CN116202623A - Single photon hyperspectral imaging method and system based on spectrum compressed sampling - Google Patents

Single photon hyperspectral imaging method and system based on spectrum compressed sampling Download PDF

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CN116202623A
CN116202623A CN202310134208.1A CN202310134208A CN116202623A CN 116202623 A CN116202623 A CN 116202623A CN 202310134208 A CN202310134208 A CN 202310134208A CN 116202623 A CN116202623 A CN 116202623A
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刘芮
田昕
肖滢
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Abstract

The invention provides a single photon hyperspectral imaging method and system based on spectrum compression sampling. Aiming at the problem that the hyperspectral compression imaging method is difficult to be applied to a light beam scanning detection system, a spatial light modulator is utilized to carry out efficient and flexible spectrum modulation on a dispersed light source, and spatial information is acquired through point-by-point scanning, so that the imaging method can be applied to the light beam scanning detection system. And then, fully utilizing the sparsity of the spectrum information to construct a hyperspectral reconstruction model, and finally, utilizing an alternate direction multiplier method to carry out iterative solution on the hyperspectral reconstruction model so as to reconstruct hyperspectral data of a target by utilizing the compressed sampling image. The method can reconstruct hyperspectral data by using a small amount of compressed sampling observation data, greatly reduces imaging time and imaging data volume, and provides convenience for hyperspectral imaging of a light beam scanning detection system.

Description

Single photon hyperspectral imaging method and system based on spectrum compressed sampling
Technical Field
The invention belongs to the field of hyperspectral compression imaging, and relates to a liquid crystal spatial light modulator-based spectrum compression sampling method and a tensor characterization-based hyperspectral image reconstruction method, which are suitable for hyperspectral imaging application scenes of a light beam scanning detection system.
Background
Compared with the traditional hyperspectral imaging, the hyperspectral compression imaging technology projects high-dimensional information into a low-dimensional space for measurement by utilizing the sparsity of signals, can greatly reduce the data volume required by acquisition, transmission and storage of spectral image data, and has been applied to the fields of biomedicine, remote sensing detection and the like.
In conventional hyperspectral imaging techniques, acquisition of multispectral spectral information is critical. Conventional spectrometers acquire information in different spectral bands by spectral band separation, but this approach can result in a large data volume and severely limited imaging speed. The spectrum separator-based method can separate multiple spectra in parallel to reduce imaging time, but the spectrum resolution of such a spectrum imaging method is limited. In order to obtain the abundant spectral information more effectively, a spectrum modulation film and a multi-section color wheel are used for spectrum intensity modulation, so that the spectrum imaging speed is increased. However, these methods require multiple measurements to obtain the spectral information, and the modulation of the spectral information by the spectral modulation film and the multi-segment color wheel is inflexible.
In recent years, hyperspectral imaging techniques based on compressed sensing have demonstrated great advantages in imaging speed. Classical coded aperture spectral imaging methods can reconstruct three-dimensional hyperspectral data using a single Zhang Yasu image. However, the coded aperture spectrum imaging method needs to perform mixed modulation on spatial information and spectrum information, can only use an area array detector to perform data acquisition, and cannot be applied to a light beam scanning detection system, such as a laser radar imaging system. In order to solve the above-mentioned problems, there is a need for a hyperspectral imaging method suitable for use in a beam scanning detection system.
The single photon hyperspectral imaging method based on spectrum compression sampling utilizes a spatial light modulator to carry out efficient and flexible spectrum modulation on the dispersed light source, and spatial information is obtained through point-by-point scanning. Then, the sparsity of spectrum information is fully utilized, and the target hyperspectral data is recovered from a small quantity of compressed observed images by a reconstruction method based on tensor characterization, so that high-quality hyperspectral compressed imaging is realized. The imaging speed of the method is obviously improved, but the method cannot be applied to a light beam scanning detection system. Therefore, how to realize the active spectrum modulation of the illumination light source and how to reconstruct the hyperspectral information with high quality by utilizing the sparsity of the information is a key problem of a single photon hyperspectral imaging method based on spectrum compression sampling.
Disclosure of Invention
Aiming at the defects of the prior art, the invention utilizes a scanning imaging method based on spectrum compressed sampling to reconstruct hyperspectral data from a small quantity of compressed observation images, and provides a single photon hyperspectral imaging method based on spectrum compressed sampling.
