CN110781974A - Dimension reduction method and system for hyperspectral image - Google Patents

Dimension reduction method and system for hyperspectral image Download PDF

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CN110781974A
CN110781974A CN201911050720.8A CN201911050720A CN110781974A CN 110781974 A CN110781974 A CN 110781974A CN 201911050720 A CN201911050720 A CN 201911050720A CN 110781974 A CN110781974 A CN 110781974A
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张焕芹
张嘉伟
毛士杰
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Science And Technology Ltd Of Upper Hiroad Army
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Abstract

The invention discloses a dimension reduction method and a dimension reduction system for a hyperspectral image, wherein the method comprises the following steps: according to an input hyperspectral image sample set D ═ { x ═ x 1,x 2,...x mH, k nearest neighbor number and d dimensionality reduced to, the sum x is calculated iNearest k nearest neighbors (x) i1,x i2,...x ik) (ii) a Computing a local covariance matrix Z of a hyperspectral image sample set D i(ii) a According to the local covariance matrix Z iCalculating its weight coefficient vector W i(ii) a According to the weight coefficient vector W iForming a weight coefficient matrix W, and obtaining a matrix according to W calculation: m ═ I (I-W) T(ii) a D +1 eigenvalues in front of the matrix M and eigenvectors { y corresponding to the d +1 eigenvalues are calculated according to the matrix M 1,y 2,...y d+1And forming a matrix which is the matrix D' ═ y of the output low-dimensional hyperspectral image sample set according to the second eigenvector to the (D + 1) th eigenvector 2,y 3,...y d+1}. The system comprises: nearest neighbor calculation module and local covariance matrixThe device comprises a calculation module, a weight coefficient vector calculation module, a matrix M calculation module and a low-order hyperspectral image sample set matrix calculation module. The method can reduce the dimension of the hyperspectral image through smaller operation complexity, and has ideal processing effect.

Description

Dimension reduction method and system for hyperspectral image
Technical Field
The invention relates to the technical field of hyperspectral image processing, in particular to a dimension reduction method and system for a hyperspectral image.
Background
The dimension reduction processing of the hyperspectral image is an important research subject in the field of hyperspectral image processing. As is known, a hyperspectral image is a three-dimensional image data cube which has abundant spectral information and spatial information and can better analyze subtle differences among different ground objects. However, the original hyperspectral image contains hundreds of wave bands, the data volume is large, and a large amount of redundant information is contained, which brings great difficulty and influence to subsequent target anomaly detection and other work.
At present, the conventional processing method is wave band selection and feature extraction aiming at the problem of dimension reduction processing of hyperspectral images. The correlation among the wave bands selected by the wave band selection method is weak, the information content in the image can be well reserved, but compared with the characteristic extraction method, the energy carried by the processed image with the original signal is less.
The existing algorithm also realizes the dimension reduction of the hyperspectral image by finding the idea of the global optimal solution of all samples, and when the data volume is large or the sample dimension is high, the calculated amount is very large and the operation time is long; many pieces of information with certain correlation in the original hyperspectral image are recombined into a group of new mutually-independent information to replace the original information, but the obtained dimensionality reduction result cannot reflect the hidden nonlinear property between sample points, and the estimation of the number of the reserved principal components is still difficult.
Disclosure of Invention
The invention provides a dimension reduction method and system for a hyperspectral image, aiming at the problems in the prior art, the dimension reduction can be performed on the hyperspectral image through smaller operation complexity, and the processing effect is ideal.
