CN110992245B - Hyperspectral image dimension reduction method and device - Google Patents

Abstract

The application discloses a hyperspectral image dimension reduction method and device. The hyperspectral image dimension reduction method comprises the following steps: acquiring a neighborhood sub-cube f of a pixel in a hyperspectral image I to be processed using a sliding kernel _i The method comprises the steps of carrying out a first treatment on the surface of the For each acquired neighborhood sub-cube f _i Performing dimension reduction processing to obtain a neighborhood hyperspectral image of each neighborhood subcube after dimension reductionAccording to the spatial position of each neighborhood subcube in the hyperspectral image, the neighborhood hyperspectral image of each neighborhood subcubeRearranging to obtain hyperspectral image after dimension reductionAccording to the technical scheme, when the dimension of the hyperspectral image is reduced, the linear dynamic system feature model is combined with the sparse feedback optimization technology, so that the wave bands with large information quantity and good class separability in the hyperspectral image are extracted, the classification precision of the hyperspectral image is improved, and meanwhile, the calculated amount of hyperspectral image classification is reduced.

Description

A hyperspectral image dimensionality reduction method and device

technical field

The present application relates to the field of dimensionality reduction of hyperspectral images, in particular to a method and device for dimensionality reduction of hyperspectral images.

Background technique

Accurate classification of hyperspectral images plays an important role in industrial, agricultural, and aerospace applications, and can be applied to many practical applications such as precision agriculture, environmental mapping, social security, mineral exploration, and biological and chemical detection.

However, the spectral dimension of hyperspectral images is high and there is a strong statistical correlation between spectral bands, resulting in redundant information, high computational complexity, and ultimately low classification accuracy, which restricts the application of hyperspectral remote sensing images. Image dimensionality reduction can weaken or eliminate the correlation between spectral bands, improve the distinguishability of pixels, reduce the amount of calculation, and thus improve the classification accuracy of remote sensing images. Therefore, it is necessary to propose an effective dimensionality reduction method to reduce the band dimension while retaining sufficient spectral information.

Existing hyperspectral image dimensionality reduction methods mainly include feature extraction methods based on mathematical transformations and feature selection methods based on band selection. For feature extraction methods based on mathematical transformations, there are mainly: Principal Component Analysis, Minimum Noise Fraction Rotation, and Nonlinear Manifold Learning; for feature selection methods based on band selection, for example, band combinations with large amounts of information, good category separability, or low correlation can be selected.

However, the existing dimensionality reduction methods for hyperspectral images ignore the spatial structure information of hyperspectral images, and the methods are computationally intensive. At the same time, the process of manually setting parameters and selecting thresholds affects the classification accuracy.

How to make up for the above deficiencies in the prior art when reducing the dimensionality of hyperspectral images, there is no relevant solution in the prior art.

Contents of the invention

In order to solve the above technical problems, this application provides a hyperspectral image dimensionality reduction method, which can improve the classification accuracy of hyperspectral images, and at the same time reduce the calculation amount of hyperspectral image classification, and solve the problems that existing hyperspectral image dimensionality reduction requires manual participation and does not make full use of the spatial structure information of hyperspectral images.

In order to achieve the purpose of this application, this application provides a hyperspectral image dimensionality reduction method, including the following steps:

Use the sliding core to obtain the neighboring cube F _I of the pixel I in the high spectrum image I to be processed. Among them, the size of i is m × n × k. M represents the number of space rows of the high spectrum image, n represents the number of space columns of the high spectral image, and K represents the number of spectral dimensions of the high spectrum image. Strange number, the value of i is not greater than MIN (m-w+1, n-w+1), the size of F _i is W × W × K;

Perform dimensionality reduction processing on each of the acquired neighborhood sub-cubes _fi , and obtain neighborhood hyperspectral images of each neighborhood sub-cube after dimensionality reduction

According to the spatial position of each neighborhood sub-cube in the hyperspectral image, the neighborhood hyperspectral image of each neighborhood sub-cube Rearrange to obtain the hyperspectral image after dimensionality reduction />

Further, performing dimensionality reduction processing on each of the acquired neighborhood sub-cubes _fi , and obtaining neighborhood hyperspectral images of each neighborhood sub-cube after dimensionality reduction Including the following steps:

Obtaining the matrix M _i obtained after tiling the respective neighborhood sub-cubes fi, wherein the size of the matrix M _i is k×s, where s= _w ×w;

Decomposing the matrix M _i , and establishing a linear dynamic system model (A _i , B _i , C _i ) of the neighborhood sub-cube according to the result of the decomposition processing;