The technical scheme adopted by the invention is as follows: the white light source is subjected to spectrum expansion in the space horizontal direction by utilizing a triangular prism, then the spectrum is randomly sampled by utilizing a spatial light modulator, the sampled light beam is subjected to space point scanning on a target by utilizing a two-dimensional galvanometer, and meanwhile, a single-pixel photon counter is used for signal acquisition. Further, a hyperspectral reconstruction model is built, a fidelity item built based on tensor characterization is built according to a spectrum compression sampling process, and prior constraint is introduced according to signal characteristics. In the spatial dimension of tensor expansion, the spatial similarity is described by using a block clustering method. Spectral similarity is described in the tensor-expanded spectral dimension using dictionary learning and sparse constraints. And finally, carrying out iterative solution on the hyperspectral reconstruction model by using an alternate direction multiplier method, thereby reconstructing hyperspectral data of the target by using the compressed sampling image. A schematic diagram of an imaging system device is shown in fig. 1. The method comprises the following steps:
step 1: and constructing an imaging system light path. The white light source performs spectrum expansion in the space horizontal direction through the triangular prism, and the expanded light beam passes through the lens and then passes through the spectrum modulation module in parallel, wherein the spectrum modulation module comprises a polarizer, a spatial light modulator and an analyzer. The modulation surface of the spatial light modulator is 380nm-780nm spectrum band from right to left. Then the light beam after spectrum modulation is converged on a two-dimensional vibrating mirror by utilizing a lens, the light beam scans a target through the vibrating mirror, and reflected light on the surface of the target is received by a single-pixel photon counter;
step 2: the spatial light modulator is directed into a spectrally random sample map. The sample plot is halved in the horizontal direction by λ, i.e., λ spectral bins. A random sampling matrix of 1×λ is generated by using a 0-1 modulation method, and a spectrum random sampling pattern is generated according to the random sampling matrix to perform random gating on λ spectral segments, and fig. 2 is an example of a random sampling pattern generated by using a random sampling matrix, where the size of the random sampling matrix is 1×20, i.e. λ=20, and the 3 rd, 6 th, 15 th, and 20 th spectral segments are gated. During imaging, each compressed sample corresponds to a spectrum random sample map. For N times of spectrum compressed sampling, the size of a total spectrum random sampling matrix psi is N multiplied by lambda, and the total spectrum random sampling matrix psi is formed by N random sampling matrixes;
step 3: and constructing a hyperspectral reconstruction model based on tensor characterization. And establishing a fidelity item established based on tensor characterization according to the spectrum compression sampling process, and introducing prior constraint based on signal characteristics. In the spatial dimension of tensor expansion, the spatial similarity is described by using a block clustering method. Describing spectrum similarity by dictionary learning and sparse constraint on the spectrum dimension of tensor expansion;
step 4: taking the observation data of N times of spectrum compression sampling as input, and carrying out iterative solution on a hyperspectral reconstruction model by using an alternating direction multiplier method so as to obtain reconstructed hyperspectral data;
further, the specific implementation of the step 3 includes the following sub-steps:
step 3.1, for the hyperspectral data to be recovered, characterizing it as a third-order tensor form
Figure BDA0004084898980000021
Where w×h denotes a spatial resolution, W denotes a horizontal resolution of hyperspectral data to be restored, H denotes a vertical resolution of the restored hyperspectral data, and λ denotes a spectral number. At the same time, the compressed observation data can also be characterized as a third-order tensor +.>
Figure BDA0004084898980000022
The spectral compression imaging process can be described as the following fidelity term:
Figure BDA0004084898980000023
wherein ,
Figure BDA0004084898980000024
is->
Figure BDA0004084898980000025
3-mode expansion matrix of +.>
Figure BDA0004084898980000026
Is->
Figure BDA0004084898980000027
A 3-mode expansion matrix of (c) is provided,
Figure BDA0004084898980000028
for a spectrum random sampling matrix, < >>
Figure BDA0004084898980000029
Is a spectrum fuzzy matrix>
Figure BDA00040848989800000210
Indicating the Frobenius norm.
Step 3.2 for hyperspectral data
Figure BDA00040848989800000211
Performing spatial dimension expansion to obtain 1-mode expansion matrix +.>
Figure BDA00040848989800000212
The spatial similarity is described by using a block clustering method. Definition f (H) (1) ) To H (1) And performing block clustering operation: will H (1) Divided into L d r ×d c Is then used withThe K-means clustering method divides all patches into K groups, where the K-th group is denoted as f (k) (H (1) ). Using the kernel norms to constrain inter-block similarity within each cluster group can be represented by the following constraint terms:
Figure BDA00040848989800000213
wherein ,λ1 In order to balance the parameters of the device, I.I * Representing the kernel norm.
Step 3.3 for hyperspectral data
Figure BDA00040848989800000214
Performing spectrum dimension expansion to obtain a 3-mode expansion matrix H (3) The sparsity of the spectral information is constrained by a dictionary learning method. Will H (3) Decomposition into dictionary matrix->
Figure BDA00040848989800000215
Sum coefficient matrix->
Figure BDA00040848989800000216
And the sparsity of the coefficient matrix is constrained by using the L1 norm, which can be represented by the following constraint terms: />
Figure BDA00040848989800000217
wherein ,λ2 and λ3 In order to balance the parameters of the device, I.I 1 Representing the L1 norm.
