CN110751144B - Canopy plant hyperspectral image classification method based on sparse representation - Google Patents

Abstract

The invention discloses a canopy plant hyperspectral image classification method based on sparse representation. The invention introduces a new weighted sparse representation model, and represents any spectrum in the hyperspectral data as a linear combination of a plurality of atoms in a pre-trained dictionary. The sparse representation of either spectrum is represented as a sparse vector whose non-zero values correspond to the weights of the selected training samples. Sparse vectors are recovered by solving a sparse constraint optimization problem, and class labels of test samples can be directly determined. The concept of correlation coefficient and threshold is introduced, the model endows different weight values to adjacent spectrums according to the correlation between the adjacent spectrums and the current spectrum, so that the constraint degree of different spectrums in the neighborhood to the attribution of the current spectrum is changed, and the change obviously improves the classification of the spectrums at the junctions of different objects.

Description

Canopy plant hyperspectral image classification method based on sparse representation

Technical Field

The invention belongs to the technical field of image recognition, and particularly relates to a hyperspectral image classification method based on sparse representation.

Background

The traditional target classification method needs to assume definite statistical distribution characteristics of data, and in addition, the spectral characteristics of the target are not sufficiently represented by a single target spectrum, because the target spectrum changes with environmental conditions. In actual hyperspectral target classification, a better classification result can be hardly obtained by only a certain feature space. The remote sensing technology is used as a rapid and macroscopic ground surface resource monitoring technical means, compared with the traditional ground survey, the remote sensing technology has the advantages of objectively, nondestructively and acquiring information in real time, and particularly provides a feasible method for distinguishing different objects due to the appearance and development of the hyperspectral remote sensing technology. The hyperspectral remote sensing can provide a plurality of characteristic spaces, and the performance of target classification is improved by jointly processing spectral information and spatial information of hyperspectral data.

The crop canopy can reflect and predict the functional status of vegetation and ecosystems, showing primary productivity and the changing process of nitrogen cycle. Its canopy information is often used as an indicator of function and biodiversity in ecosystems. The hyperspectrum of the vegetation canopy is often combined with information of photosynthetic pigments, moisture, nitrogen, cellulose and the like of leaves, so that the growth condition of crops can be reflected. However, due to the limitation of the spectral information in the hyperspectral image to the conditions such as atmosphere, illumination intensity, earth surface radiation and the like, the spectral information in the real hyperspectral image cannot be completely matched with the spectral information in the spectral information base. Meanwhile, targets in the hyperspectral images generally exist in a low probability form, and the low exposure probability of the targets also becomes a difficult point of classification. Therefore, the quantization processing of the original hyperspectral image is particularly important. In recent years, the sparse representation theory developed by the method can be well applied to the field of hyperspectral image classification by virtue of better signal representation capability. The original hyperspectrum is expressed in a linear combination mode of a group of substrates or a very small number of atoms in an over-complete dictionary by utilizing a sparse representation theory, so that the rich structural characteristics in the hyperspectral image are analyzed. It is generally considered that each spectrum in a hyperspectral image can be linearly represented by a set of bases, which are usually spectral characteristics of a target or a background, and are generally provided by a spectrum information base. The sparse representation-based hyperspectral image automatic classification algorithm proposed by Yi Chen et al is different from the traditional classification method, and the method is characterized in that the sparse representation theory developed in recent years is successfully introduced into the classification theory, so that the defects of the traditional classification method are effectively overcome.

The spectral reflectance curve of a substance is unique and contains spectral information which is unique, and the uniqueness of the spectral reflectance curve is the basis for substance differentiation. However, in reality, there are many interference factors, which may cause the occurrence of the same-spectrum foreign matter or the same-spectrum foreign matter, and bring many difficulties to the actual object differentiation.

