CN108280486B - Hyperspectral image unmixing method based on end member cluster - Google Patents

Hyperspectral image unmixing method based on end member cluster Download PDF

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CN108280486B
CN108280486B CN201810104197.1A CN201810104197A CN108280486B CN 108280486 B CN108280486 B CN 108280486B CN 201810104197 A CN201810104197 A CN 201810104197A CN 108280486 B CN108280486 B CN 108280486B
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尹继豪
黄晨雨
罗晓燕
罗旭坤
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Abstract

A novel hyperspectral image unmixing method based on end member clusters achieves self-adaptive accurate unmixing of hyperspectral images through two steps of end member cluster extraction and end member cluster-based abundance inversion. The method comprises the following steps: (1) sparse representation based on a global image; (2) alternative end member screening based on voting; (3) constructing an end member cluster by extracting spectral shape characteristics; (4) constructing a block overcomplete dictionary; (5) traversing the whole image, and selecting the optimal end member based on block sparsity aiming at each pixel; (6) and performing abundance estimation by using a fully constrained least square method, and outputting end member cluster spectrum and abundance results. The method mainly aims at the problem of spectral variation existing in the hyperspectral image, can effectively reduce errors caused by the spectral variation, improves the unmixing precision, and meanwhile, the self-adaptability of the algorithm is strong due to the end member cluster extraction based on the image.