Step 3.4, based on the formula (1-3), a hyperspectral reconstruction model can be obtained:
Figure BDA0004084898980000031
further, the specific implementation of the step 4 includes the following sub-steps:
step 4.1, the hyperspectral is subjected to the multiplication method in the alternating directionAnd (5) modeling to carry out iterative solution. For equation (4), let u=h (3) B，P (k) ＝f (k) (H (1) ) Q=c, giving the following formula:
Figure BDA0004084898980000032
wherein ,Y1 、Y 2 and Y3 For Lagrangian, μ 1 、μ 2 and μ3 Is a balanced operator. C is the variable to be solved, but in the model C is constrained by two constraint terms (the last two terms of equation 4), it is difficult to solve directly. Thus, a lagrangian Q is introduced, and let q=c. Then C in one of the constraint terms may be replaced with Q and the sub-problem solution is performed step-by-step by Q and C sub-problems, respectively. After the Lagrangian operator Q is introduced, the Q sub-problem and the C sub-problem respectively correspond to different constraint terms, and the Q is solved according to the first constraint term, and then the C is solved based on the second constraint term.
And 4.2, decomposing the formula (5) into 7 sub-problems for iterative solution.
U sub-problem: solving U from t+1
Figure BDA0004084898980000033
Is available in the form of
Figure BDA0004084898980000034
wherein ,
Figure BDA0004084898980000035
for the identity matrix, the superscript t indicates the t-th iteration.
Q sub-problem: solving for Q from t+1
Figure BDA0004084898980000036
Using a threshold shrink algorithm, it is possible to obtain
Figure BDA0004084898980000037
P (k) Sub-problems: the singular value reduction method can be used to solve the [ P ] (k) ] t+1
Figure BDA0004084898980000038
D sub-problem: solving for D from t+1
Figure BDA0004084898980000039
Is available in the form of
Figure BDA00040848989800000310
/>
C sub-problem: solving for C from t+1
Figure BDA0004084898980000041
Is available in the form of
Figure BDA0004084898980000042
wherein ,
Figure BDA0004084898980000043
is an identity matrix.
Figure BDA0004084898980000044
Sub-problems: solving for +.>
Figure BDA0004084898980000045
and />
Figure BDA0004084898980000046
Figure BDA0004084898980000047
Is available in the form of
Figure BDA0004084898980000048
Figure BDA0004084898980000049
wherein ,
Figure BDA00040848989800000410
is an identity matrix.
Figure BDA00040848989800000411
Can be by->
Figure BDA00040848989800000412
and />
Figure BDA00040848989800000413
Obtaining
Figure BDA00040848989800000414
Finally, lagrangian operator Y 1 、Y 2 and Y3 Can be updated by
Figure BDA00040848989800000415
After t iterations
Figure BDA00040848989800000416
I.e. reconstructed hyperspectral data.
The invention also provides a single photon hyperspectral imaging system based on spectrum compression sampling, which comprises the following modules:
the imaging system building module is used for building an imaging system light path; the white light source performs spectrum expansion in the horizontal direction of space through a triple prism, the expanded light beams pass through a lens and then pass through a spectrum modulation module in parallel, the spectrum modulation module comprises a polarizer, a spatial light modulator and an analyzer, the spectrum of the light beams is 380nm-780nm from right to left on the modulation surface of the spatial light modulator, then the light beams subjected to spectrum modulation are converged on a two-dimensional vibrating mirror through the lens, the light beams pass through the vibrating mirror to scan a target, and reflected light on the surface of the target is received by a single-pixel photon counter;
the random sampling diagram generation module is used for leading the spatial light modulator into a spectrum random sampling diagram, dividing the sampling diagram by lambda along the horizontal direction, namely lambda spectral fragments, generating a 1 x lambda random sampling matrix by using a 0-1 modulation method, and generating the spectrum random sampling diagram according to the random sampling matrix to randomly gate the lambda spectral fragments; in the imaging process, each compressed sampling corresponds to a spectrum random sampling graph, and for N times of spectrum compressed sampling, the total spectrum random sampling matrix ψ is N multiplied by lambda and is composed of N random sampling matrixes;
the hyperspectral reconstruction model construction module is used for constructing a hyperspectral reconstruction model based on tensor characterization, establishing a fidelity item based on tensor characterization according to a spectrum compression sampling process, introducing priori constraint based on signal characteristics, describing spatial similarity by using a block clustering method on the spatial dimension of tensor expansion, and describing spectral similarity by using dictionary learning and sparse constraint on the spectral dimension of tensor expansion;
and the solving module is used for taking the observation data of N times of spectrum compression sampling as input, and carrying out iterative solving on the hyperspectral reconstruction model by using an alternating direction multiplier method so as to obtain reconstructed hyperspectral data.