Acquire the sparse matrix of matrix C i according to the matrix A _{i and} matrix B _i in the linear dynamic system model (A _i , B _i , C _i )

For the sparse matrix Perform normalization processing, and obtain the neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction according to the normalization processing result

Further, wherein, said decomposing the matrix M _i includes the following steps:

Using the singular value decomposition SDV to decompose the matrix M _i through the following formula, the decomposed matrix U _i , matrix Λ _i and matrix V _i are obtained:

M _i = U _i Λ _i V _i ^T ;

Wherein, the size of the matrix U _i is k×s and U _i ^T ×U _i =I, the size of the matrix V _i and the matrix Λ _i is s×s, V _i ^T ×V _i =I;

The establishment of the linear dynamic system model (A _i , B _i , C _i ) of the neighborhood sub-cube according to the decomposition processing results includes the following steps:

Using the matrix U _i , the matrix Λ _i and the matrix V _i to establish the linear dynamic system model (A _i , B _i , C _i ) of the neighborhood sub-cube, specifically:

C _i =U _i

Among them, X _i =Λ _i V _i ^T ;

When calculating B _i , first calculate Then use the formula G _i = U' _i Λ' _i V' _i to decompose the matrix G _i to get U' _i and Λ' _i , and then calculate B _i ;

Among them, the size of the matrix A _i is s×s, the matrix _Xi is the system state variable matrix, and its size is s×s, Indicates extracting the 1 to s rows and 2 to s columns of the matrix X _i , /> means extracting the rows 1 to s and columns 1 to s-1 of the matrix _Xi , Indicates the first column of the extraction matrix U′ _i , /> Represents the element in the first row and the first column of the extraction matrix Λ' _i .

Further, the sparse matrix of matrix C _i is obtained according to the matrix A _i and matrix B _i in the linear dynamic system model (A _i , B _i , C _i ) Including the following steps:

Using Lyapunov stability conditions and sparsity assumptions, the matrix is obtained by the following equation and sparse matrix /> The optimal solution of the equation is the matrix and the sparse matrix />

||Y _i || _col →min,

in,

Calculation matrix

The sparse matrix by the matrix /> with the sparse matrix /> It consists of the rows corresponding to the column indexes that are not 0.

Further, the pair of the sparse matrix Perform normalization processing, including the following steps:

build zero matrix will matrix /> fill each row in the matrix /> , fill the position for the row in the matrix /> The row index in the padded /> That is, for the sparse matrix /> The normalized processing result after the normalized processing is performed;

The neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction is obtained according to the normalization processing result Including the following steps:

The neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction is obtained by the following formula

The present application also provides a hyperspectral image dimensionality reduction device, including:

The neighborhood sub-cube acquisition module is configured to use the sliding kernel to acquire the neighborhood sub-cube f _i of the pixels in the hyperspectral image I to be processed, wherein the size of I is m×n×k, m represents the number of spatial rows of the hyperspectral image, n represents the number of spatial columns of the hyperspectral image, k represents the spectral dimension of the hyperspectral image, the size of the sliding kernel is w×w, w is an odd number greater than 1, and the value of i is a positive integer not greater than min(m-w+1, n-w+1) , the size of f _i is w×w×k;

The neighborhood hyperspectral image generation module is configured to perform dimensionality reduction processing on each of the acquired neighborhood sub-cubes _fi to obtain the neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction

The neighborhood hyperspectral image rearrangement module is configured to, according to the spatial position of each neighborhood sub-cube in the hyperspectral image, the neighborhood hyperspectral image of each neighborhood sub-cube Rearrange to obtain the hyperspectral image after dimensionality reduction />

Further, the neighborhood hyperspectral image generation module includes:

The neighborhood sub-cube matrix generating module is configured to obtain the matrix M _i obtained after tiling each neighborhood sub-cube f _i , wherein the size of the matrix M _i is k×s, where s=w×w;

A linear dynamic system model building module, configured to decompose the matrix M _i , and establish a linear dynamic system model (A _i , B _i , C _i ) of the neighborhood sub-cube according to the decomposition processing result;

The sparse matrix acquisition module is configured to acquire the sparse matrix of matrix C _i according to the matrix A _i and matrix B _i in the linear dynamic system model (A _i , B _i , C _i )

Sparse matrix processing module, set to process the sparse matrix Perform normalization processing, and obtain the neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction according to the normalization processing result

Further, said decomposing the matrix M _i includes:

Using the singular value decomposition SDV to decompose the matrix M _i through the following formula, the decomposed matrix U _i , matrix Λ _i and matrix V _i are obtained:

M _i = U _i Λ _i V _i ^T ;

Wherein, the size of the matrix U _i is k×s and U _i ^T ×U _i =I, the size of the matrix V _i and the matrix Λ _i is s×s, V _i ^T ×V _i =I;

The establishment of the linear dynamic system model (A _i , B _i , C _i ) of the neighborhood sub-cube according to the decomposition processing results includes:

Using the matrix U _i , the matrix Λ _i and the matrix V _i to establish the linear dynamic system model (A _i , B _i , C _i ) of the neighborhood sub-cube, specifically:

C _i =U _i

Among them, X _i =Λ _i V _i ^T ;

When calculating B _i , first calculate Then use the formula G _i = U' _i Λ' _i V' _i to decompose the matrix G _i to get U' _i and Λ' _i , and then calculate B _i ;

Among them, the size of the matrix A _i is s×s, the matrix _Xi is the system state variable matrix, and its size is s×s, Indicates extracting the 1 to s rows and 2 to s columns of the matrix X _i , /> means extracting the rows 1 to s and columns 1 to s-1 of the matrix _Xi , Indicates the first column of the extraction matrix U′ _i , /> Represents the element in the first row and the first column of the extraction matrix Λ' _i .

Further, the sparse matrix acquisition module is specifically set as:

Using Lyapunov stability conditions and sparsity assumptions, the matrix is obtained by the following equation and sparse matrix /> The optimal solution of the equation is the matrix and the sparse matrix />

||Y _i || _col →min,

in,

Calculation matrix

The sparse matrix by the matrix /> with the sparse matrix /> It consists of the rows corresponding to the column indexes that are not 0.

Further, the sparse matrix processing module is specifically set to:

build zero matrix will matrix /> fill each row in the matrix /> , fill the position for the row in the matrix /> The row index in the padded /> That is, for the sparse matrix /> The normalized processing result after the normalized processing is performed;

The neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction is obtained according to the normalization processing result include:

The neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction is obtained by the following formula

Compared with the prior art, the hyperspectral image dimensionality reduction method in the present application includes: using the sliding kernel to obtain the neighborhood sub-cube _fi of the pixel in the hyperspectral image I to be processed; performing dimensionality reduction processing on each acquired neighborhood sub-cube _fi , and obtaining the neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction According to the spatial position of each neighborhood sub-cube in the hyperspectral image, the neighborhood hyperspectral image of each neighborhood sub-cube/> Rearrange to obtain the hyperspectral image after dimensionality reduction /> In the technical solution provided by this application, when reducing the dimensionality of hyperspectral images, the linear dynamic system feature model combined with sparse feedback optimization technology is used to extract the bands with large amount of information and good category separability in hyperspectral images, thereby improving the classification accuracy of hyperspectral images and reducing the calculation amount of hyperspectral image classification.

Description of drawings

The accompanying drawings are used to provide a further understanding of the technical solution of the present application, and constitute a part of the specification, and are used together with the embodiments of the present application to explain the technical solution of the present application, and do not constitute a limitation to the technical solution of the present application. In the attached picture:

Fig. 1 is the processing flowchart of hyperspectral image dimensionality reduction method in the present application;

FIG. 2 is a schematic structural diagram of a hyperspectral image dimensionality reduction device in the present application;

The realization, functional features and advantages of the present application will be further described in conjunction with the embodiments and with reference to the accompanying drawings.

Detailed ways

It should be understood that the specific embodiments described here are only used to explain the present application, and are not intended to limit the present application.

In order to make the purpose, technical solution and advantages of the present application clearer, the present invention will be described in detail below in conjunction with the accompanying drawings. It should be noted that, in the case of no conflict, the features in this application can be combined with each other arbitrarily.

Fig. 1 is the processing flowchart of hyperspectral image dimensionality reduction method in the present application, as shown in Fig. 1, comprises the following steps:

Step 101: Using the sliding kernel to obtain the neighborhood sub-cube f _i of the pixel in the hyperspectral image I to be processed;

Specifically, in this step, the spatial domain rigid partition method is adopted. In the hyperspectral image I, the sliding kernel is used to slide horizontally and vertically in the entire spatial domain of the image, thereby defining the spatial local neighborhood range of each pixel. The hyperspectral image is divided into neighborhood subcubes, which retain all the spectral information associated with each pixel; where the size of I is m×n×k, m represents the number of spatial rows of the hyperspectral image, n represents the number of spatial columns of the hyperspectral image, and k represents the spectral dimension of the hyperspectral image. The size of the sliding kernel is w×w, w is an odd number greater than 1, and the obtained neighborhood sub-cube is expressed as f_i, the value of i is a positive integer not greater than min(m-w+1,n-w+1), f_iThe size of is w×w×k;

Here, w can be defined as an odd number within the range of 3-21.