Description

Hyperspectral image unmixing method based on end member cluster
Technical Field
The invention relates to a novel hyperspectral image unmixing method based on an end member cluster, which can effectively reduce errors caused by spectral variation during unmixing through technical means and belongs to the field of remote sensing image processing.
Background
The hyperspectral remote sensing refers to a remote sensing technology with hyperspectral resolution, and the detected waveband covers spectral regions (0.4-2.5 μm) including ultraviolet, visible light, near infrared, middle infrared and thermal infrared with spectral resolution of nanometer level. The hyperspectral remote sensing can continuously and finely describe the spectrum of the ground object and has outstanding advantages in the aspects of exploration, detection and identification. The development potential of hyperspectral remote sensing is huge, and the hyperspectral remote sensing and imaging radar are considered as two most important technical breakthroughs in remote sensing technology together since the 20 th century and the 80 th generation. Since the 90 s of the 20 th century, hyperspectral remote sensing has gradually become the mainstream direction of international photoelectric remote sensing and the hot topic of remote sensing technology. China is one of a few countries in the world with independent autonomous hyperspectral remote sensing technology intellectual property rights. In recent years, the development of hyperspectral remote sensing technology is greatly supported by the nation, and a lot of scientific researchers have gained remarkable results in the research fields of resource investigation, environmental monitoring, engineering construction, agricultural identification, medical diagnosis and the like under the support of the tasks of 863 projects, national natural science fund and the like.
Under the limitation of the spatial resolution of a spectrometer and the influence of the diversity of ground feature distribution, one pixel in a hyperspectral image often contains various ground features, and the pixel is called as a mixed pixel. In contrast to mixed pixels, we refer to pixels that contain only one type of terrain as clear pixels, or end members, while in mixed pixels the percentage of each substance is referred to as abundance. The purpose of hyperspectral unmixing is to acquire the characteristic spectrum of the end member in the image and then calculate the proportion of each ground feature in the mixed image element. The hyperspectral unmixing can solve the problems of ground object distribution detection and material identification caused by mixing pixels, so that the hyperspectral unmixing plays an important role in theoretical research and application of hyperspectral remote sensing images.
The existing hyperspectral unmixing algorithm generally represents an end member by calculating or selecting a spectral curve. However, there are limitations to representing an end member with only one spectral curve. In one image, due to factors of uneven illumination, different mineral particle size distribution and different contained organic matters and impurities, the spectrum of the same substance is easy to have a spectrum variation phenomenon. Spectral variations cause variations in the spectral values, which in turn lead to unmixing errors. In order to solve the problem of spectrum variation in the hyperspectral unmixing process in a complex environment, the invention provides a brand-new efficient and accurate hyperspectral unmixing model by utilizing the concept of an end member cluster, namely, representing a substance by using a group of spectra and combining a sparse representation theoretical model.
Disclosure of Invention
Aiming at the spectrum variation phenomenon of an image, the invention designs a brand-new hyperspectral unmixing method, which has the core of the method that the end member cluster is constructed in a self-adaptive manner and unmixing is carried out based on the end member cluster, and unmixing errors caused by the spectrum variation phenomenon are weakened through the omnibearing expression of the end member cluster to the end member. The method can directly extract the end member cluster from the image and unmix the end member cluster without using a spectrum library as prior information, has strong adaptability and wide applicable environment, and can effectively improve the unmixing precision.
In order to achieve the purpose, the invention adopts the technical scheme that: a brand-new hyperspectral unmixing method mainly comprises the following steps: extracting alternative end members, constructing end member clusters and estimating abundance. The purpose of the alternative end member extraction is to find out points with the properties of end members from the image, wherein the variation spectrum of each end member is contained. The construction of end member clusters requires the aggregation of spectra of the same kind under the unsupervised condition, and the invention completes the accurate spectrum classification by extracting the shape characteristics of the spectra. And finally, on the basis of the extracted end member clusters, finding out the optimal matching spectral combination for each pixel to carry out abundance estimation.
The method flow related by the invention comprises the following steps: (1) sparse representation based on a global image; (2) alternative end member screening based on voting; (3) constructing an end member cluster by extracting spectral shape characteristics; (4) constructing a block overcomplete dictionary; (5) traversing the whole image, and selecting the optimal end member based on block sparsity aiming at each pixel; (6) and performing abundance estimation by using a fully constrained least square method, and outputting end member cluster spectrum and abundance results.
The process steps of the process are described in detail below.
(1) Sparse representation based on global images
A hyperspectral image X with m rows and n columns and l wave bands is given, wherein X is { X ═ X }1,x2,...,xi,...,xm×nIn which xi＝{xi1,xi2,...,xil}. Then, each pixel is sparsely represented by a matching pursuit method, and the pixel x is aimed atiIs constructed as
Figure GDA0002231967310000021
The number of the material types in the image, namely the number of the end members is k, and the sparsity in the sparse representation is also set to be k. Sparse expression is carried out by utilizing a matching pursuit method to obtain a sparse coefficient yiThe method comprises the following specific steps:
1) initialization residual r0＝xiSet of indices
Figure GDA0002231967310000022
Original subset
Figure GDA0002231967310000023
And the number of iterations t is 1.