Further, the specific implementation mode of the hyperspectral reconstruction model building module is as follows;
step 3.1, for the hyperspectral data to be recovered, characterizing it as a third-order tensor form
Figure BDA0004084898980000051
Wherein W×H represents spatial resolution, W represents horizontal resolution of hyperspectral data to be recovered, H represents vertical resolution of the hyperspectral data to be recovered, and lambda represents the number of spectra; at the same time, the compressed observation data can also be characterized as a third-order tensor +.>
Figure BDA0004084898980000052
The spectral compression imaging process can be described as the following fidelity term:
Figure BDA0004084898980000053
wherein ,
Figure BDA0004084898980000054
is->
Figure BDA0004084898980000055
3-mode expansion matrix of +.>
Figure BDA0004084898980000056
Is->
Figure BDA0004084898980000057
A 3-mode expansion matrix of (c) is provided,
Figure BDA0004084898980000058
for a spectrum random sampling matrix, < >>
Figure BDA0004084898980000059
Is a spectrum fuzzy matrix>
Figure BDA00040848989800000510
Representing the Frobenius norm;
step 3.2 for hyperspectral data
Figure BDA00040848989800000521
Performing spatial dimension expansion to obtain 1-mode expansion matrix +.>
Figure BDA00040848989800000511
Spatial similarity is described by using a method of block clustering, and f (H (1) ) To H (1) And performing block clustering operation: will H (1) Divided into L d r ×d c Then all the patches are divided into K groups by a K-means clustering method, wherein the K-th group is denoted as f (k) (H (1) ) The inter-block similarity within each cluster group is constrained by a kernel norm, which can be represented by the following constraint terms:
Figure BDA00040848989800000512
wherein ,λ1 In order to balance the parameters of the device, I.I * Representing a kernel norm;
step 3.3 for hyperspectral data
Figure BDA00040848989800000513
Performing spectrum dimension expansion to obtain a 3-mode expansion matrix H (3) Constraint of sparsity of spectrum information by dictionary learning method, and H is as follows (3) Decomposition into dictionary matrix->
Figure BDA00040848989800000514
Sum coefficient matrix->
Figure BDA00040848989800000515
And the sparsity of the coefficient matrix is constrained by using the L1 norm, which can be represented by the following constraint terms:
Figure BDA00040848989800000516
wherein ,λ2 and λ3 In order to balance the parameters of the device, I.I 1 Represents an L1 norm;
step 3.4, obtaining a hyperspectral reconstruction model based on the formula (1-3):
Figure BDA00040848989800000517
further, the specific implementation manner of the solving module is as follows;
step 4.1, iteratively solving the hyperspectral reconstruction model by using an alternate direction multiplier method, wherein for formula (4), let u=h (3) B，P (k) ＝f (k) (H (1) ) Q=c, giving the following formula:
Figure BDA00040848989800000518
wherein ,Y1 、Y 2 and Y3 For Lagrangian, μ 1 、μ 2 and μ3 Is a balance operator;
step 4.2, decomposing the formula (5) into 7 sub-problems for iterative solution;
u sub-problem: solving for U from equation (6) t+1
Figure BDA00040848989800000519
Is available in the form of
Figure BDA00040848989800000520
wherein ,
Figure BDA0004084898980000061
the upper mark t represents the t-th iteration;
q sub-problem: from the type(8) Solution of Q t+1
Figure BDA0004084898980000062
Using a threshold shrink algorithm, it is possible to obtain
Figure BDA0004084898980000063
P (k) Sub-problems: solving [ P ] from formula (10) by singular value reduction (k) ] t+1
Figure BDA0004084898980000064
D sub-problem: solving for D from equation (11) t+1
Figure BDA0004084898980000065
Is available in the form of
Figure BDA0004084898980000066
C sub-problem: solving for C from equation (13) t+1
Figure BDA0004084898980000067
Is available in the form of
Figure BDA0004084898980000068
wherein ,
Figure BDA0004084898980000069
is a unit matrix;
Figure BDA00040848989800000610
sub-problems: solving for +.>
Figure BDA00040848989800000611
and />
Figure BDA00040848989800000612
Figure BDA00040848989800000613
Is available in the form of
Figure BDA00040848989800000614
Figure BDA00040848989800000615
wherein ,
Figure BDA00040848989800000616
is a unit matrix;
Figure BDA00040848989800000617
can be by->
Figure BDA00040848989800000618
and />
Figure BDA00040848989800000619
Obtaining; />
Figure BDA00040848989800000620
Finally, lagrangian operator Y 1 、Y 2 and Y3 Can be represented by (1)9) Updating
Figure BDA00040848989800000621
After t iterations
Figure BDA00040848989800000622
I.e. reconstructed hyperspectral data.