In order to solve the technical problems, the invention is realized by the following technical scheme:
the invention provides a dimension reduction method of a hyperspectral image, which comprises the following steps:
s11: according to an input hyperspectral image sample set D ═ { x ═ x 1,x 2,...x mH, k nearest neighbor number and d dimensionality reduced to, the sum x is calculated iNearest k nearest neighbors (x) i1,x i2,...x ik)；
S12: computing a local covariance matrix Z of a hyperspectral image sample set D i；
S13: according to the local covariance matrix Z calculated in the S12 iCalculating its weight coefficient vector W i；
S14: the weight coefficient vector W calculated according to the S13 iForming a weight coefficient matrix W, and obtaining a matrix according to W calculation: m ═ I (I-W) T；
S15: d +1 eigenvalues in front of the matrix M and eigenvectors { y corresponding to the d +1 eigenvalues are calculated according to the matrix M 1,y 2,...y d+1And forming a matrix which is the matrix D' ═ y of the output low-dimensional hyperspectral image sample set according to the second eigenvector to the (D + 1) th eigenvector 2,y 3,...y d+1}。
Preferably, the sum x in S11 is calculated iNearest k nearest neighbors (x) i1,x i2,...x ik) The method specifically comprises the following steps: distance in Europe as a measure, calculating the sum x iNearest k nearest neighbors (x) i1,x i2,...x ik)。
Preferably, the local covariance matrix Z in S12 iThe formula of (1) is: z i＝(x i-x j)(x i-x j) T。
Preferably, the method for calculating the weight coefficient vector in S13 is: solving a weight coefficient W of an m multiplied by k dimension corresponding to the minimized loss function, taking the positions of the W which are not in the neighborhood positions as 0, and expanding the W to the m multiplied by m dimension; the formula of the minimization loss function is:
Figure BDA0002255271830000021
preferably, the weight coefficient vector W in S13 iThe formula of (1) is:
wherein 1 is kRepresenting a k-dimensional all-1 vector.
The invention also provides a dimension reduction system of the hyperspectral image, which comprises the following components: the system comprises a nearest neighbor calculation module, a local covariance matrix calculation module, a weight coefficient vector calculation module, a matrix M calculation module and a low-order hyperspectral image sample set matrix calculation module; wherein,
the nearest neighbor calculation module is used for calculating a nearest neighbor according to an input hyperspectral image sample set D ═ x 1,x 2,...x mH, k nearest neighbor number and d dimensionality reduced to, the sum x is calculated iNearest k nearest neighbors (x) i1,x i2,...x ik)；
The local covariance matrix calculation module is used for calculating a local covariance matrix Z of a hyperspectral image sample set D i；
The weight coefficient vector calculation module is used for calculating a local covariance matrix Z according to the local covariance matrix calculated by the local covariance matrix calculation module iCalculating its weight coefficient vector W i；
The matrix M calculation module is used for calculating a weight coefficient vector W according to the weight coefficient vector calculated by the weight coefficient vector calculation module iForming a weight coefficient matrix W, and obtaining a matrix according to W calculation: m ═ I (I-W) T；
The low-level hyperspectral image sample set matrix calculation module is used for calculating d +1 characteristic values in front of the matrix M and characteristic vectors { y) corresponding to the d +1 characteristic values according to the matrix M 1,y 2,...y d+1And forming a matrix which is the matrix D' ═ y of the output low-dimensional hyperspectral image sample set according to the second eigenvector to the (D + 1) th eigenvector 2,y 3,...y d+1}。
Preferably, the sum of computations in the nearest neighbor computation module x iNearest k nearest neighbors (x) i1,x i2,...x ik) The method specifically comprises the following steps: distance in Europe as a measure, calculating the sum x iNearest k nearest neighbors (x) i1,x i2,...x ik)。
Preferably, the local covariance matrix Z in the local covariance matrix calculation module iThe formula of (1) is: z i＝(x i-x j)(x i-x j) T。
Preferably, the method for calculating the weight coefficient vector in the weight coefficient vector calculation module is: solving a weight coefficient W of an m multiplied by k dimension corresponding to the minimized loss function, taking the positions of the W which are not in the neighborhood positions as 0, and expanding the W to the m multiplied by m dimension; the formula of the minimization loss function is:
preferably, the weight coefficient vector W in the weight coefficient vector calculation module iThe formula of (1) is:
Figure BDA0002255271830000041
wherein 1 is kRepresenting a k-dimensional all-1 vector.
Compared with the prior art, the invention has the following advantages:
(1) the dimension reduction method and system of the hyperspectral image provided by the invention calculate the first d +1 eigenvalues of the matrix M and eigenvectors { y corresponding to the d +1 eigenvalues 1,y 2,...y d+1Forming a matrix from the second eigenvector to the (d + 1) th eigenvector, reducing the dimension of the hyperspectral image through smaller operation complexity, and achieving ideal processing effect;
(2) the dimension reduction method and system of the hyperspectral image provided by the invention calculate the local covariance matrix Z iAnd its weight coefficient vector W iThe mean square error loss function is minimized, so that a good linear relation can be kept after dimension reduction.