Step 102: Perform dimensionality reduction processing on each of the acquired neighborhood sub-cubes _fi , and obtain neighborhood hyperspectral images of each neighborhood sub-cube after dimensionality reduction

Specifically, this step can be divided into the following sub-steps:

Step 1021: Obtain the matrix M _i obtained after tiling each neighborhood sub-cube fi, wherein the size of the matrix _{M i is} k×s, where s=w×w;

Specifically, the neighborhood sub-cube f _i is tiled into a matrix along the direction of the spectral dimension, that is, each pixel in the neighborhood sub-cube is extracted as a column to form a matrix M _i .

Step 1022: Decompose the matrix M _i , and establish a linear dynamic system model (A _i , B _i , C _i ) of the neighborhood sub-cube according to the result of the decomposition process;

Specifically, in this step, the singular value decomposition SDV is first used to decompose the matrix M _i through the formula (1), and the decomposed matrix U _i , matrix Λ _i and matrix V _i are obtained:

M _i = U _i Λ _i V _i ^T (1)

Wherein, the size of matrix U _i is k×s and U _i ^T ×U _i =I, the size of matrix V _i and matrix Λ _i is s×s, V _i ^T ×V _i =I;

Among them, singular value decomposition is an important matrix decomposition method in linear algebra and matrix theory, which is suitable for signal processing and statistics and other fields.

After that, the linear dynamic system model (A _i , B _i , C _i ) of the neighborhood sub-cube is established according to the decomposition processing results, including:

Using the matrix U _i , matrix Λ _i and matrix V _i to establish the linear dynamic system model (A _i , B _i , C _i ) of the neighborhood sub-cube, specifically: first use the following formula (2) to calculate the model parameters A _i and C _i ,

The size of the matrix A _i in the formula (2) is s×s, the matrix _Xi is the system state variable matrix, and its size is s×s, Represents the 1 to s rows and 2 to s columns of the extraction matrix X _i , /> Represents the 1 to s rows and 1 to s-1 columns of the extraction matrix X _i , /> Indicates the first column of the extraction matrix U′ _i , /> Represents the element in the first row and the first column of the extraction matrix Λ'_i;

Then use the following formula (3) to obtain the matrix B _i using the calculation results of the matrices A _i and X _i :

It should be noted that when calculating _Bi , first calculate G _i through A _i and _Xi , and then decompose G _i to get U′ _i , Λ′ _i and V′ _i , so as to obtain matrix B _i , where, Indicates the first column of the extraction matrix U′ _i , /> Represents the element in the first row and the first column of the extraction matrix Λ' _i .

Step 1023: Obtain the sparse matrix of matrix C _i according to the matrix A _i and matrix B _i in the linear dynamic system model (A _i , B _i , C _i )

This step is to use sparse state feedback constraints to automatically find bands with a large amount of information.

When the linear dynamic system model (A _i , B _i , C _i ) matrix calculated in the above step 1022 is used to represent the neighborhood sub-cube hyperspectral image, the original neighborhood sub-cube hyperspectral image is described as the system output variable y _i =C _i X _i , where _Xi is the system state variable matrix with a size of s×s, which is calculated from the formula (2); therefore, to obtain the dimension-reduced neighborhood sub-cube hyperspectral image Need to obtain the sparse matrix of the output matrix C _i /> Specific steps are as follows:

Step 1. Establishment of the Lyapunov stability condition based on the sparse state feedback system;

For the original system model (A _i , B _i , C _i ) adopt state feedback to form a closed-loop system, the feedback matrix is K _i , and the system model is (A _i -B _i K _i , B _i , C _i ), according to the Lyapunov stability principle, if there is a positive definite symmetric matrix P _i that satisfies the formula (4), then the closed-loop system matrix A _i -B _i K _i is stable;

Multiply the left and right sides of formula (4) by P _i ^-1 and sort them out to get formula (5),

Let the matrix P _i ^-1 =W _i , and The size of the matrix W _i is k×k, and Y _i =K _i W is set at the same time, and formula (5) is arranged to obtain the Lyapunov stability condition as described in formula (6):

Step 2, the sparsity of matrix C _i is determined;

||C _i || _col → min (7)

in, Equation (7) represents the column sparse representation of matrix C _i ;

Step 3, using convex function optimization to obtain the sparsity matrix C _i ;

According to the formula (8), the matrix can be obtained and sparse matrices /> and/> There is a column with all 0 in it, and then calculate Finally get the sparse matrix /> for the matrix /> in and /> The row composition corresponding to the column index that is not 0.