Common classification models of hyperspectral images include an euclidean distance model, a statistical probability model, and a spatial model. Due to the influence of uncertain factors of spectral characteristics of objects in the hyperspectral image, the classification effect of the classification algorithm based on the Euclidean distance model is not ideal. The classification by adopting the subspace model usually suppresses the background, and because a global method is basically adopted, the complexity of the background can be reduced, the background is suppressed to improve the residual energy of the target, and the classification effect is enhanced, but the classification of the small target cannot be realized. Most of the existing classification algorithms utilize the spectral information of all wave bands of the detected image, and do not consider the spatial similarity existing between adjacent pixels. However, due to the extremely high spectral resolution of the hyperspectral remote sensing image, adjacent wave bands of the image show extremely high similarity or redundancy. In this case, both redundant information and resolution information are contained between adjacent single-band picture elements, and the redundant spectral information prevents the classification from being performed efficiently. When the classification is carried out in reality, the remote sensing imaging distance is long, the exposure probability of a target is low, so that the sub-pixel state of the target can appear, and the classification work of the sub-pixels and the hidden pixels in the hyperspectral image can be realized by introducing the sparse representation theory.

The traditional sparse representation model has the defects of same spectrum of mixed pixels and foreign matters, and the like, and the combined sparse representation model provided aiming at the defects utilizes the characteristic that adjacent spectrums have high spatial correlation, restricts the attribution of the current spectrum by using the attribution condition of the adjacent spectrums in training, but brings another difficult problem, namely the phenomenon of spectrum classification confusion at the junctions of different objects. To solve the problem, the invention provides a new weighted sparse representation model, and hyperspectral pixels to be observed can be sparsely represented by linear combination of some training samples from a structured dictionary. The sparse representation of the unknown pixels is represented as a sparse vector whose non-zero entries correspond to the weights of the selected training samples. Sparse vectors are recovered by solving a sparse constraint optimization problem, and class labels of test samples can be directly determined. The concept of correlation coefficient and threshold is introduced, the model endows different weight values to adjacent spectrums according to the correlation between the adjacent spectrums and the current spectrum, so that the constraint degree of different spectrums in the neighborhood to the attribution of the current spectrum is changed, and the change obviously improves the classification of the spectrums at the junctions of different objects.

Disclosure of Invention

The invention provides a canopy plant hyperspectral image classification method based on sparse representation, aiming at the defect of disordered spectrum classification at junctions of different objects in the existing hyperspectral image classification method. The invention uses the SOMP algorithm, fully utilizes the sparsity of signals and the correlation among spectra, and obviously improves the classification of the spectra at the junctions of different objects.

The method specifically comprises the following steps:

and (1) preprocessing data.

1.1 obtaining hyperspectral images of plants to be classified

1.2 spectral unitization:

and performing unitization processing on each spectrum in the plant hyperspectral image.

1.3 dividing training samples and testing samples:

the hyperspectral image data processed in the unitization mode in the step 1.2 is used as a training sample A according to the proportion that the sample contains 15% of each class of objects in the M classes of objects, and the rest 85% of the hyperspectral image data are test samples.

Where the matrix size of a is D x N,

N_mrepresenting the number of pixels of the mth class object; a. the_mDictionary of size DxN representing the composition of class m object samples_m。

Is the Nth of the m-th class object_mStrip spectrum

α_mAnd representing a sparse matrix consisting of all sparse coefficients corresponding to the training samples of the mth class of objects, wherein the matrix only contains a few non-zero values.

Step (2) establishing a weighted joint sparse model

The sparse representation of adjacent spectra is based on the same sparse model, with similar sparse coefficients. The hyperspectral remote sensing image spectrums which are adjacent in space can be approximately represented by sparse linear combination of a plurality of atoms in a constructed dictionary, but the representation coefficients of the hyperspectral remote sensing image spectrums are different.

In the weighted joint sparse model, at the boundary, we consider the adjacent hyperspectral spectrum x_iAnd x_jAre made up of different objects. x is a radical of a fluorine atom_iFrom a constructed dictionary A_iExpressed as:

x_i＝A_iα_i

x_jfrom a constructed dictionary A_jExpressed as:

x_j＝A_jα_j

by the same token, we extend to adjacent spectra N_εT spectra were included and represented linearly using the same training samples. When the object type of the boundary of the hyperspectral image object is judged, the conventional combined sparse representation model usually ignores the difference between adjacent spectrums at the boundary and lacks the correct judgment on the effective spectrum and the invalid adjacent spectrum, so that the object type at the boundary of the object is finally judged incorrectly. Here we introduce the weight w_iAs shown in fig. 4. Let X be [ w ]₁x₁w₂x₂…w_Tx_T]Is a D × T matrix, where { x_t}_t＝1，...T∈N_εAdjacent spectra in hyperspectral space. So X can be represented as:

X＝[w₁x₁w₂x₂…w_Tx_T]＝[A₁S₁A₂S₂…A_MS_M]＝[A₁A₂…A_M][S₁S₂…S_M]＝AS

wherein x is₁For the spectrum currently to be classified, x₂…x_TIs given by x₁The adjacent spectrum within a central square region. w is a_iRepresenting the weight of the ith spectrum, T representing the number of adjacent spectrums in hyperspectral space, M representing the number of classes of objects, S_MIs X in the A_MSparse vectors under a training dictionary. S is a sparse matrix of sparse vectors. thr is a threshold value for determining whether the adjacent spectrum is valid, and is set artificially. To pairAt x₁And x_iThe correlation coefficient between them is not less than the spectrum of thr, and we consider that they are very similar to the central test spectrum, so they are valid spectra. Therefore, their weights are reset to 1. For x₁And x_iSpectra with a correlation coefficient smaller than thr are considered as invalid adjacent spectra, and therefore their weights are reset to 0.

Step (3) solving the sparse matrix

Given a training dictionary A, the matrix S can be solved by the joint sparse reconstruction problem of the following formula.

minimize||S||_row，0

subjectto：AS＝X

Wherein the symbol | | S | | non-calculation_row，0Representing the number of non-zero rows in the sparse matrix S. Now requires an optimal solution for S

A sparse matrix of D × M consists of only a few non-zero rows. According to the actual situation, the influence of the error is considered

The solution of (c) can also be written in the form:

wherein | · | purple_FRepresenting the Frobenius norm. σ denotes its error margin, K₀The number of non-zero elements is expressed by the limitation of the sparsity condition. As with sparse representation reconstruction of a single spectrum, the problem of solving weighted combined sparse representation is also an NP-Hard problem, and the problem of sparse reconstruction can be solved through a combined orthogonal matching pursuit (SOMP) algorithm.

Step (4), spectrum classification

Once the sparse matrix S is solved, we can calculate all classes to train the dictionary and get the reconstruction error of x. Then the error of x reconstructed by the training dictionary for the mth class of objects is:

and representing the optimal solution of the sparse matrix obtained by the mth class of training dictionary. Then the final classification result for x is the type of object with the least reconstruction error, i.e.:

wherein r is_m(x) Representing sparse representation of test samples x and x in an m-th class object

The smaller the value, the closer x is to the M-th class object.

The invention has the beneficial effects that:

the invention introduces a new weighting sparse representation model, observed hyperspectral pixels can be sparsely represented by linear combination of some training samples from a structured dictionary, the sparse representation of unknown pixels is represented as a sparse vector, the non-zero entries of the unknown pixels correspond to the weights of the selected training samples, the sparse vector is recovered by solving a sparse constraint optimization problem, class labels of test samples can be directly determined, and concepts of correlation coefficients and threshold values are introduced.

Description of the drawings:

FIG. 1 is a weighted joint sparse representation model;

FIG. 2 is a reset distribution of weights; (a) in the real situation of a small land, the light gray pixels belong to the A class, and the dark gray pixels belong to the b class; (b) ideal distribution;

FIG. 3 is a hyperspectral image of example data;

FIG. 4 is a dictionary consisting of random samples of the spectrum of an object;

FIG. 5 is a diagram illustrating the classification results of data obtained by the method of the present invention.

Detailed Description

The invention is further examined with the aid of the following examples and with reference to the accompanying drawings.

In this example, the example data is used to synthesize a hyperspectral image of plant hyperspectral data, as shown in FIG. 3.

And (1) preprocessing data.

1.1 acquiring hyperspectral images of plants to be classified.

1.2 spectral unitization:

and performing unitization processing on each spectrum in the plant hyperspectral image.

