CN110309822B - Hyperspectral image band selection method based on quantum evolution particle swarm algorithm - Google Patents
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Abstract
The invention relates to a hyperspectral image band selection method based on a quantum evolution particle swarm algorithm, and belongs to the field of image processing. Inputting a hyperspectral image of a waveband to be selected, and setting the scale, dimension and maximum iteration number of a population; mapping the position occupied by each particle to a solution space of an optimization problem from a unit space, and selecting the combination of inter-class separability and the optimal index as a fitness function; introducing the variation probability into a quantum evolution particle swarm algorithm, classifying the output optimal band combined image by adopting a maximum likelihood method, calculating the overall classification precision, and calculating the correlation by adopting the average correlation among the band combined bands. The invention combines the quantum evolution algorithm and the particle swarm algorithm, overcomes the defect of easy falling into local optimum, has faster convergence rate, shortens the operation time of the algorithm, has more stable algorithm and high classification precision when selecting wave bands, and has wide application prospect.
Description
Technical Field
The invention relates to a hyperspectral image band selection method based on quantum evolution particle swarm optimization, and belongs to the field of image processing.
Background
The hyperspectral images are narrow in wave band width and large in spectrum range, so that the fact that the correlation among the wave bands of the hyperspectral images is large, the information quantity is large, and the wave band selection of the hyperspectral images is very difficult. The hyperspectral image band selection is to select a band combination with large information quantity and small correlation and high resolution from the hyperspectral image band selection, namely, a band combination meeting corresponding conditions is searched from hundreds of hyperspectral image band databases with high correlation and large data quantity.
With the development of intelligent group algorithms in recent years, a plurality of search algorithms are applied to dimensionality reduction, for example, a genetic algorithm is utilized by Zhao winter and Zhao Guang to select hyperspectral image wave bands; the band selection based on the genetic algorithm can better solve the problems of large number of band combinations and difficult traversal in the band selection process, but the convergence speed problem cannot be satisfactorily solved at present. Carrying out hyperspectral image dimensionality reduction treatment by using an ant colony algorithm; the waveband selection of the ant colony algorithm can search a waveband combination with better performance, but the waveband selection generally needs longer search time, and stagnation phenomena are easy to occur to generate precocity. The borui utilizes a particle swarm algorithm to perform hyperspectral remote sensing data characteristic reduction, the particle swarm algorithm is an optimization algorithm based on population iteration, although the convergence speed is high, the convergence precision is not high, and the boresight is easy to get early.
Disclosure of Invention
The invention aims to provide a hyperspectral image band selection method based on a quantum evolution particle swarm algorithm, which aims to obtain smaller correlation under the condition of ensuring classification accuracy, improve the band selection performance and obtain a globally optimal band subset.
The invention aims to realize the method, and particularly relates to a hyperspectral image band selection method based on quantum evolution particle swarm optimization, which comprises the following steps of:
step 3, setting the size of the population to be N according to the divided subspaces, setting the number of dimensions N according to the number of the subspaces, setting the maximum iteration number Nmax, and randomly initializing the speed value and the position vector of the individual population in the feasible region of the position;
step 4, in QEPSO, each dimension is [ -1,1 ] because of the traversal space of the particles]In order to calculate the superiority and inferiority of the current positions of the particles, a solution space transformation is required, and 2 positions occupied by each particle are defined by a unit space I [ -1,1] n Mapping to a solution space of an optimization problem, each probability amplitude of a qubit corresponding to an optimization variable of the solution space;
step 5, the wave band selection method based on the information quantity is to calculate the corresponding information quantity of the wave band according to the information quantity contained in each wave band image as a screening standard, so as to obtain the wave band with the maximum information quantity; two fitness function schemes are selected, and the first scheme selects the separability between classes, namely the J-M distance; the second scheme is that the wave bands with good inter-class separability and large information quantity are obtained at the same time, and the combination of the inter-class separability and an Optimal Index (OIF) is selected as a fitness function;
step 6, in order to increase the diversity of the particle swarm and avoid premature convergence, introducing variation probability into a quantum evolution particle swarm algorithm, wherein in the quantum evolution algorithm, the movement of the particle position is realized by a quantum revolving gate, so that the updating of the particle movement speed in the common particle swarm algorithm is converted into the updating of the corner of the quantum revolving gate, and the updating of the particle position is converted into the updating of the quantum bit probability amplitude on the particle;
step 7, judging whether all algebras are iterated completely, if so, finishing the calculation, and outputting an optimal individual; if not, continuing iteration, returning to the step 6, and continuing to calculate the fitness function value until iteration is finished;
and 8, classifying the output optimal band combined image by adopting a maximum likelihood method in the experiment, calculating the overall classification precision, and calculating the correlation by adopting the average correlation among the band combined bands.