Of course, it is not necessary for any product in which the invention is practiced to achieve all of the above-described advantages at the same time.
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Embodiments of the invention are further described below with reference to the accompanying drawings:
FIG. 1 is a flow chart of a dimension reduction method for hyperspectral images according to an embodiment of the invention;
FIG. 2 is a band 1 image after the dimension reduction of the airport area in the AVIRIS hyperspectral image according to the embodiment of the invention;
FIG. 3 is a band 5 image after the dimension reduction of the airport area in the AVIRIS hyperspectral image according to the embodiment of the invention;
FIG. 4 is a band 10 image after the dimension reduction of the airport area in the AVIRIS hyperspectral image according to the embodiment of the invention;
FIG. 5 is a band 1 image after dimensionality reduction of an Urban region in a HYDICE hyperspectral image according to an embodiment of the invention;
FIG. 6 is a band 5 image after dimensionality reduction of an Urban region in a HYDICE hyperspectral image according to an embodiment of the invention;
fig. 7 is a band 10 image after dimensionality reduction of an Urban region in a hyper-spectral image according to an embodiment of the present invention.
Detailed Description
The following examples are given for the detailed implementation and specific operation of the present invention, but the scope of the present invention is not limited to the following examples.
Fig. 1 is a schematic flow chart of a dimension reduction method for a hyperspectral image according to an embodiment of the invention.
Referring to fig. 1, the dimension reduction method for the hyperspectral image of the embodiment includes the following steps:
s11: according to an input hyperspectral image sample set D ═ { x ═ x 1,x 2,...x mH, k nearest neighbor number and d dimensionality reduced to, the sum x is calculated iNearest k nearest neighbors (x) i1,x i2,...x ik)；
S12: computing a local covariance matrix Z of a hyperspectral image sample set D i；
S13: according to the local covariance matrix Z calculated in S12 iComputingObtain its weight coefficient vector W i；
S14: the weight coefficient vector W calculated from S13 iForming a weight coefficient matrix W, and obtaining a matrix according to W calculation: m ═ I (I-W) T；
S15: d +1 eigenvalues in front of the matrix M and eigenvectors { y corresponding to the d +1 eigenvalues are calculated according to the matrix M 1,y 2,...y d+1And forming a matrix which is the matrix D' ═ y of the output low-dimensional hyperspectral image sample set according to the second eigenvector to the (D + 1) th eigenvector 2,y 3,...y d+1}。
In one embodiment, S11 specifically includes: inputting a hyperspectral image sample set D ═ x 1,x 2,...x mCalculating the sum x by using Euclidean distance as a measure, wherein the nearest neighbor number k and the dimensionality d obtained by dimensionality reduction are from i to 1 to i to m iNearest k nearest neighbors (x) i1,x i2,...x ik)。
In one embodiment, S12 specifically includes: computing a local covariance matrix Z of a hyperspectral image sample set D i＝(x i-x j)(x i-x j) T。
In one embodiment, S13 specifically includes: after dimensionality reduction, it is desirable that the linear relationship be maintained in the lower dimension. Let n-dimensional sample set { x 1,x 2,...x mThe low-dimensional corresponding projection in dimension d is y 1,y 2,...y mAre expected to maintain a linear relationship, i.e., the corresponding mean square error loss function is expected to be minimal, minimizing the loss function J (y) as
Figure BDA0002255271830000061
The formula is almost the same as the high-dimensional loss function, but in the high-dimensional formula, the high-dimensional data is known, and the aim is to solve the weight coefficient W of the m × k dimension corresponding to the minimized loss function, take the positions of W which are not in the neighborhood positions to be 0, and expand W to the m × m dimension.
In one embodiment, the weight coefficient vector W in S13 iThe expression of (a) is:
wherein 1 is kRepresenting a k-dimensional all-1 vector.