1.3 dividing training samples and testing samples:

the hyperspectral image data processed in the unitization processing in the step 1.2 is used as a training sample A according to the proportion that the sample contains 30% of each class of objects in the M classes of objects, and the rest 70% of the hyperspectral image data are test samples (shown in FIG. 4).

Where the matrix size of a is D x N,

N_mthe number of spectra representing the mth class of objects; a. the_mDictionary of size DxN representing sample composition of m-th class of objects_m。

Is that the mth class object is in the Nth class object_mIndividual spectrum

α_mAnd representing a sparse matrix consisting of all sparse coefficients corresponding to the training samples of the mth class of objects, wherein the matrix only contains a few non-zero values.

Step (2) establishing a weighted joint sparse model

The sparse representation of adjacent spectra is based on the same sparse model, with similar sparse coefficients. The hyperspectral remote sensing image spectrums which are adjacent in space can be approximately represented by sparse linear combination of a plurality of atoms in a constructed dictionary, but the representation coefficients of the hyperspectral remote sensing image spectrums are different.

In the weighted joint sparse model (as shown in FIG. 1), at the boundary, we consider the adjacent hyperspectral spectra x_iAnd x_jAre made up of different objects. x is a radical of a fluorine atom_iFrom a constructed dictionary A_iExpressed as:

x_i＝A_iα_i

x_jfrom a constructed dictionary A_jExpressed as:

x_j＝A_jα_j

by the same token, we extend to adjacent spectra N_εT spectra were included and represented linearly using the same training samples. When the object type of the boundary of the hyperspectral image object is judged, the conventional combined sparse representation model usually ignores the difference between adjacent spectrums at the boundary and lacks the correct judgment on the effective spectrum and the invalid adjacent spectrum, so that the object type at the boundary of the object is finally judged incorrectly. Here, we introduce the weight w_iAs shown in fig. 2. Let X be [ w ]₁x₁w₂x₂…w_Tx_T]Is a D × T matrix, where { x_t}_t＝1，...T∈N_εFor high spectral space adjacent lightSpectra. So X can be represented as:

X＝[w₁x₁w₂x₂…w_Tx_T]＝[A₁S₁A₂S₂…A_MS_M]＝[A₁A₂…A_M][S₁S₂…S_M]＝AS

wherein x is₁For the spectrum currently to be classified, x₂…x_TIs represented by x₁The adjacent spectrum within a central square region. x is the number of_iDenotes the ith test specimen, w_iRepresenting the weight of the ith test sample, T representing the number of adjacent spectra in hyperspectral space, M representing the number of classes of objects, S_MIs X in the A_MSparse vectors under each training sample. And S is a sparse matrix consisting of sparse vectors. w is a_iThe weights of the different spectra. thr is a parameter to determine whether the adjacent spectrum is valid. For x₁And x_iThe correlation coefficient between them is not less than the spectrum of thr, and we consider that they are very similar to the central test spectrum, so they are valid spectra. Therefore, their weights are reset to 1. For x₁And x_iSpectra with a correlation coefficient smaller than thr are considered as invalid adjacent spectra, and therefore their weights are reset to 0.

Step (3) solving the sparse matrix

Given a training dictionary A, the matrix S can be solved by the joint sparse reconstruction problem of the following formula.

minimize||S||_row，0

subject to：AS＝X

Wherein the symbol | | S | | non-calculation_row，0Representing the number of non-zero rows in the sparse matrix S. Now it is required to

A sparse matrix of D × M consists of only a few non-zero rows. According to the actual situation, the influence of the error is considered

The solution of (c) can also be written in the form:

wherein | · | charging_FRepresenting the Frobenius norm. σ denotes its error margin, K₀The number of non-zero elements is expressed by the limitation of the sparsity condition. As with sparse representation reconstruction of a single spectrum, the problem of solving weighted combined sparse representation is also an NP-Hard problem, and the problem of sparse reconstruction can be solved through a combined orthogonal matching pursuit (SOMP) algorithm.