The invention also includes such structural features:
step 5, the inter-class separability is to calculate the classification distance between different classes, find out the wave band which enables the classification distance to be maximum, and achieve the purpose of easily distinguishing the classification of the ground objects; b, introducing a primary statistical variable and a secondary statistical variable into the distance, and calculating the optimal measurement of two types of statistics; the J-M distance is a metric function based on the difference between the two types of probability densities, is established on the basis of the B distance, uses the J-M distance as a measuring criterion of the separability between the types,
the formula for calculating the distance B is as follows:
the formula for calculating the J-M distance is:
wherein sigma i 、σ j Mean vectors of i, j class ground object spectra respectively，B ij Representing the distance B between the class i ground object and the class j ground object under different waveband combinations, the larger the value of the distance B, the closer the obtained solution is to the optimal solution, and the JM ij Represents the J-M distance between the i-class ground object and the J-class ground object under different wave band combinations, sigma i and sigma J represent covariance matrixes of the i-class ground object and the J-class ground object under different wave band combinations, and the larger the value of the covariance matrixes, the closer the obtained solution is to the optimal solution.
The optimal index method (OIF) comprehensively considers two factors of the information content of each band image and the correlation between the bands, can be used as a criterion for measuring the information content in the hyperspectral image band selection process, the larger the information content and the Optimal Index (OIF) are in direct proportion, namely the larger the OIF index value is, the more the information content is, the more the calculation expression is:
wherein, alpha represents the alpha wave band, beta represents the beta wave band; s in the formula α Is the standard deviation, r, of the band α data αβ Representative are the values of the correlation coefficients for the alpha and beta bands.
Step 5, the second scheme is to obtain the bands with good inter-class separability and large information amount at the same time, and select the combination of the inter-class separability and the Optimal Index (OIF) as the fitness function to obtain the weighting formula as follows:
f()＝x×J+y×OIF
wherein x and y are weight coefficients, calculating the fitness values of all individuals according to the formula, and taking out the maximum value of the fitness values and the minimum value of the fitness values to apply to the quality function.
And 8, the overall classification precision is as follows:
wherein: c is the number of categories; c is the total number of the C-type test samples; m is a unit of i The number of correct classifications for the ith class.
The correlation calculation in step 8 adopts the average correlation between the combined bands of the bands, and the calculation formula is as follows:
compared with the prior art, the invention has the beneficial effects that:
the invention combines the quantum evolution algorithm and the particle swarm algorithm, overcomes the defect of easy falling into local optimum, carries out the search of the wave band selection by using the quantum evolution particle swarm algorithm, has higher convergence speed compared with other existing search algorithms for wave band selection, shortens the operation time of the algorithm, and has more stable algorithm and high classification precision when carrying out the wave band selection. The algorithm uses double-chain search and combines quantum theory, the algorithm is not easy to fall into local optimum, and the stability of the algorithm is ensured. The method can be used for selecting the wave band combination with higher classification precision and smaller correlation from a plurality of wave bands of the hyperspectral images before the hyperspectral images are classified.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a prior art Indiana pine hyperspectral image;
FIG. 3 is a comparison graph of the classification results of the 3-class ground objects;
FIG. 4 is a comparison chart of the classification results of 5 kinds of land features;
fig. 5 is a comparison graph of the classification results of the 9-class ground objects.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of an implementation of the present invention; FIG. 2 is a prior art Indiana pine hyperspectral image; FIG. 3 is a comparison graph of the classification results of the 3-class ground objects; FIG. 4 is a comparison graph of the classification results of 5 types of land objects; fig. 5 is a comparison graph of the classification results of the 9-class ground objects. The technical scheme of the invention comprises the following steps:
(1) and inputting a hyperspectral image to be selected in a wave band, and converting the image into hyperspectral data in a matrix form.
