A band selection method for hyperspectral images based on grouping sparsity

Abstract

The present invention discloses a hyperspectral image band selection method based on group sparsity, and the method comprises the following steps: step 1, constructing a group sparse prior regularization; step 2, constructing a labeled indicator matrix; step 3, band selection of the hyperspectral image. The band selection method proposed in the present invention is a method that can be used to select important bands in a hyperspectral image. The method can effectively remove the bands that are severely affected by noise in the hyperspectral image, and at the same time can completely retain the important information in the original hyperspectral image. After the band selection method proposed in the present invention is used to select the bands of the hyperspectral image, the performance of the downstream classification task can be further improved. Therefore, the present invention has the characteristics of strong practical application value and good reliability, and is suitable for popularization and use. The present invention can provide a certain theoretical analysis basis for the further analysis and application of hyperspectral images by relevant professionals.

Description

Technical Field

[0001] The present invention belongs to the research field of remote sensing technology and relates to a band selection method for a hyperspectral image, and specifically to a method for removing noise bands of a hyperspectral image to further improve the performance of downstream hyperspectral classification tasks. Background Art

[0002] Remote sensing technology originated in the late 1960s and has been continuously developed over the past century. Remote sensing technology is a comprehensive earth observation technology that uses electromagnetic radiation as a medium of interaction to obtain data from a target at a long distance without directly contacting the target or area being studied, and analyzes the acquired data to obtain the required information. With the continuous advancement of remote sensing technology, in the early 1980s, people organically combined spectral technology with imaging technology, developed the first generation of imaging spectrometers, and gradually formed a new remote sensing technology with high spectral resolution-hyperspectral remote sensing technology. Hyperspectral remote sensing technology can use many very narrow electromagnetic bands to obtain relevant information from objects of interest. It can image in the ultraviolet, visible light, near-infrared and mid-infrared regions of the electromagnetic spectrum, and its images contain dozens to hundreds of very narrow continuous bands. Since the obtained hyperspectral images can be used to identify different substances with small spectral differences, they are widely used in various fields, such as land cover mapping, coastal land monitoring, precision agriculture and mineral exploration.

[0003] However, the high dimensionality of hyperspectral image bands and the strong correlation between bands usually lead to the "Seuss phenomenon" and high computational costs. In addition, during the acquisition process, hyperspectral images are disturbed by factors such as illumination, acquisition conditions, and the equipment itself, which usually causes some bands in the image to contain a lot of noise. The occurrence of these phenomena has greatly limited the further application of hyperspectral images. Band selection of hyperspectral images is an effective way to solve the above problems. Band selection refers to selecting some discriminative bands from the original hyperspectral image to represent the original image, which can physically retain the information of the original image and make the hyperspectral image after dimensionality reduction more interpretable. Since the different wavelength ranges of hyperspectral images can represent the unique attribute information of different substances, there are certain grouping characteristics between different bands in the image. Imposing grouping sparsity constraints on the bands of hyperspectral images is conducive to the correct selection of bands, thereby further improving the accuracy of downstream tasks such as hyperspectral image classification. Summary of the invention

[0004] Based on the fact that the bands of hyperspectral remote sensing images have the characteristic of group sparseness, the present invention provides a hyperspectral image band selection method based on group sparsity. The method imposes l on the projection selection matrix in the band selection model. 2,1-norm constraint, which can effectively characterize the grouping sparse characteristics of hyperspectral image bands, thus helping to obtain more accurate band index information. Then, based on the ADMM algorithm framework, the band selection model is optimized and solved to obtain a projection matrix with band selection effect, so that the projection selection matrix can be used to further perform effective band selection for hyperspectral images.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A hyperspectral image band selection method based on grouping sparsity includes the following steps:

[0007] Step 1: Construct a group sparse prior regularization:

[0008] Step 1.1: Given the input hyperspectral image X = [x 1 ,L,x d ]∈R m×d , where m is the number of bands of the input hyperspectral image, and d is the number of pixels with labels;

[0009] Step 1.2, matrix P = [p 1 ,L,p m ]∈R k×m Represents a projection selection matrix containing k category labels, grouping them into sparse projection regularization constraints The following formula is defined as:

[0010]

[0011] Among them, ||·|| 2,1 l represents the matrix 2,1 -norm;

[0012] Step 2: Construct a labeled indicator matrix:

[0013] Step 2.1, matrix Z = [z 1 ,L,z d ]∈R k×d Represents an indicator matrix containing k category labels, each component z j ∈{0,1} k It is represented by one-hot encoding;

[0014] Step 2.2: If the i-th pixel x in the hyperspectral image X contains a label i belongs to the jth category among the k categories, then z i The jth element of is 1 and the other elements are all 0, z i is further expressed as:

[0015] z i=[0,L,0,1,0,L0] T ∈R k

[0016] Among them, component 1 is z i The position of the jth element in ;

[0017] Step 3: Band selection of hyperspectral image:

[0018] Step 3.1, calculate the projection selection matrix:

[0019] In the tth iteration of band selection, the projection selection matrix P is calculated as follows:

[0020] P t+1 =(ZX T +μ(U t -V t ))(XX T +μI) -1

[0021] Among them, the superscript T represents the transpose operation of the matrix, the superscript -1 represents the matrix inversion operation, the matrix I represents the unit matrix of size m×m, the matrix U is the auxiliary variable, the matrix V represents the Lagrangian multiplier, and the parameter μ is the penalty parameter;

[0022] Step 3.2, calculate auxiliary variables:

[0023] In the tth iteration of band selection, the auxiliary variable U is calculated as follows:

[0024]

[0025] Among them, the function vsoft(·) is the soft threshold function of the vector;

[0026] Step 3.3, update the Lagrangian multiplier:

[0027] During the tth iteration of band selection, the Lagrangian multiplier V is updated as follows:

[0028] V t+1 =V t +P t+1 -U t+1

[0029] Step 3.4, termination condition of the algorithm:

[0030] When the number of iterations of the above band selection process t = Q or the algorithm reaches convergence, the iteration is terminated and the matrix P is output t+1 , otherwise go to step 3.1 to continue execution; when the iteration stops according to step 3.4, the output Pt+1 That is, it is a projection selection matrix with band selection effect;

[0031] Step 3.5, calculate the importance of each column of the projection selection matrix:

[0032] Let vector The index vector for band selection, each component of which ||p j || 2 is defined by:

[0033]

[0034] in, represents the square operation of all elements in the jth column of the projection selection matrix P. The bands corresponding to the indices of the first r largest components in are regarded as the important bands selected in the hyperspectral image X, and r is the number of selected bands input.

[0035] Compared with the prior art, the present invention has the following advantages:

[0036] 1. The band selection method proposed in the present invention is a method that can be used to select important bands in hyperspectral images. This method can effectively remove the bands in the hyperspectral images that are more seriously affected by noise, and at the same time can completely retain the important information in the original hyperspectral images.

[0037] 2. The method of the present invention can perform dimensionality reduction processing on the original hyperspectral image, so that the hyperspectral image after dimensionality reduction has the same interpretability as the original image, and at the same time can reduce the computational cost of subsequent hyperspectral image processing tasks to a certain extent.

[0038] 3. After the band selection method proposed in the present invention is used to select the bands of the hyperspectral image, the performance of the downstream classification task can be further improved. Therefore, the present invention has the characteristics of strong practical application value and good reliability, and is suitable for promotion and use.

[0039] 4. The present invention can provide certain theoretical analysis basis for further analysis and application of hyperspectral images for relevant professionals. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Flow chart of the hyperspectral image band selection method based on group sparsity;

[0041] Figure 2 Spectral curves of four substances extracted from the hyperspectral image in the Kamalan River Basin, wherein (a) represents the spectral curve of the original image, and (b) represents the spectral curve after band selection using the method of the present invention;

[0042] Figure 3 The classification map obtained by directly classifying the hyperspectral images in the Kamalan River Basin area using the hyperspectral classification methods SAM and RF;

[0043] Figure 4 In order to first select the bands of the hyperspectral images in the Kamalan River basin area using the band selection method of the present invention, and then further apply the hyperspectral classification methods SAM and RF to classify the hyperspectral images after band selection to obtain a classification map. DETAILED DESCRIPTION

[0044] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0045] The present invention provides a hyperspectral image band selection method based on grouping sparsity, such as Figure 1 As shown, the method comprises the following steps:

[0046] Step 1: Construct a group sparse prior regularization:

[0047] Step 1.1: Given the input hyperspectral image X = [x 1 ,L,x d ]∈R m×d , where m is the number of bands of the input hyperspectral image, and d is the number of pixels with labels;

[0048] Step 1.2, matrix P = [p 1 ,L,p m ]∈R k×m Represents a projection selection matrix containing k category labels, grouping them into sparse projection regularization constraints The following formula is defined as:

[0049]

[0050] Among them, ||·|| 2,1 l represents the matrix 2,1 -norm can be defined as:

[0051]

[0052] Among them, ||p i || 2 It describes the importance of the i-th column in the projection selection matrix P and corresponds to only one band in the hyperspectral image X, so the above regularization constraint With band selection effect.