Step (4), spectrum classification

Once the sparse matrix S is solved, we can calculate all classes to train the dictionary and get the reconstruction error of x. Then the error of x reconstructed by the training dictionary for the mth class of objects is:

and representing the optimal solution of the sparse matrix obtained by the mth class of training dictionary. The final classification result for x is then the type of object for which the reconstruction error is the smallest, i.e.:

wherein r is_m(x) Representing sparse representation of test samples x and x in an m-th class object

The smaller the value, the closer x is to the M-th class object. The results are shown in FIG. 5.

In conclusion, the method provided by the invention greatly solves the phenomenon that the mixed spectrum and the foreign matter are in the same spectrum in the traditional sparse representation classification of the plant hyperspectral image, also greatly improves the problem that the spectrum at the junction of different objects in the joint sparse representation classification is difficult to classify, and provides great support for the development of high-precision plant hyperspectral image classification in the future.

Claims (1)

1. A canopy plant hyperspectral image classification method based on sparse representation is characterized by comprising the following steps:

step (1) data preprocessing

1.1 obtaining hyperspectral images of plants to be classified

1.2 spectral unitization:

performing unitization processing on each spectrum in the plant hyperspectral image;

1.3 dividing training samples and testing samples:

in the step 1.2, 15% of the hyperspectral image data subjected to unitization processing in the sample containing M types of ground objects is used as a training sample A, and the rest 85% are used as test samples;

where the matrix size of a is D x N,

N_mrepresenting the number of spectra of the m-th type of feature; a. the_mDictionary of size DxN representing sample composition of m-th class of objects_m；

Is the Nth of the mth class object_mStrip spectrum

α_mRepresenting a sparse matrix consisting of all sparse coefficients corresponding to the mth class of object training samples, wherein the matrix only contains a few nonzero values;

step (2) establishing a weighted joint sparse model

Assuming adjacent hyperspectral spectra x_iAnd x_jAre composed of different objects;

x_ifrom the constructed dictionary A_iExpressed as:

x_i＝A_iα_i

x_jfrom a constructed dictionary A_jExpressed as:

x_j＝A_jα_j

assuming adjacent spectra N_εContaining T spectra, let X ═ w₁x₁ w₂x₂ … w_Tx_T]Is a D × T matrix, where { x_t}_t＝1,…T∈N_εFor hyperspectral space adjacent spectra, so X can be expressed as:

X＝[w₁x₁ w₂x₂ … w_Tx_T]＝[A₁S₁ A₂S₂ … A_MS_M]

＝[A₁ A₂ … A_M][S₁ S₂ … S_M]＝AS

wherein x₁For the spectrum currently to be classified, x₂…x_TIs given by x₁Adjacent spectra within a centered square region; w is a_iRepresenting the weight of the ith spectrum, T representing the number of adjacent spectrums in hyperspectral space, M representing the number of classes of objects, S_MIs X in the A_MSparse vectors under a training dictionary; s is a sparse matrix composed of sparse vectors; thr is a threshold for determining whether the adjacent spectra are valid;

step (3) solving the sparse matrix

Given a training dictionary A, a matrix S can be obtained by a joint sparse reconstruction problem of the following formula;

minimize ||S||_row,0

subjectto:AS＝X

wherein the symbol | | S | | non-calculation_row,0Representing the number of non-zero rows in the sparse matrix S; optimal solution of S

The DxM sparse matrix is composed of only a few non-zero rows; according to the actual situation, the influence of the error is considered

The solution of (c) can also be written in the form:

wherein | · | purple_FRepresents a Frobenius norm; σ denotes its error margin, K₀The number of non-zero elements is expressed by expressing the limitation of the sparse condition; and withThe reconstruction of the sparse representation of the single spectrum is the same, the problem of solving the weighted combined sparse representation is also an NP-Hard problem, and the problem of solving the sparse reconstruction can be solved through a combined orthogonal matching pursuit algorithm;

step (4), spectrum classification

Calculating all category training dictionaries to obtain a reconstruction error of x by solving a sparse matrix S; then the error of x reconstructed by the training dictionary for the mth class of objects is:

representing the optimal solution of the sparse matrix obtained by the mth class of training dictionary; the final classification result for x is then the type of object for which the reconstruction error is the smallest, i.e.:

wherein r is_m(x) Representing sparse representation of test samples x and x in an m-th class object

The two norms of (a).

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