(2) And dividing the subspace.
(3) Setting the size of the population to be N according to the divided subspaces, setting the number of dimensions N according to the number of the subspaces, setting the maximum iteration number Nmax, and randomly initializing the speed value and the position vector of the population individual in the feasible region of the position.
(4) In QEPSO, each dimension is [ -1,1 ] due to the traversal space of the particle]To calculate the superiority and inferiority of the current positions of the particles, a solution space transformation is required, and 2 positions occupied by each particle are defined by a unit space I [ -1,1] n Mapping to the solution space of the optimization problem. Each probability bin of qubits corresponds to an optimization variable of the solution space.
(5) The band selection method based on the information quantity is to calculate the corresponding information quantity of the band according to the information quantity contained in each band image as a screening standard, thereby obtaining the band with the maximum information quantity. The optimal index method (OIF) comprehensively considers two factors of the information content of each band image and the correlation between the bands, is more suitable to be used as a criterion for measuring the information content in the hyperspectral image band selection process, and indicates that the more the information content is contained when the information content and the Optimal Index (OIF) are in a direct proportional relation, namely the larger the OIF index value is, the more the information content is contained.
(5a) The main part of the inter-class separability is to calculate the classification distances between different classes, and find out the wave bands with the largest classification distances, so as to achieve the purpose of easily distinguishing the classes of the ground features. The distance B introduces a primary statistical variable and a secondary statistical variable, and is the best measure for calculating statistics of the two categories. The J-M distance is a measurement function based on the difference between the two types of probability densities, is established on the basis of the B distance, and uses the J-M distance as a measurement criterion of the separability between the types.
(5b) The invention selects two fitness function schemes, the first scheme selects the separability between classes, namely the J-M distance. In the second scheme, in order to simultaneously obtain the bands with good inter-class separability and large information quantity, the combination of the inter-class separability and an Optimal Index (OIF) is selected as a fitness function.
(6) In order to increase the diversity of particle swarm and avoid premature convergence, mutation probability is introduced into a quantum evolution particle swarm algorithm, and in the quantum evolution algorithm, the movement of particle positions is realized by a quantum revolving gate. Therefore, in the general particle swarm optimization, the update of the particle moving speed is converted into the update of the rotation angle of the quantum rotating gate, and the update of the particle position is converted into the update of the probability amplitude of the quantum bit on the particle.
(7) And judging whether all algebra are iterated completely, if so, finishing the calculation, and outputting an optimal individual. If not, continuing the iteration, and performing the step (6) to continue calculating the fitness function value until the iteration is finished.
(8) In the experiment, the maximum likelihood method is adopted to classify the output optimal band combined image, and the overall classification precision is calculated.
The invention may also be described as follows:
1. and inputting a hyperspectral image of a waveband to be selected, and converting the image into hyperspectral data in a matrix form.
2. Setting the size of the population to be N according to the divided subspaces, setting the number of dimensions N according to the number of the subspaces, setting the maximum iteration number Nmax, and randomly initializing the speed value and the position vector of the population individual in the feasible region beyond the position.
3. In the quantum evolution particle swarm algorithm, each dimension of the traversal space of the particles is [ -1,1 [ -1 ])]To calculate the superiority and inferiority of the current positions of the particles, a solution space transformation is required, and 2 positions occupied by each particle are defined by a unit space I [ -1,1] n Mapping to the solution space of the optimization problem. Each probability bin of qubits corresponds to an optimization variable of the solution space.