[0053] Step 2: Construct a labeled indicator matrix:

[0054] Step 2.1, matrix Z = [z 1 ,L,z d ]∈R k×d Represents an indicator matrix containing k category labels, each component z j ∈{0,1} k It is represented by one-hot encoding;

[0055] Step 2.2: If the i-th pixel x in the hyperspectral image X contains a label i belongs to the jth category among the k categories, then z i The jth element of is 1 and the other elements are all 0, z i It can be further expressed as:

[0056] z i =[0,L,0,1,0,L0] T ∈R k

[0057] Among them, component 1 is z i The position of the jth element in .

[0058] Step 3: Band selection of hyperspectral image:

[0059] Step 3.1, calculate the projection selection matrix:

[0060] In the tth iteration of band selection, the projection selection matrix P is calculated as follows:

[0061] P t+1 =(ZX T +μ(U t -V t ))(XX T +μI) -1

[0062] Among them, the superscript T represents the transpose operation of the matrix, the superscript -1 represents the matrix inversion operation, the matrix I represents the unit matrix of size m×m, the matrix U is the auxiliary variable, the matrix V represents the Lagrangian multiplier, and the parameter μ is the penalty parameter;

[0063] Step 3.2, calculate auxiliary variables:

[0064] In the tth iteration of band selection, the auxiliary variable U is calculated as follows:

[0065]

[0066] Among them, the function vsoft(·) is the soft threshold function of the vector, and its generalized expression is defined as:

[0067]

[0068] where max(·) represents the maximization function, ||·|| 2 l represents the vector 2 -norm, x is the input variable of the vsoft function, and θ represents the threshold of the vsoft function;

[0069] Step 3.3, update the Lagrangian multiplier:

[0070] During the tth iteration of band selection, the Lagrangian multiplier V is updated as follows:

[0071] V t+1 =V t +P t+1 -U t+1

[0072] Step 3.4, termination condition of the algorithm:

[0073] When the number of iterations of the above band selection process t = Q (Q is the maximum number of iterations of the algorithm) or the algorithm reaches convergence, the iteration is terminated and the matrix P is output. t+1 , otherwise go to step 3.1 to continue execution; when the iteration stops according to step 3.4, the output P t+1 That is, it is a projection selection matrix with band selection effect;

[0074] Step 3.5, calculate the importance of each column of the projection selection matrix:

[0075] Let vector The index vector for band selection, each component of which ||p j || 2 is defined by:

[0076]

[0077] in, represents the square operation of all elements in the jth column of the projection selection matrix P, so The bands corresponding to the indices of the first r largest components in can be regarded as the important bands selected in the hyperspectral image X, and r is the number of selected bands input.

[0078] Example:

[0079] The present invention provides a hyperspectral image band selection method based on grouping sparsity, the method comprising the following steps:

[0080] Step 1: Construct a group sparse prior regularization:

[0081] In the process of constructing the group sparse prior regularization, the relevant parameters are set as follows:

[0082] The number of bands of the input hyperspectral image is m = 150;

[0083] The number of pixels with labels is d = 500;

[0084] The number of categories containing labeled pixels k=5.

[0085] Step 2: Construct a labeled indicator matrix

[0086] In the process of constructing the labeled indicator matrix, the relevant parameters are set as follows:

[0087] The number of bands of the input hyperspectral image is m = 150;

[0088] The number of pixels with labels is d = 500;

[0089] The number of categories containing labeled pixels k = 5;

[0090] Step 3: Band selection of hyperspectral image

[0091] In the process of band selection of hyperspectral images, the relevant parameters of the algorithm and the method of variable initialization are set as follows:

[0092] The input selected band number r = 118;

[0093] The number of categories containing labeled pixels k = 5;

[0094] The number of bands of the input hyperspectral image is m = 150;

[0095] The regularization parameter of the band selection algorithm is λ = 0.01;

[0096] The penalty parameter of the band selection algorithm is μ = 0.01;

[0097] The maximum number of iterations of the band selection algorithm is Q = 500;

[0098] Lagrangian multiplier V 0 Initialize to a full zero matrix of size k×m;

[0099] Auxiliary variable U 0 Initialize to U 0 =rand(k,m), where rand function is the random generation function in matlab.

[0100] In order to verify the effectiveness of the band selection method proposed in the present invention, this embodiment verifies the effectiveness of band selection based on the downstream hyperspectral classification task. Two classic classification algorithms are used for experiments, namely spectral angle mapper (SAM) and random forest (RF). The data set used for the experiment is a hyperspectral image in the Kamalan River Basin area acquired by a DJI M600 Pro drone equipped with a Resonon Pika L model hyperspectral imager. The data set contains 500×500 pixels, each pixel consists of 150 bands, and the image contains 5 end members.