Step 1024: To the sparse matrix Perform normalization processing, and obtain the neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction according to the normalization processing result

Since the convex function optimization method is an automatic solution process, there is no artificial setting of parameters, and the obtained by step 1023 The dimensionality of the pixels is different, resulting in different spectral dimensions between pixels after dimensionality reduction; moreover, even if the spectral dimensions between pixels are the same, but the spectral information comes from different bands, the comparison calculation between pixels cannot be performed and the image classification processing cannot be realized. Therefore, after the data dimensionality reduction is completed, normalization processing is required.

Specifically, the normalization processing method is: find the matrix obtained in step 1023 The sum of each column, let /> Indicates the maximum value of the sum of each column, the matrix /> The value of the column sum is less than /> Set the column of σ to 0, where the value range of σ is 0<σ<0.5, write down the column index that is not 0; at this time, the sparse matrix /> for the matrix /> Composition of rows corresponding to the above indexes in will matrix /> fill the rows in the matrix /> , fill the position for the row in the matrix /> The row index in the padded /> That is, for the sparse matrix /> The normalized processing result after normalization processing; calculate the neighborhood sub-cube pixels /> Complete pixel normalization, and finally realize automatic dimension reduction of hyperspectral images.

Step 103: According to the spatial position of each neighborhood sub-cube in the hyperspectral image, the neighborhood hyperspectral image of each neighborhood sub-cube Rearrange to obtain the hyperspectral image after dimensionality reduction />

Use step 102 to obtain the dimensionality reduction result of each neighborhood sub-cube According to the spatial position of each neighborhood sub-cube in the original whole hyperspectral image I will /> Rearrange them together to finally obtain the dimensionality-reduced hyperspectral remote sensing image/>

Compared with the prior art, the beneficial effects of the present application are:

(1) This application effectively makes full use of spatial and spectral information, establishes an integrated feature model based on a linear dynamic system model, and more accurately and effectively realizes dimensionality reduction of hyperspectral images;

(2) This application establishes a linear dynamic integrated feature model of hyperspectral images, effectively utilizes sparse feedback technology, fully considers the overall relationship between spatial and spectral features in hyperspectral images, uses convex function optimization and constraints to retain spectral information with large amount of information and strong separability, weakens or even deletes redundant spectral information, and realizes automatic dimensionality reduction of hyperspectral remote sensing images;

(3) This application has more practical application value and demand for improving the classification accuracy of hyperspectral images, reducing the calculation amount of hyperspectral image classification methods, and improving the application level of hyperspectral images in the fields of industry, agriculture and aerospace.

FIG. 2 is a schematic structural diagram of a hyperspectral image dimensionality reduction device in the present application. As shown in Figure 2, the hyperspectral image dimensionality reduction device includes:

The neighborhood sub-cube acquisition module is configured to use the sliding kernel to acquire the neighborhood sub-cube f _i of the pixels in the hyperspectral image I to be processed, wherein the size of I is m×n×k, m represents the number of spatial rows of the hyperspectral image, n represents the number of spatial columns of the hyperspectral image, k represents the spectral dimension of the hyperspectral image, the size of the sliding kernel is w×w, w is an odd number greater than 1, and the value of i is a positive integer not greater than min(m-w+1, n-w+1) , the size of f _i is w×w×k;

The neighborhood hyperspectral image generation module is configured to perform dimensionality reduction processing on each of the acquired neighborhood sub-cubes _fi to obtain the neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction

The neighborhood hyperspectral image rearrangement module is configured to, according to the spatial position of each neighborhood sub-cube in the hyperspectral image, the neighborhood hyperspectral image of each neighborhood sub-cube Rearrange to obtain the hyperspectral image after dimensionality reduction />

Specifically, the neighborhood hyperspectral image generation module includes:

The neighborhood sub-cube matrix generating module is configured to obtain the matrix M _i obtained after tiling each neighborhood sub-cube f _i , wherein the size of the matrix M _i is k×s, where s=w×w;