4. The band selection method based on the information quantity is to calculate the corresponding information quantity of each band according to the information quantity contained in each band image as a screening standard so as to obtain the band with the maximum information quantity, an optimal index method (OIF) comprehensively considers two factors of the information quantity of each band image and the correlation among the bands, the optimal index method is more suitable to be used as a criterion for measuring the information quantity content in the hyperspectral image band selection process, and the information quantity and the Optimal Index (OIF) are in a direct proportional relation, namely the OIF index value is larger, the more the information quantity contained in the hyperspectral image band selection method is. The calculation expression is as follows:
in the expression (1), α represents an α -th band, and β represents a β -th band; s in the formula α Is the standard deviation, r, of the band α data αβ Representative are the values of the correlation coefficients for the alpha and beta bands.
The main part of the inter-class separability is to calculate the classification distances between different classes, and find out the wave bands with the largest classification distances, so as to achieve the purpose of easily distinguishing the classes of the ground features. The distance B introduces a primary statistical variable and a secondary statistical variable, and is the best measure for calculating statistics of the two categories. The J-M distance is a measurement function based on the difference between the two types of probability densities, the J-M distance is established on the basis of the B distance, the J-M distance is used as a measurement criterion of the separability between the types, and the calculation expressions of the B distance and the J-M distance are shown in (2) and (3).
The formula for calculating the distance B is as follows:
the formula for calculating the distance from J to M is as follows:
wherein sigma i 、σ j Are the mean vectors of the spectra of the i and j classes of ground objects, B ij Representing the distance B between the class i ground object and the class j ground object under different waveband combinations, the larger the value of the distance B, the closer the obtained solution is to the optimal solution, and the JM ij Represents the J-M distance between the i-class ground object and the J-class ground object under different wave band combinations, and the larger the values of the covariance matrixes of the i-class ground object and the J-class ground object under different wave band combinations are, the closer the obtained solution is to the optimal solution is represented.
The invention selects two fitness function schemes, the first scheme selects the separability between classes, namely the J-M distance. In the second scheme, in order to obtain a band with good inter-class separability and large information amount, the combination of the inter-class separability and an Optimal Index (OIF) is selected as a fitness function, and the weighting formula is obtained as follows:
f()＝x×J+y×OIF (4)
wherein x and y are weight coefficients. And calculating the fitness values of all the individuals according to the formula. The maximum value of the fitness value and the minimum value of the fitness value are taken and applied to the quality function.
5. Particle renewal and mutation
In qespso, the movement of the particle position is achieved by a quantum rotating gate. Therefore, the update of the particle moving speed in the ordinary PSO is converted into the update of the quantum rotating gate corner, the update of the particle position is converted into the update of the quantum bit probability amplitude on the particle, and the particle P is set without loss of generality i The currently searched optimal position is a cosine position, that is:
P il ＝(cos(θ il1 ),cos(θ il2 ),…,cos(θ iln )) (5)
the optimal position searched by the whole population at present is as follows:
P g ＝(cos(θ g1 ),cos(θ g2 ),…,cos(θ gn )) (6)
based on the above assumptions, the particle state update rule can be described as follows.
5.1. Particle P i The upper qubit argument increment is updated as follows:
Δθ ij (t+1)＝ωΔθ ij (t)+c 1 r 1 (Δθ l )+c 2 r 2 (Δθ g ) (7)
wherein (8) (9):
5.2. quantum bit probability amplitude updating based on quantum revolving gate:
wherein i is 1,2, …, m; j is 1,2, …, n.
The two new positions after the particle update are respectively:
the loss of population diversity during the search process results in the PSO algorithm being prone to fall into a local optimum. A mutation operator is introduced into the evolutionary algorithm, and the purpose is to increase the diversity of the population and avoid premature convergence. The quantum not gate in QEPSO realizes the mutation operation process as follows:
where i is {1,2, …, m }, and j is {1,2, …, n }.
Let the mutation probability be P m Each particle is set with a random number rand between (0, 1), if rand<P m Then randomly selecting n/2 quantum bits on the particle, and exchanging two probability amplitudes by using a quantum not gate, wherein the memorized self position and the rotation direction of the particle remain unchanged.