Compared with the prior art, the invention has the following advantages: the invention utilizes the spatial light modulator to carry out high-efficiency and flexible spectrum modulation on the dispersed light source and obtains the spatial information through point-by-point scanning, and the proposed hyperspectral compression imaging method can be applied to a light beam scanning detection system. And then, fully utilizing the sparsity of the spectrum information to construct a hyperspectral reconstruction model. In the spatial dimension of the hyperspectral tensor, the spatial similarity is described by using a block clustering method. Spectral similarity is described in the spectral dimension of the hyperspectral tensor using dictionary learning and sparse constraints. And finally, carrying out iterative solution on the hyperspectral reconstruction model by using an alternate direction multiplier method, thereby reconstructing hyperspectral data of the target by using the compressed sampling image. Compared with the prior art, the method can reconstruct higher-quality hyperspectral data based on fewer spectrum compression observation data, and can be applied to a light beam scanning detection system.
Drawings
FIG. 1 is a schematic diagram of a single photon hyperspectral imaging method based on spectral compression sampling.
Fig. 2 is an example of a random sampling graph.
Fig. 3 is a 20 spectral band scan image of an embodiment.
Fig. 4 is a 20 spectral bins reconstructed image of an embodiment.
Detailed Description
In order to facilitate the understanding and practice of the invention, one of ordinary skill in the art will now recognize in view of the drawings and examples that follow, it will be understood that the examples described herein are illustrative of the invention and are not intended to be limiting.
The invention provides a single-photon hyperspectral imaging method based on spectrum compression sampling, which mainly aims at the problem that a hyperspectral compression imaging method is difficult to apply to a light beam scanning detection system. The spectrum of the illumination light source is randomly compressed and sampled by a spatial light modulator, the modulated light beam is scanned by a two-dimensional galvanometer to form an image of a space point, and a reflected signal of the target is received by a single-pixel photon counter. Then, the hyperspectral data of the target are reconstructed from the compressed observed data by a tensor-characterization-based hyperspectral reconstruction model. In contrast, with the imaging system described above, each spectral band is individually gated to obtain scanned images of each band of the target, as shown in fig. 3.
The embodiment provides a single photon hyperspectral imaging method based on spectrum compression sampling for hyperspectral compression imaging, which specifically comprises the following steps:
step 1: and constructing an imaging system light path. The white light source performs spectrum expansion in the space horizontal direction through the triangular prism, and the expanded light beam passes through the lens and then passes through the spectrum modulation module in parallel, wherein the spectrum modulation module comprises a polarizer, a spatial light modulator and an analyzer. The modulation surface of the spatial light modulator has a spectrum of 780nm-380nm from left to right. And then the light beam after spectrum modulation is converged on a two-dimensional galvanometer by using a lens, the light beam scans a target through the galvanometer, and reflected light on the surface of the target is received by a single-pixel photon counter. The imaging time of single scanning is 10s, and 100×100 spatial pixel points are acquired;
step 2: the spatial light modulator is directed into a spectrally random sample map. The sample plot is divided into 20 equally along the horizontal direction, i.e. into 20 spectral bands. And generating a 1 multiplied by 20 random sampling matrix by using a 0-1 modulation method, generating a spectrum random sampling graph according to the random sampling matrix, and randomly gating 20 spectral bands. In this embodiment, 2 spectrum compression samples are performed, and each spectrum compression sample corresponds to a spectrum random sampling chart. The size of the spectrum random sampling matrix psi is 2 multiplied by 20, and the spectrum random sampling matrix consists of 2 random sampling matrixes;
step 3: and constructing a hyperspectral reconstruction model based on tensor characterization. And establishing a fidelity item established based on tensor characterization according to the spectrum compression sampling process, and introducing prior constraint based on signal characteristics. In the spatial dimension of tensor expansion, the spatial similarity is described by using a block clustering method. Spectral similarity is described in the tensor-expanded spectral dimension using dictionary learning and sparse constraints. The specific implementation comprises the following substeps:
step 3.1: for hyperspectral data to be recovered, the hyperspectral data is characterized as a third-order tensor form
Figure BDA0004084898980000081
At the same time, the compressed observation data can also be characterized as a third-order tensor +.>
Figure BDA0004084898980000082
The spectral compression imaging process can be described as the following fidelity term:
Figure BDA0004084898980000083
wherein ,
Figure BDA0004084898980000084
is->
Figure BDA0004084898980000085
3-mode expansion matrix of +.>
Figure BDA0004084898980000086
Is->
Figure BDA0004084898980000087
3-mode expansion matrix of +.>
Figure BDA0004084898980000088
For a spectrum random sampling matrix, < >>
Figure BDA0004084898980000089
Is a spectrum fuzzy matrix.
Step 3.2 for hyperspectral data
Figure BDA00040848989800000818
Performing spatial dimension expansion to obtain 1-mode expansion matrix +.>
Figure BDA00040848989800000810
The spatial similarity is described by using a block clustering method. Definition f (H) (1) ) To H (1) And performing block clustering operation: will H (1) Divided into 2000 7 x 15 patches, and then all patches are divided into 20 groups by k-means clustering, where the k-th group is denoted as f (k) (H (1) ). Using the kernel norms to constrain inter-block similarity within each cluster group can be represented by the following constraint terms:
Figure BDA00040848989800000811
wherein ,λ1 Is a balance parameter.