A linear dynamic system model building module, configured to decompose the matrix M _i , and establish a linear dynamic system model (A _i , B _i , C _i ) of the neighborhood sub-cube according to the decomposition processing result;

The sparse matrix acquisition module is configured to acquire the sparse matrix of matrix C _i according to the matrix A _i and matrix B _i in the linear dynamic system model (A _i , B _i , C _i )

Sparse matrix processing module, set to process the sparse matrix Perform normalization processing, and obtain the neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction according to the normalization processing result

Wherein, the decomposing process on the matrix M _i includes:

Using the singular value decomposition SDV to decompose the matrix M _i through the following formula, the decomposed matrix U _i , matrix Λ _i and matrix V _i are obtained:

M _i = U _i Λ _i V _i ^T ;

Wherein, the size of the matrix U _i is k×s and U _i ^T ×U _i =I, the size of the matrix V _i and the matrix Λ _i is s×s, V _i ^T ×V _i =I;

The establishment of the linear dynamic system model (A _i , B _i , C _i ) of the neighborhood sub-cube according to the decomposition processing result includes:

Using the matrix U _i , the matrix Λ _i and the matrix V _i to establish the linear dynamic system model (A _i , B _i , C _i ) of the neighborhood sub-cube, specifically:

C _i =U _i

Among them, X _i = Λ _i V _i ^T ;

When calculating B _i , first calculate Then use the formula G _i = U' _i Λ' _i V' _i to decompose the matrix G _i to get U' _i and Λ' _i , and then calculate B _i ;

Among them, the size of the matrix A _i is s×s, the matrix _Xi is the system state variable matrix, and its size is s×s, Indicates extracting the 1 to s rows and 2 to s columns of the matrix X _i , /> means extracting the rows 1 to s and columns 1 to s-1 of the matrix _Xi , Indicates the first column of the extraction matrix U′ _i , /> Represents the element in the first row and the first column of the extraction matrix Λ' _i .

Specifically, the sparse matrix acquisition module is specifically set to:

Using Lyapunov stability conditions and sparsity assumptions, the matrix is obtained by the following equation and sparse matrix /> The optimal solution of the equation is the matrix and the sparse matrix />

||Y _i || _col →min,

in,

Calculation matrix

The sparse matrix by the matrix /> with the sparse matrix /> It consists of the rows corresponding to the column indexes that are not 0.

Specifically, the sparse matrix processing module is specifically set to:

build zero matrix will matrix /> fill the rows in the matrix /> , fill the position for the row in the matrix /> The row index in the padded /> That is, for the sparse matrix /> The normalized processing result after the normalized processing is performed;

The neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction is obtained according to the normalization processing result include:

The neighborhood hyperspectral image of each neighborhood sub-cube after dimensionality reduction is obtained by the following formula

It should be noted that, in this document, the term "comprising", "comprising" or any other variation thereof is intended to cover a non-exclusive inclusion, such that a process, method, article or device comprising a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such a process, method, article or device. Without further limitations, an element defined by the phrase "comprising a ..." does not preclude the presence of additional identical elements in the process, method, article, or apparatus comprising that element.

The serial numbers of the above embodiments of the present application are for description only, and do not represent the advantages and disadvantages of the embodiments.

Through the description of the above embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus a necessary general-purpose hardware platform, and of course also by hardware, but in many cases the former is a better implementation. Based on such an understanding, the technical solution of the present application can be embodied in the form of a software product in essence or the part that contributes to the prior art. The computer software product is stored in a storage medium (such as ROM/RAM, magnetic disk, optical disk), and includes several instructions to make a terminal device (which can be a mobile phone, computer, server, air conditioner, or network equipment, etc.) execute the method described in each embodiment of the application.

Although the embodiments disclosed in the present invention are as above, the described content is only an embodiment adopted for understanding the present invention, and is not intended to limit the present invention. Any person skilled in the field of the present invention, without departing from the spirit and scope disclosed by the present invention, can make any modifications and changes in the form and details of the implementation, but the patent protection scope of the present invention must still be based on the scope defined in the appended claims.

The above are only optional embodiments of the present application, and do not limit the patent scope of the present application. Any equivalent structure or equivalent process conversion made by using the description of the application and the contents of the accompanying drawings, or directly or indirectly used in other related technical fields, are all included in the scope of patent protection of the present application.