6. And judging whether all algebra are iterated completely, if so, finishing the calculation, and outputting an optimal individual. If not, continuing the iteration, and performing the step 5 to continue calculating the fitness function value until the iteration is finished. The implementation flow is shown in the following figure 1:
the experiment adopts the maximum likelihood method to classify the output optimal wave band combination image, and the calculation formula of the overall classification precision is as follows:
wherein: c is the number of categories; c is the total number of the C-type test samples; m is i The number of correct classifications for the ith class.
The correlation adopts the average correlation among the combined bands of the bands, and the calculation formula is as follows:
simulation experiment
The effects of the present invention can be further illustrated by the following experiments:
1. simulation conditions are as follows:
the hardware environment of the invention is: the CPU is a PC with Intel Core i3-3240, 3.40GHz and 4GB of memory; the software environment is that a Window 7 operating system carries out simulation experiment on a wave band selection algorithm by utilizing Matlab 2017 b;
2. contents and results of the experiments
The hyperspectral AVIRIS data adopted by the experiment is a hyperspectral image of an agriculture and forestry mixed test field in Indiana, northwest of America, 6.1992, the spectral range is 0.41-2.45 mu m, the spatial resolution is 25m, the spectral resolution is 10nm, the size of the image is 144 multiplied by 144pixel, in the original 220 wave band images, the wave bands of water vapor absorption and low signal-to-noise ratio are removed, and the number of the wave bands of the images participating in processing is 200. Through a plurality of experiments, the parameters in the algorithm are set as follows: the inertia factor is 0.2, the self factor is 2.5, the global factor is 1.5, and the variation probability is 0.1. The invention compares the wave band selection algorithm with Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC) and mimicry physics (APO) in the aspects of optimal wave band combination correlation, information quantity, classification precision and the like, and the results of the algorithms are shown in tables 1,2 and 3.
Table 13 results of each index for ground features
Table 25 results of each index for land feature
Table 39 results of each index for various ground features
From the above table, it can be seen that: the QEPSO algorithm provided by the invention is generally superior to other algorithms in the aspect of overall classification precision, the ergodicity of searching can be expanded by adopting quantum bit coding under the condition that the population scale is not changed, and the searching becomes finer by adopting the particle moving mode of the quantum revolving door, so that the optimization efficiency of the algorithm is favorably improved. The correlation uniformity is an average value of pairwise correlations of the optimal band combination, the smaller the average correlation is, the better the average correlation is, the correlation of the QEPSO algorithm is lower than that of other algorithms in the case of three land features, the correlation average value of ABC is lower than that of QEPSO in the case of five and nine land features, but the correlation average value of QEPSO is lower than that of APO and PSO, and the two algorithms; in the aspect of information quantity, QEPSO is superior to two algorithms of ABC and APO, in addition, in the aspect of three ground features, the information quantity is superior to PSO, in the aspect of running time, the QEPSO algorithm is superior to other algorithms, because the quantum revolving gate realizes the simultaneous movement of two positions by changing the phase of a qubit describing the position of a particle, and simultaneously, the QEPSO algorithm is superior to the method added with self-adaptive variation probability, so that the QEPSO is more rapid in variation processing.