Step 3.3 for hyperspectral data
Figure BDA00040848989800000812
Performing spectrum dimension expansion to obtain a 3-mode expansion matrix H (3) The sparsity of the spectral information is constrained by a dictionary learning method. Will H (3) Decomposition into dictionary matrix->
Figure BDA00040848989800000813
Sum coefficient matrix
Figure BDA00040848989800000814
And the sparsity of the coefficient matrix is constrained by using the L1 norm, which can be represented by the following constraint terms:
Figure BDA00040848989800000815
wherein ,λ2 and λ3 Is a balance parameter.
Step 3.4, obtaining a hyperspectral reconstruction model:
Figure BDA00040848989800000816
step 4: taking the observation data of 2 times of spectrum compression sampling as input, and carrying out iterative solution on the hyperspectral reconstruction model by using an alternate direction multiplier method so as to obtain reconstructed hyperspectral data. The specific implementation comprises the following substeps:
and 4.1, carrying out iterative solution on the hyperspectral reconstruction model by using an alternate direction multiplier method. For equation (4), let u=h (3) B，P (k) ＝f (k) (H (1) ) Q=c, giving the following formula:
Figure BDA00040848989800000817
wherein ,Y1 、Y 2 and Y3 For Lagrangian, μ 1 、μ 2 and μ3 Is a balanced operator.
And 4.2, decomposing the above formula into 7 sub-problems to carry out iterative solution.
U sub-problem: solving U from t+1
Figure BDA0004084898980000091
Is available in the form of
Figure BDA0004084898980000092
wherein ,
Figure BDA0004084898980000093
for the identity matrix, the superscript t indicates the t-th iteration.
Q sub-problem: solving for Q from t+1
Figure BDA0004084898980000094
Using a threshold shrink algorithm, it is possible to obtain
Figure BDA0004084898980000095
P (k) Sub-problems: the singular value reduction method can be used to solve the [ P ] (k) ] t+1
Figure BDA0004084898980000096
D sub-problem: solving for D from t+1
Figure BDA0004084898980000097
Is available in the form of
Figure BDA0004084898980000098
C sub-problem: solving for C from t+1
Figure BDA0004084898980000099
Is available in the form of
Figure BDA00040848989800000910
wherein ,
Figure BDA00040848989800000911
is an identity matrix.
Figure BDA00040848989800000912
Sub-problems: solving for +.>
Figure BDA00040848989800000913
and />
Figure BDA00040848989800000914
/>
Figure BDA00040848989800000915
Is available in the form of
Figure BDA0004084898980000101
Figure BDA0004084898980000102
wherein ,
Figure BDA0004084898980000103
is an identity matrix.
Figure BDA0004084898980000104
Can be by->
Figure BDA0004084898980000105
and />
Figure BDA0004084898980000106
Obtaining
Figure BDA0004084898980000107
Finally, lagrangian operator Y 1 、Y 2 and Y3 Can be updated by
Figure BDA0004084898980000108
After t iterations
Figure BDA0004084898980000109
I.e. reconstructed hyperspectral data. In this embodiment, the iteration number t is 30, the parameter λ 1 ＝0.55，λ 2 ＝0.3，λ 3 ＝0.15，μ 1 ＝0.03，μ 2 ＝0.1，μ 3 ＝0.08。
Based on the above steps, hyperspectral data of the target are obtained, and fig. 4 is a reconstructed image of 20 spectral bands of the target. Compared with the single-spectrum scanning image in the attached figure 3, the method provided by the invention can reconstruct hyperspectral images of 20 spectrum bands by using the observation data of two spectrum compression imaging, realizes reconstructing high-quality hyperspectral data by using a small amount of spectrum compression observation data, and can realize high-quality hyperspectral compression imaging.
The invention also provides a single photon hyperspectral imaging system based on spectrum compression sampling, which comprises the following modules:
the imaging system building module is used for building an imaging system light path; the white light source performs spectrum expansion in the horizontal direction of space through a triple prism, the expanded light beams pass through a lens and then pass through a spectrum modulation module in parallel, the spectrum modulation module comprises a polarizer, a spatial light modulator and an analyzer, the spectrum of the light beams is 380nm-780nm from right to left on the modulation surface of the spatial light modulator, then the light beams subjected to spectrum modulation are converged on a two-dimensional vibrating mirror through the lens, the light beams pass through the vibrating mirror to scan a target, and reflected light on the surface of the target is received by a single-pixel photon counter;
the random sampling diagram generation module is used for leading the spatial light modulator into a spectrum random sampling diagram, dividing the sampling diagram by lambda along the horizontal direction, namely lambda spectral fragments, generating a 1 x lambda random sampling matrix by using a 0-1 modulation method, and generating the spectrum random sampling diagram according to the random sampling matrix to randomly gate the lambda spectral fragments; in the imaging process, each compressed sampling corresponds to a spectrum random sampling graph, and for N times of spectrum compressed sampling, the total spectrum random sampling matrix ψ is N multiplied by lambda and is composed of N random sampling matrixes;
the hyperspectral reconstruction model construction module is used for constructing a hyperspectral reconstruction model based on tensor characterization, establishing a fidelity item based on tensor characterization according to a spectrum compression sampling process, introducing priori constraint based on signal characteristics, describing spatial similarity by using a block clustering method on the spatial dimension of tensor expansion, and describing spectral similarity by using dictionary learning and sparse constraint on the spectral dimension of tensor expansion;
and the solving module is used for taking the observation data of N times of spectrum compression sampling as input, and carrying out iterative solving on the hyperspectral reconstruction model by using an alternating direction multiplier method so as to obtain reconstructed hyperspectral data.