[0101] In the experiment, ENVI 5.3 was first used to extract the spectral curves of four types of objects from the original hyperspectral image, such as Figure 2 As shown in (a). It can be clearly seen from the figure that the bands of the hyperspectral images collected by the drone contain a lot of noise, which will seriously affect the accuracy of the downstream classification task. For this reason, the band selection method of the present invention is used to select the bands of the data set. The corresponding spectral curve after band selection is shown in Figure 2 As shown in (b), it can be seen from the figure that the band selection of the hyperspectral image using the method of the present invention can further remove the band containing noise in the image and retain the original important information of the data.

[0102] In addition, in order to further verify the effectiveness of the present invention, the classification methods are used to verify the classification accuracy of the original image and the image after band selection. The classification performance of the classification methods in the original image and the image after band selection is quantitatively analyzed and compared by using the classification accuracy of each category, the overall classification accuracy (OA) and the Kappa coefficient. The classification diagrams obtained by the SAM and RF methods are shown in Figure 2. Figure 3 and Figure 4 As shown in Table 1, the quantitative classification results show that the classification accuracy after band selection using the method of the present invention is significantly improved. This experiment further confirms the effectiveness of the method proposed in the present invention.

[0103] Table 1 Classification accuracy of each classification method for hyperspectral images in the Kamalan River Basin with or without band selection

[0104]

[0105]

Claims

1. A hyperspectral image band selection method based on group sparsity, characterized in that The method comprises the following steps: Step 1: Construct a group sparse prior regularization: Step 1.1: Given the input hyperspectral image X = [x1,…,x d ]∈R m×d , where m is the number of bands of the input hyperspectral image, and d is the number of pixels with labels; Step 1.2, matrix P = [p1,…,p m ]∈R k×m Represents a projection selection matrix containing k category labels, grouping them into sparse projection regularization constraints The following formula is defined as: Among them, ||·|| 2,1 l represents the matrix 2,1 -norm; Step 2: Construct a labeled indicator matrix: Step 2.1, matrix Z = [z1,…,z d ]∈R k×d Represents an indicator matrix containing k category labels, each component z j ∈{0,1} k It is represented by one-hot encoding; Step 2.2: If the i-th pixel x in the hyperspectral image X contains a label i belongs to the jth category among the k categories, then z i The jth element of is 1 and the other elements are all 0, z i is further expressed as: With i =[0,…,0,1,0,…0] T ∈R k Among them, component 1 is z i The position of the jth element in ; Step 3: Band selection of hyperspectral image: Step 3.1, calculate the projection selection matrix: In the tth iteration of band selection, the projection selection matrix P is calculated as follows: P t+1 =(ZX T +μ(U t -V t ))(XX T +μI) -1 Among them, the superscript T represents the transpose operation of the matrix, the superscript -1 represents the matrix inversion operation, the matrix I represents the unit matrix of size m×m, the matrix U is the auxiliary variable, the matrix V represents the Lagrangian multiplier, and the parameter μ is the penalty parameter; Step 3.2, calculate auxiliary variables: In the tth iteration of band selection, the auxiliary variable U is calculated as follows: Among them, the function vsoft(·) is the soft threshold function of the vector; Step 3.3, update the Lagrangian multiplier: During the tth iteration of band selection, the Lagrangian multiplier V is updated as follows: V t+1 =V t +P t+1 -U t+1 Step 3.4, termination condition of the algorithm: When the number of iterations of the above band selection process t = Q or the algorithm reaches convergence, the iteration is terminated and the matrix P is output t+1 , Q is the maximum number of iterations of the algorithm, otherwise go to step 3.1 to continue execution; when the iteration stops according to step 3.4, the output P t+1 That is, it is a projection selection matrix with band selection effect; Step 3.5, calculate the importance of each column of the projection selection matrix: Let vector The index vector for band selection, each component of which ||p j ||2 is defined as: in, represents the square operation of all elements in the jth column of the projection selection matrix P. The bands corresponding to the indices of the first r largest components in are regarded as the important bands selected in the hyperspectral image X, and r is the number of selected bands input.

2. The hyperspectral image band selection method based on grouping sparsity according to claim 1 is characterized in that In step 1.2, Among them, ||p i ||2 describes the importance of the i-th column in the projection selection matrix P and corresponds to only one band in the hyperspectral image X.

3. The hyperspectral image band selection method based on grouping sparsity according to claim 1 is characterized in that In step 3.2, the expression of function vsoft(·) is defined as: Where max(·) represents the maximization function, ||·||2 represents the l2-norm of the vector, x is the input variable of the vsoft function, and θ represents the threshold of the vsoft function.

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