Claims (6)

1. The hyperspectral image dimension reduction method is characterized by comprising the following steps of:

acquiring a neighborhood sub-cube f of a pixel in a hyperspectral image I to be processed using a sliding kernel _i Wherein the size of I is m multiplied by n multiplied by k, m represents the number of spatial lines of the hyperspectral image, n represents the number of spatial columns of the hyperspectral image, k represents the spectral dimension of the hyperspectral image, the size of the sliding kernel is w multiplied by w, w is an odd number greater than 1, the value of I is a positive integer not greater than min (m-w+1, n-w+1), f _i Is w×w×k;

for each acquired neighborhood sub-cube f _i Performing dimension reduction processing to obtain a neighborhood hyperspectral image of each neighborhood subcube after dimension reduction

According to the spatial position of each neighborhood subcube in the hyperspectral image, the neighborhood hyperspectral image of each neighborhood subcubeRearranging to obtain the hyperspectral image +.>

Wherein the pair of acquired respective neighborhood subcubes f _i Performing dimension reduction processing to obtain a neighborhood hyperspectral image of each neighborhood subcube after dimension reductionThe method comprises the following steps:

acquiring each neighborhood subcube f _i Matrix M obtained after tiling _i Wherein the matrix M _i Is k×s, where s=w×w;

for the matrix M _i Performing decomposition processing, and establishing a linear dynamic system model (A) of the neighborhood subcube according to the decomposition processing result _i ,B _i ,C _i )；

According to the linear dynamic system model (A _i ,B _i ,C _i ) In said matrix A _i Sum matrix B _i Acquisition matrix C _i Is a sparse matrix of (2)

For the sparse matrixCarrying out normalization processing, and obtaining the neighborhood hyperspectral image ++of each neighborhood subcubes after dimension reduction according to the normalization processing result>

Wherein said pair of said matrices M _i The decomposing treatment is carried out, which comprises the following steps:

decomposing the SDV with singular values to the matrix M by the following formula _i Decomposing to obtain a decomposed matrix U _i Matrix lambda _i Sum matrix V _i ：

M _i ＝U _i Λ _i V _i ^T ；

Wherein the matrix U _i Is k x s and U _i ^T ×U _i =i, the matrix V _i And the matrix lambda _i Is s x s, V _i ^T ×V _i ＝I；

The linear dynamic system model (A) of the neighborhood subcube is built according to the decomposition processing result _i ,B _i ,C _i ) The method comprises the following steps:

by using the matrix U _i The matrix lambda _i And the matrix V _i A linear dynamic system model (A _i ,B _i ,C _i ) The method specifically comprises the following steps:

C _i ＝U _i

wherein X is _i ＝Λ _i V _i ^T ；

In calculation B _i When first calculateThen utilize formula G _i ＝U _i 'Λ' _i V _i ' decomposition matrix G _i Obtaining U' _i Sum Λ'. _i Thereby calculating to obtain B _i ；

Wherein matrix A _i Is s X s, matrix X _i Is a system state variable matrix, the size of which is s x s,representing extraction of the matrix X _i 1 to s rows and 2 to s columns, < ->Representing extraction of the matrix X _i 1 to s rows and 1 to s-1 columns,/->Representing an extraction matrix U _i ' column 1>Representing the extraction matrix Λ' _i 1 st row 1 st column element of (c).

2. The method according to claim 1, characterized in that the method according to the linear dynamic system model (a _i ,B _i ,C _i ) In said matrix A _i Sum matrix B _i Acquisition matrix C _i Is a sparse matrix of (2)Comprising the following steps:

matrix is obtained by using Lyapunov stabilization condition and sparsity assumption condition through the following equationAnd sparse matrix->The optimal solution of the equation is the matrix +.>And the sparse matrix->

||Y _i || _col →min,

s.t.A _i W _i +W _i A _i ^T -B _i Y _i -Y _i ^T B _i ^T ＜0

Wherein W is _i ＞0,W _i ＝W _i ^T ；

Computing a matrix

The sparse matrixFrom the matrix->Is equal to the sparse matrix->A row corresponding to a column index of not 0.