Further, the specific implementation mode of the hyperspectral reconstruction model building module is as follows;
step 3.1, for the hyperspectral data to be recovered, characterizing it as a third-order tensor form
Figure BDA00040848989800001010
Wherein W×H represents spatial resolution, W represents horizontal resolution of hyperspectral data to be recovered, H represents vertical resolution of the hyperspectral data to be recovered, and lambda represents the number of spectra; at the same time, the compressed observation data can also be characterized as a third-order tensor +.>
Figure BDA0004084898980000111
The spectral compression imaging process can be described as the following fidelity term:
Figure BDA0004084898980000112
wherein ,
Figure BDA0004084898980000113
is->
Figure BDA0004084898980000114
3-mode expansion moment of (2)Array (S)>
Figure BDA0004084898980000115
Is->
Figure BDA0004084898980000116
A 3-mode expansion matrix of (c) is provided,
Figure BDA0004084898980000117
for a spectrum random sampling matrix, < >>
Figure BDA0004084898980000118
Is a spectrum fuzzy matrix>
Figure BDA0004084898980000119
Representing the Frobenius norm;
step 3.2 for hyperspectral data
Figure BDA00040848989800001110
Performing spatial dimension expansion to obtain 1-mode expansion matrix +.>
Figure BDA00040848989800001111
Spatial similarity is described by using a method of block clustering, and f (H (1) ) To H (1) And performing block clustering operation: will H (1) Divided into L d r ×d c Then all the patches are divided into K groups by a K-means clustering method, wherein the K-th group is denoted as f (k) (H (1) ) The inter-block similarity within each cluster group is constrained by a kernel norm, which can be represented by the following constraint terms:
Figure BDA00040848989800001112
wherein ,λ1 In order to balance the parameters of the device, I.I * Representing a kernel norm;
step 3.3 for hyperspectral data
Figure BDA00040848989800001122
Performing spectrum dimension expansion to obtain a 3-mode expansion matrix H (3) Constraint of sparsity of spectrum information by dictionary learning method, and H is as follows (3) Decomposition into dictionary matrix->
Figure BDA00040848989800001113
Sum coefficient matrix->
Figure BDA00040848989800001114
And the sparsity of the coefficient matrix is constrained by using the L1 norm, which can be represented by the following constraint terms:
Figure BDA00040848989800001115
wherein ,λ2 and λ3 In order to balance the parameters of the device, I.I 1 Represents an L1 norm;
step 3.4, obtaining a hyperspectral reconstruction model based on the formula (1-3):
Figure BDA00040848989800001116
further, the specific implementation manner of the solving module is as follows;
step 4.1, iteratively solving the hyperspectral reconstruction model by using an alternate direction multiplier method, wherein for formula (4), let u=h (3) B，P (k) ＝f (k) (H (1) ) Q=c, giving the following formula:
Figure BDA00040848989800001117
wherein ,Y1 、Y 2 and Y3 For Lagrangian, μ 1 、μ 2 and μ3 Is a balance operator;
step 4.2, decomposing the formula (5) into 7 sub-problems for iterative solution;
u sub-problem: from the type(6) Solution U t+1
Figure BDA00040848989800001118
Is available in the form of
Figure BDA00040848989800001119
wherein ,
Figure BDA00040848989800001120
the upper mark t represents the t-th iteration;
q sub-problem: solving for Q from equation (8) t+1
Figure BDA00040848989800001121
Using a threshold shrink algorithm, it is possible to obtain
Figure BDA0004084898980000121
P (k) Sub-problems: solving [ P ] from formula (10) by singular value reduction (k) ] t+1
Figure BDA0004084898980000122
D sub-problem: solving for D from equation (11) t+1
Figure BDA0004084898980000123
Is available in the form of
Figure BDA0004084898980000124
C sub-problem: solving for C from equation (13) t+1
Figure BDA0004084898980000125
Is available in the form of
Figure BDA0004084898980000126
wherein ,
Figure BDA0004084898980000127
is a unit matrix;
Figure BDA00040848989800001220
sub-problems: solving for +.>
Figure BDA0004084898980000128
and />
Figure BDA0004084898980000129
Figure BDA00040848989800001210
Is available in the form of
Figure BDA00040848989800001211
Figure BDA00040848989800001212
wherein ,
Figure BDA00040848989800001213
is a unit matrix;
Figure BDA00040848989800001214
can be by->
Figure BDA00040848989800001215
and />
Figure BDA00040848989800001216
Obtaining; />
Figure BDA00040848989800001217
Finally, lagrangian operator Y 1 、Y 2 and Y3 Can be updated by (19)
Figure BDA00040848989800001218
After t iterations
Figure BDA00040848989800001219
I.e. reconstructed hyperspectral data.