The invention also provides a dimension reduction system of a hyperspectral image, which is used for realizing the dimension reduction method in the embodiment and comprises the following steps: the device comprises a nearest neighbor calculation module, a local covariance matrix calculation module, a weight coefficient vector calculation module, a matrix M calculation module and a low-order hyperspectral image sample set matrix calculation module. The nearest neighbor calculation module is used for calculating a nearest neighbor according to an input hyperspectral image sample set D ═ x 1,x 2,...x mH, k nearest neighbor number and d dimensionality reduced to, the sum x is calculated iNearest k nearest neighbors (x) i1,x i2,...x ik). The local covariance matrix calculation module is used for calculating a local covariance matrix Z of the hyperspectral image sample set D i. The weight coefficient vector calculation module is used for calculating a local covariance matrix Z according to the local covariance matrix iCalculating its weight coefficient vector W i. The matrix M calculation module is used for calculating a weight coefficient vector W according to the weight coefficient vector calculated by the weight coefficient vector calculation module iForming a weight coefficient matrix W, and obtaining a matrix according to W calculation: m ═ I (I-W) T. The low-order hyperspectral image sample set matrix calculation module is used for calculating d +1 characteristic values in front of the matrix M and characteristic vectors { y corresponding to the d +1 characteristic values according to the matrix M 1,y 2,...y d+1And forming a matrix which is the matrix D' ═ y of the output low-dimensional hyperspectral image sample set according to the second eigenvector to the (D + 1) th eigenvector 2,y 3,...y d+1}。
In one embodiment, the sum of computations in the nearest neighbor computation module x iNearest k nearest neighbors (x) i1,x i2,...x ik) The method specifically comprises the following steps: distance in Europe as a measure, calculating the sum x iNearest k nearest neighbors (x) i1,x i2,...x ik)。
In one embodiment, the local covariance matrix Z in the local covariance matrix calculation module iThe formula of (1) is: z i＝(x i-x j)(x i-x j) T。
In one embodiment, the method for calculating the weight coefficient vector in the weight coefficient vector calculation module includes: solving a weight coefficient W of an m multiplied by k dimension corresponding to the minimized loss function, taking the positions of the W which are not in the neighborhood positions as 0, and expanding the W to the m multiplied by m dimension; the formula of the minimization loss function is:
Figure BDA0002255271830000071
in one embodiment, the weight coefficient vector W in the weight coefficient vector calculation module iThe formula of (1) is:
Figure BDA0002255271830000072
wherein 1 is kRepresenting a k-dimensional all-1 vector.
A simulation experiment is performed on the dimension reduction method of the above embodiment, and 6 images shown in fig. 2 to 7 are taken as an example, the input nearest neighbor number k set in the experiment is 20, the dimension d obtained by dimension reduction is 10, fig. 2 to 4 are respectively images of a band 1, a band 5 and a band 10 after the dimension reduction of an airport area in an AVRIS hyperspectral image, and fig. 5 to 7 are respectively images of a band 1, a band 5 and a band 10 after the dimension reduction of an Urban area in a HYDICE hyperspectral image.
As can be seen from the effect graph, the abnormal objects in the image processed by the method are obvious and can be well distinguished from the background, and the main objects such as the road and the like in the background are still clear and visible, so that the method has a good processing effect.
The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, and not to limit the invention. Any modifications and variations within the scope of the description, which may occur to those skilled in the art, are intended to be within the scope of the invention.