2) Selecting the nearest to the residual, i.e. inner productMaximum atom, whose index λ is recordedtThen update the set of indices Λt＝Λt-1∪{λtAnd Atom set Atomt＝[Atomt-1；dλt]。
λt＝arg max|＜rt-1,Di＞| (1)
3) Obtaining estimated coefficients by a least squares problem and updating the residual rt
Figure GDA0002231967310000024
rt＝xi-εtAtomt(3)
4) Update t +1 and return to step 2) until the residual converges gradually or the iteration stops when t K.
5) Finally obtaining the sparse coefficient yi＝εt。
(2) Alternative end member screening based on voting
For pixel xiAnd its corresponding sparse coefficient yiWe find the sparse coefficient yiThe image comprises m × n pixels, namely m × n votes are cast, the number of votes obtained by each atom is accumulated, all atoms are sorted according to the votes, the number cn of alternative end members is calculated according to the number k of the end members, wherein cn is k × 5, the atom with cn before the number of votes is selected as the alternative end member, and an alternative end member set X is obtainedcand。
(3) End member cluster construction by extracting spectral shape features
In the step, the characteristic extraction is carried out on the alternative end members obtained in the step 2, so that the aim of accurately constructing an end member cluster is fulfilled. For a spectrum containing l bands
Figure GDA0002231967310000031
The spectrum is first cut into N spectra of length l0In which N ═ l/l0]. If l cannot be replaced by l0Dividing by the remaining wave length in the last part of the spectrumThe number of stages.
Figure GDA0002231967310000032
Then, a straight line is used for fitting each spectrum section, the slope of the straight line is extracted to represent the shape of the spectrum section, and then the slope vector of the whole curve is obtained
Figure GDA0002231967310000033
Least square fitting method for straight line fitting
Figure GDA0002231967310000034
That is, alternative end members X can be obtainedcandCharacteristic F ofcand＝[f1；f2；...；fc...；fcn]The features are then input into an unsupervised classifier to obtain k classes Fbundle＝[Fb1；Fb2...；Fbi；...；Fbk]. Then forming an end member cluster X by the corresponding alternative end members according to the classification resultbundle＝[Xb1；Xb2...；Xbi；...Xbk],Xbi＝[xh|fh∈Fbi]And outputs the result.
(4) Constructing a segmented overcomplete dictionary
For the obtained end member cluster Xbundle＝[Xb1；Xb2...；Xbi；...Xbk]Each block of the overcomplete dictionary consists of a cluster of end-members, i.e., D ═ Db1；Db2；...；Dbi；...；DbK],Dbi＝Xbi。
(5) Traversing the whole image, and selecting the optimal end member based on block sparsity for each pixel
For arbitrary pixel xiThe specific calculation steps are as follows:
1) initialization residual r0＝xiSet of indices
Figure GDA0002231967310000035
Terminal unit set
Figure GDA0002231967310000036
Dictionary D0And D, setting the iteration number t to be 1 and the iteration termination number K.
2) Finding the exponent λ in the whole dictionarytSo that it satisfies (6)
λt＝arg max|＜rt-1,Dt-1＞| (6)
Updating the set of indices Λt＝Λt-1∪{λt}, end member set
Figure GDA0002231967310000041
Dictionary
Figure GDA0002231967310000042
3) Solving the optimization problem in (7) by using least square method, and updating residual rt。
Figure GDA0002231967310000043
4) If the residual is less than the set threshold, the iteration is stopped, otherwise t +1 is increased and 2 is returned) until t K.
(6) And performing abundance estimation by using a fully constrained least square method, and outputting end member cluster spectrum and abundance results.
Drawings
FIG. 1 is a flow chart of a hyperspectral image unmixing method based on end member clusters.
FIG. 2 is a schematic diagram of curve shape feature extraction: a) is the original curve, b) is the extracted feature.
FIG. 3 is the lunar surface hyperspectral data and the results obtained after unmixing, a) is a schematic diagram of the processed image and its position on the lunar surface, b) is the obtained end-member cluster spectrum, c) is the abundance distribution diagram of each substance obtained by unmixing.
Detailed Description
The method of application of the present invention is further illustrated below with reference to examples.
The hyperspectral data processed at this time is 300 × 128 in size, has a wavelength range of 480-.
(1) Sparse representation based on global images
An overcomplete dictionary of size 38400 × 20 was built and sparse representation was performed for each pixel, the sparsity of the sparse representation in this example was set to 3 and the number of candidate end-members was set to 15.
(2) Alternative end member screening based on voting
And voting the atom corresponding to the item with the maximum sparse coefficient for each pixel and the sparse coefficient obtained by the pixel. The votes of all atoms are counted, and the first 15 pixels are selected as alternative end members in the example.
(3) End member cluster construction by extracting spectral shape features
Segmenting the spectrum of the alternative end member, wherein the length of each segment is 2 wave bands in the example, then extracting the shape characteristics of the curve to obtain a characteristic vector
Figure GDA0002231967310000044
The curve is fitted based on least square method, wherein the solution method of the slope coefficient is
Figure GDA0002231967310000045
After the slope characteristics are obtained, the extracted characteristics are grouped into 3 types by using a k-means method, and the construction of the end member cluster is completed.
(4) Constructing a segmented overcomplete dictionary
Constructing a block dictionary D ═ Db with the size of 15 × 20 by using the extracted 3-type end member cluster spectrum1；Db2；Db3]。
(5) Traversing the whole image, and selecting the optimal end member based on block sparsity for each pixel
For arbitrary pixel xi，
1) Initialization residual r0＝xiSet of indices
Figure GDA0002231967310000051
Terminal unit set
Figure GDA0002231967310000052
Dictionary D0And D, setting the iteration number t to be 1 and the iteration termination number K.
2) Finding the exponent λ in the whole dictionarytSo that it satisfies (8)
λt＝arg max|＜rt-1,Dt-1＞| (8)
Updating the set of indices Λt＝Λt-1∪{λt}, end member set
Figure GDA0002231967310000053
Dictionary
Figure GDA0002231967310000054
3) Solving the optimization problem in (9) by using least square method, and updating residual error rt。
Figure GDA0002231967310000055
4) If the residual is less than the set threshold, the iteration is stopped, otherwise t +1 is increased and 2 is returned) until t K.
(6) And performing abundance estimation by using a fully constrained least square method, and outputting end member cluster spectrum and abundance results.

