pixels, and wijThe weighted value is j, the number of local neighborhood pixels is j, and i is the number of central pixels;
and obtaining a weight matrix of the local neighborhood based on the weight value calculated by the weight calculation formula.
4. The method for depth nonnegative matrix image unmixing based on local neighborhood constraint according to claim 2, wherein the first objective function is:
Figure FDA0003383906450000021
wherein, A end member matrix, S is abundance matrix, the first item on the left of plus sign represents reconstruction error, the second item on the right of plus sign represents local neighborhood constraint, N is end member number, N (i) is local neighborhood set of pixel point i, lambda is regularization parameter, S is normalized parameterlLayer I, S, representing the abundance matrixliThe l-th layer abundance matrix of the pixel point i, SliThe l-th layer abundance matrix of pixel point j, AlLayer I, S, representing an end-member matrix0Denotes X, wlijRepresenting the local neighborhood weight of the l-th layer.
5. The method of claim 2, wherein iterating the weight matrix added to the first objective function by using a gradient descent method comprises:
and calculating partial derivatives of the abundance matrix and the end member matrix in the first objective function, and performing optimization iteration by using a gradient descent method until convergence.
6. A depth non-negative matrix image unmixing device based on local neighborhood constraint, wherein the depth non-negative matrix image unmixing device is operable to implement a depth non-negative matrix image unmixing method based on local neighborhood constraint according to any one of claims 1 to 5, the depth non-negative matrix image unmixing method comprising:
the data processing module is used for inputting original data of an image, splitting the original data into a plurality of layers, and initializing each layer of the original data to obtain initialized data;
the training module is used for pre-training the initialization data;
and the fine tuning module is used for inputting the pre-trained initialization data into the NMF model again for optimization iteration until convergence and outputting a converged unmixing result.
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