3. The method of claim 2, wherein the pair of sparse matricesThe normalization processing is carried out, which comprises the following steps:

establishing a zero matrixMatrix->Is filled into the matrix +.>The filled position is the row in the matrix +.>Row index of (2), filled +.>Namely +.>Normalization processing results after normalization processing;

obtaining the neighborhood hyperspectral image of each neighborhood subcube after dimension reduction according to the normalization processing resultThe method comprises the following steps:

obtaining the neighborhood hyperspectral image of each neighborhood subcube after dimension reduction through the following formula

4. A hyperspectral image dimension reduction device, comprising:

a neighborhood subcube acquisition module configured to acquire a neighborhood subcube f of a pixel in the hyperspectral image I to be processed using a sliding kernel _i Wherein the dimension of I is m multiplied by n multiplied by k, m represents the number of spatial lines of the hyperspectral image, and n represents the heightThe number of spatial columns of the spectral image, k represents the spectral dimension of the hyperspectral image, the size of the sliding kernel is w×w, w is an odd number greater than 1, i is a positive integer not greater than min (m-w+1, n-w+1), f _i Is w×w×k;

a neighborhood hyperspectral image generation module configured to generate, for each acquired neighborhood subcube f _i Performing dimension reduction processing to obtain a neighborhood hyperspectral image of each neighborhood subcube after dimension reduction

A neighborhood hyperspectral image rearrangement module configured to rearrange neighborhood hyperspectral images of the respective neighborhood subcubes according to spatial positions of the respective neighborhood subcubes in the hyperspectral imagesRearranging to obtain the hyperspectral image +.>

The neighborhood hyperspectral image generation module comprises:

a neighborhood subcube matrix generation module configured to obtain the neighborhood subcubes f _i Matrix M obtained after tiling _i Wherein the matrix M _i Is k×s, where s=w×w;

a linear dynamic system model building module configured to build the matrix M _i Performing decomposition processing, and establishing a linear dynamic system model (A) of the neighborhood subcube according to the decomposition processing result _i ,B _i ,C _i )；

A sparse matrix acquisition module arranged to acquire a sparse matrix based on the linear dynamic system model (A _i ,B _i ,C _i ) In said matrix A _i Sum matrix B _i Acquisition matrix C _i Is a sparse matrix of (2)

A sparse matrix processing module configured to process the sparse matrixCarrying out normalization processing, and obtaining the neighborhood hyperspectral image ++of each neighborhood subcubes after dimension reduction according to the normalization processing result>

Wherein said pair of said matrices M _i Performing decomposition processing, including:

decomposing the SDV with singular values to the matrix M by the following formula _i Decomposing to obtain a decomposed matrix U _i Matrix lambda _i Sum matrix V _i ：

M _i ＝U _i Λ _i V _i ^T ；

Wherein the matrix U _i Is k x s and U _i ^T ×U _i =i, the matrix V _i And the matrix lambda _i Is s x s, V _i ^T ×V _i ＝I；

The linear dynamic system model (A) of the neighborhood subcube is built according to the decomposition processing result _i ,B _i ,C _i ) Comprising:

by using the matrix U _i The matrix lambda _i And the matrix V _i A linear dynamic system model (A _i ,B _i ,C _i ) The method specifically comprises the following steps:

C _i ＝U _i

wherein X is _i ＝Λ _i V _i ^T ；

In calculation B _i When first calculateThen utilize formula G _i ＝U _i 'Λ' _i V _i ' decomposition matrix G _i Obtaining U' _i Sum Λ'. _i Thereby calculating to obtain B _i ；

Wherein matrix A _i Is s X s, matrix X _i Is a system state variable matrix, the size of which is s x s,representing extraction of the matrix X _i 1 to s rows and 2 to s columns, < ->Representing extraction of the matrix X _i 1 to s rows and 1 to s-1 columns,/->Representing the extraction matrix U' _i ' column 1>Representing the extraction matrix Λ' _i 1 st row 1 st column element of (c).

5. The apparatus of claim 4, wherein the sparse matrix acquisition module is specifically configured to:

matrix is obtained by using Lyapunov stabilization condition and sparsity assumption condition through the following equationAnd sparse matrix->The optimal solution of the equation is the matrix +.>And the sparse matrix->

||Y _i || _col →min,

s.t.A _i W _i +W _i A _i ^T -B _i Y _i -Y _i ^T B _i ^T ＜0

Wherein W is _i ＞0,W _i ＝W _i ^T ；

Computing a matrix

The sparse matrixFrom the matrix->Is equal to the sparse matrix->A row corresponding to a column index of not 0.

6. The apparatus of claim 5, wherein the sparse matrix processing module is specifically configured to:

establishing a zero matrixMatrix->Is filled into the matrix +.>The filled position is the row in the matrix +.>Row index of (2), filled +.>Namely +.>Normalization processing results after normalization processing;

obtaining the neighborhood hyperspectral image of each neighborhood subcube after dimension reduction according to the normalization processing resultComprising the following steps:

obtaining the neighborhood hyperspectral image of each neighborhood subcube after dimension reduction through the following formula