Claims (2)

1. An end member cluster extraction method is characterized in that: analyzing the relationship among pixels based on sparse representation, voting and screening alternative end members for the pixels by using a sparse coefficient, extracting spectral shape characteristics and constructing an end member cluster, wherein the method can realize automatic extraction of the end member cluster based on an image and comprises the following steps:
step 1, sparse representation based on global image
A hyperspectral image X with m rows and n columns and l wave bands is given, wherein X is { X ═ X }1,x2,...,xi,...,xm×nIn which xi＝{xi1,xi2,...,xil}; firstly, each pixel is sparsely represented by a matching pursuit method aiming at a pixel xiIs constructed as
Figure FDA0002231967300000011
The number of the material types in the image, namely the number of the end members is k, the sparsity in the sparse representation is also set as k, then the sparse representation is carried out by utilizing a matching tracking method, and a sparse coefficient y is obtainediThe sparse coefficient solving method comprises the following specific steps:
1) initialization residual r0＝xiSet of indices
Figure FDA0002231967300000012
Original subset
Figure FDA0002231967300000013
And the iteration number t is 1;
2) selecting the atom closest to the residual, i.e. with the largest inner product, and recording the index lambda thereoftThen updating the exponent set Λt＝Λt-1∪{λtAnd Atom set Atomt＝[Atomt-1；dλt]；
λt＝arg max|＜rt-1,Di＞| (1)
3) Obtaining estimated sparseness by a least squares problem and updating residual rt；
Figure FDA0002231967300000014
rt＝xi-εtAtomt(3)
4) Updating t +1 and returning to step 2), stopping iteration until the residual converges gradually or t K;
5) finally obtaining the sparse coefficient yi＝εt；
Step 2, alternative end member screening based on voting
For pixel xiAnd its corresponding sparse coefficient yiWe find the sparse coefficient yiThe method comprises the steps of selecting atoms with maximum absolute values, voting, leading an image to comprise m × n pixels, namely casting m × n votes, accumulating the number of votes obtained by each atom, sequencing all atoms according to the votes, calculating the number cn of alternative end members by the number k of the end members, wherein the cn is k × 5, selecting the atom with cn before the number of votes as the alternative end member, and obtaining an alternative end member set Xcand；
Step 3, constructing end member clusters by extracting spectral shape characteristics
In the step, the characteristic extraction is carried out on the alternative end members obtained in the step 2 so as to achieve the aim of accurately constructing an end member cluster; for a spectrum containing l bands
Figure FDA0002231967300000015
The spectrum is first cut into N spectra of length l0In which N ═ l/l0](ii) a If l cannot be replaced by l0Dividing, the length of the last section of the spectrum is the number of the rest wave bands;
Figure FDA0002231967300000016
then, a straight line is used for fitting each spectrum section, the slope of the straight line is extracted to represent the shape of the spectrum section, and then the slope vector of the whole curve is obtained
Figure FDA0002231967300000021
Least square fitting method for straight line fitting
Figure FDA0002231967300000022
That is, alternative end members X can be obtainedcandCharacteristic F ofcand＝[f1；f2；...；fc...；fcn](ii) a The features are then input into an unsupervised classifier to obtain k classes Fbundle＝[Fb1；Fb2...；Fbi；...；Fbk]Then, the corresponding alternative end members are formed into an end member cluster X according to the classification resultbundle＝[Xb1；Xb2...；Xbi；...Xbk],Xbi＝[xh|fh∈Fbi]And outputs the result.
2. An abundance estimation method based on end-member clusters is characterized in that: the method is characterized in that a known end member cluster spectrum library is utilized, a block sparse thought is combined, a most matched end member combination is selected for each pixel, and inversion is carried out by utilizing a fully constrained least square method to obtain abundance distribution, wherein the method is different from the traditional method that only a single end member is extracted for one kind of ground, a plurality of candidate end members are extracted for one kind of ground to form a cluster, namely an end member cluster, and the abundance estimation method based on the end member cluster comprises the following specific steps:
step 1, constructing a block overcomplete dictionary
For the obtained end member cluster Xbundle＝[Xb1；Xb2...；Xbi；...Xbk]Each block of the overcomplete dictionary consists of a cluster of end-members, i.e., D ═ Db1；Db2；...；Dbi；...；DbK],Dbi＝Xbi；
Step 2, traversing the whole image, and selecting the optimal end member based on block sparsity aiming at each pixel
For arbitrary pixel xiThe specific calculation steps are as follows:
1) initialization residual r0＝xiSet of indices
Figure FDA0002231967300000023
Terminal unit set
Figure FDA0002231967300000024
Dictionary D0Setting the iteration time t as 1 and the iteration termination time K as D;
2) finding the exponent λ in the whole dictionarytSo that it satisfies (6)
λt＝arg max|＜rt-1,Dt-1＞| (6)
Updating the set of indices Λt＝Λt-1∪{λt}, end member set
Figure FDA0002231967300000025
Dictionary
Figure FDA0002231967300000026
3) Solving the optimization problem in (7) by using least square method, and updating residual rt；
Figure FDA0002231967300000027
4) If the residual error is smaller than a set threshold value, stopping iteration, otherwise, increasing t to t +1, and returning to 2) until t to K;
and 3, carrying out abundance estimation by using a fully constrained least square method, and outputting end member cluster spectra and abundance results.
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