Claims (10)

1. A dimension reduction method for a hyperspectral image is characterized by comprising the following steps:
s11: according to an input hyperspectral image sample set D ═ { x ═ x 1,x 2,…x mH, k nearest neighbor number and d dimensionality reduced to, the sum x is calculated iNearest k nearest neighbors (x) i1,x i2,…x ik)；
S12: computing a local covariance matrix Z of a hyperspectral image sample set D i；
S13: according to the local covariance matrix Z calculated in the S12 iCalculating its weight coefficient vector W i；
S14: the weight coefficient vector W calculated according to the S13 iForming a weight coefficient matrix W, and obtaining a matrix according to W calculation: m ═ I (I-W) T；
S15: d +1 eigenvalues in front of the matrix M and eigenvectors { y corresponding to the d +1 eigenvalues are calculated according to the matrix M 1,y 2,…y d+1And forming a matrix which is the matrix D' ═ y of the output low-dimensional hyperspectral image sample set according to the second eigenvector to the (D + 1) th eigenvector 2,y 3,…y d+1}。
2. The dimension reduction method for hyperspectral images according to claim 1, wherein the sum x of the calculations in S11 iNearest k nearest neighbors (x) i1,x i2,…x ik) The method specifically comprises the following steps: distance in Europe as a measure, calculating the sum x iNearest k nearest neighbors (x) i1,x i2,…x ik)。
3. The dimension reduction method for hyperspectral images according to claim 1, wherein the local covariance matrix Z in S12 iThe formula of (1) is: z i＝(x i-x j)(x i-x j) T。
4. The dimension reduction method for the hyperspectral image according to claim 1, wherein the weight coefficient vector in S13 is calculated by: solving a weight coefficient W of an m multiplied by k dimension corresponding to the minimized loss function, taking the positions of the W which are not in the neighborhood positions as 0, and expanding the W to the m multiplied by m dimension; the formula of the minimization loss function is:
Figure FDA0002255271820000011
5. the dimension reduction method for hyperspectral images according to claim 4, wherein the weight coefficient vector W in S13 iThe formula of (1) is:
Figure FDA0002255271820000021
wherein 1 is kRepresenting a k-dimensional all-1 vector.
6. A dimension reduction system for hyperspectral images, comprising: the system comprises a nearest neighbor calculation module, a local covariance matrix calculation module, a weight coefficient vector calculation module, a matrix M calculation module and a low-order hyperspectral image sample set matrix calculation module; wherein,
the nearest neighbor calculation module is used for calculating a nearest neighbor according to an input hyperspectral image sample set D ═ x 1,x 2,…x mH, k nearest neighbor number and d dimensionality reduced to, the sum x is calculated iNearest k nearest neighbors (x) i1,x i2,...x ik)；
The local covariance matrix calculation module is used for calculating a local covariance matrix Z of a hyperspectral image sample set D i；
The weight coefficient vector calculation module is used for calculating a local covariance matrix Z according to the local covariance matrix calculated by the local covariance matrix calculation module iCalculating its weight coefficient vector W i；
The matrix M calculation module is used for calculating a vector according to the weight coefficientThe weight coefficient vector W calculated by the calculation module iForming a weight coefficient matrix W, and obtaining a matrix according to W calculation: m ═ I (I-W) T；
The low-level hyperspectral image sample set matrix calculation module is used for calculating d +1 characteristic values in front of the matrix M and characteristic vectors { y) corresponding to the d +1 characteristic values according to the matrix M 1,y 2,...y d+1And forming a matrix which is the matrix D' ═ y of the output low-dimensional hyperspectral image sample set according to the second eigenvector to the (D + 1) th eigenvector 2,y 3,...y d+1}。
7. The dimension reduction system for hyperspectral images according to claim 6, wherein the sum of computations in the nearest neighbor computation module x iNearest k nearest neighbors (x) i1,x i2,...x ik) The method specifically comprises the following steps: distance in Europe as a measure, calculating the sum x iNearest k nearest neighbors (x) i1,x i2,...x ik)。
8. The dimension reduction system for hyperspectral images according to claim 6, wherein the local covariance matrix Z in the local covariance matrix calculation module iThe formula of (1) is: z i＝(x i-x j)(x i-x j) T。
9. The dimension reduction system for hyperspectral images according to claim 6 is characterized in that the calculation method of the weight coefficient vector in the weight coefficient vector calculation module is as follows: solving a weight coefficient W of an m multiplied by k dimension corresponding to the minimized loss function, taking the positions of the W which are not in the neighborhood positions as 0, and expanding the W to the m multiplied by m dimension; the formula of the minimization loss function is:
10. the dimensionality reduction system of the hyperspectral image of claim 9,wherein the weight coefficient vector W in the weight coefficient vector calculation module iThe formula of (1) is:
wherein 1 is kRepresenting a k-dimensional all-1 vector.
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