Claims (6)
1. A hyperspectral image band selection method based on quantum evolution particle swarm optimization is characterized by specifically comprising the following steps of:
step 1, inputting a hyperspectral image of a waveband to be selected, and converting the image into hyperspectral data in a matrix form;
step 2, dividing subspaces;
step 3, setting the size of the population to be N according to the divided subspaces, setting the number of dimensions N according to the number of the subspaces, setting the maximum iteration number Nmax, and randomly initializing the speed value and the position vector of the individual population in the position feasible region;
step 4, in QEPSO, each dimension of the traversal space of the particle is [ -1,1 [ -1 [ ]]In order to calculate the superiority and inferiority of the current positions of the particles, a solution space transformation is required, and 2 positions occupied by each particle are defined by a unit space I [ -1,1] n Mapping to a solution space of the optimization problem, each probability amplitude of the qubit corresponding to an optimization variable of the solution space;
step 5, the wave band selection method based on the information quantity is to calculate the corresponding information quantity of the wave band according to the information quantity contained in each wave band image as a screening standard, so as to obtain the wave band with the maximum information quantity; there are two fitness function schemes, the first scheme selects the separability between classes, i.e. the J-M distance; the second scheme is that the wave bands with good inter-class separability and large information quantity are obtained simultaneously, and the combination of the inter-class separability and the optimal index, namely OIF, is selected as a fitness function;
step 6, introducing the variation probability into a quantum evolution particle swarm algorithm, wherein in the quantum evolution algorithm, the movement of the particle position is realized by a quantum revolving gate, so that the updating of the particle movement speed in the common particle swarm algorithm is converted into the updating of the corner of the quantum revolving gate, and the updating of the particle position is converted into the updating of the quantum bit probability amplitude on the particle;
step 7, judging whether all algebras are iterated completely, if so, finishing the calculation, and outputting an optimal individual; if not, continuing iteration, returning to the step 6, and continuing to calculate the fitness function value until iteration is finished;
and 8, classifying the output optimal band combined image by adopting a maximum likelihood method in the experiment, calculating the overall classification precision, and calculating the correlation by adopting the average correlation among the band combined bands.
2. The method for selecting the wave bands of the hyperspectral image based on the quantum evolution particle swarm optimization algorithm according to claim 1 is characterized in that: step 5, the inter-class separability is to calculate the classification distance between different classes, find out the wave band which enables the classification distance to be maximum, and achieve the purpose of easily distinguishing the classes of the ground objects; the distance B introduces a primary statistical variable and a secondary statistical variable, and is the optimal measure for calculating statistics of two categories; the J-M distance is a measurement function based on the difference between the two types of probability densities, is established on the basis of the B distance, uses the J-M distance as a measurement criterion of the separability between the classes,
the formula for calculating the distance B is as follows:
the formula for calculating the J-M distance is:
wherein sigma i 、σ j Are the mean vectors of the spectra of the i and j classes of ground objects, B ij Representing the distance B between the class i ground object and the class j ground object under different waveband combinations, the larger the value of the distance B, the closer the obtained solution is to the optimal solution, and the JM ij Represents the J-M distance, sigma, between the class i and the class J ground objects under different wave band combinations i 、∑ j The covariance matrixes of the i-class and the j-class ground objects under different wave band combinations are represented, and the larger the value of the covariance matrixes, the closer the obtained solution is to the optimal solution is represented.
3. The method for selecting the wave bands of the hyperspectral image based on the quantum evolution particle swarm optimization algorithm according to claim 2 is characterized in that: the optimal index method (OIF) comprehensively considers two factors of the information content of each band image and the correlation between the bands, can be used as a criterion for measuring the information content in the hyperspectral image band selection process, the larger the information content and the Optimal Index (OIF) are in direct proportion, namely the OIF index value is, the more the information content is, the more the calculation expression is:
wherein, alpha represents the alpha wave band, beta represents the beta wave band; s in the formula α Is the standard deviation, r, of the band α data αβ Representative are the values of the correlation coefficients for the alpha and beta bands.
4. The method for selecting the wave bands of the hyperspectral image based on the quantum evolutionary particle swarm algorithm according to claim 3 is characterized in that: step 5, the second scheme is to obtain the bands with good inter-class separability and large information amount at the same time, and select the combination of the inter-class separability and the Optimal Index (OIF) as a fitness function to obtain a weighting formula as follows:
f()＝x×J+y×OIF
and x and y are weight coefficients, the fitness values of all individuals are calculated according to the formula, and the maximum value of the fitness values and the minimum value of the fitness values are taken out and applied to the quality function.
5. The method for selecting the hyperspectral image bands based on the quantum-evolutionary particle swarm optimization algorithm according to any one of claims 1 to 4, wherein the overall classification precision in the step 8 is as follows:
wherein: c is the number of categories; c is the total number of the C-type test samples; m is i The number of correct classifications for the ith class.
6. The method for selecting the wave bands of the hyperspectral images based on the quantum-evolutionary particle swarm optimization algorithm according to claim 5, wherein the computing correlation in the step 8 is an average correlation between wave bands of a wave band combination, and the computing formula is as follows:
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