It should be understood that parts of the specification not specifically set forth herein are all prior art.
It should be understood that the foregoing description of the embodiments is not intended to limit the scope of the invention, but rather to make substitutions and modifications within the scope of the invention as defined by the appended claims without departing from the scope of the invention.

Claims (10)

1. A single photon hyperspectral imaging method based on spectral compressive sampling, comprising: the white light source is subjected to spectrum expansion in the space horizontal direction by utilizing a triple prism, then the spectrum is randomly sampled by utilizing a spatial light modulator, the sampled light beam is subjected to space point scanning on a target by utilizing a two-dimensional galvanometer, and meanwhile, a single-pixel photon counter is used for signal acquisition; further, a hyperspectral reconstruction model is built, a fidelity item based on tensor characterization is built according to a spectrum compression sampling process, prior constraint is introduced according to signal characteristics, spatial similarity is described by using a block clustering method in the tensor expansion space dimension, and spectral similarity is described by using dictionary learning and sparse constraint in the tensor expansion spectrum dimension; and finally, carrying out iterative solution on the hyperspectral reconstruction model by using an alternate direction multiplier method, thereby reconstructing hyperspectral data of the target by using the compressed sampling image.
2. The method for single photon hyperspectral imaging based on spectrum compressive sampling as claimed in claim 1, comprising the steps of:
step 1, constructing an imaging system light path; the white light source performs spectrum expansion in the horizontal direction of space through a triple prism, the expanded light beams pass through a lens and then pass through a spectrum modulation module in parallel, the spectrum modulation module comprises a polarizer, a spatial light modulator and an analyzer, the spectrum of the light beams is 380nm-780nm from right to left on the modulation surface of the spatial light modulator, then the light beams subjected to spectrum modulation are converged on a two-dimensional vibrating mirror through the lens, the light beams pass through the vibrating mirror to scan a target, and reflected light on the surface of the target is received by a single-pixel photon counter;
step 2, leading the spatial light modulator into a spectrum random sampling graph, equally dividing the sampling graph by lambda along the horizontal direction, namely lambda spectral bands, generating a 1 x lambda random sampling matrix by using a 0-1 modulation method, generating the spectrum random sampling graph according to the random sampling matrix, and randomly gating the lambda spectral bands; in the imaging process, each compressed sampling corresponds to a spectrum random sampling graph, and for N times of spectrum compressed sampling, the total spectrum random sampling matrix ψ is N multiplied by lambda and is composed of N random sampling matrixes;
step 3, constructing a hyperspectral reconstruction model based on tensor characterization, constructing a fidelity item based on tensor characterization according to a spectrum compression sampling process, introducing priori constraint based on signal characteristics, describing spatial similarity by using a block clustering method on the spatial dimension of tensor expansion, and describing spectral similarity by using dictionary learning and sparse constraint on the spectral dimension of tensor expansion;
and step 4, taking the observation data of N times of spectrum compression sampling as input, and carrying out iterative solution on the hyperspectral reconstruction model by using an alternate direction multiplier method so as to obtain reconstructed hyperspectral data.
3. A single photon hyperspectral imaging method based on spectral compression sampling as claimed in claim 2 wherein: the specific implementation of the step 3 comprises the following substeps;
step 3.1, for the hyperspectral data to be recovered, characterizing it as a third-order tensor form
Figure FDA0004084898970000011
Wherein W×H represents spatial resolution, W represents horizontal resolution of hyperspectral data to be recovered, H represents vertical resolution of the hyperspectral data to be recovered, and lambda represents the number of spectra; at the same time, the compressed observation data can also be characterized as a third-order tensor +.>
Figure FDA0004084898970000021
The spectral compression imaging process can be described as the following fidelity term:
Figure FDA0004084898970000022
wherein ,
Figure FDA0004084898970000023
is->
Figure FDA0004084898970000024
3-mode expansion matrix of +.>
Figure FDA0004084898970000025
Is->
Figure FDA0004084898970000026
A 3-mode expansion matrix of (c) is provided,
Figure FDA0004084898970000027
for a spectrum random sampling matrix, < >>
Figure FDA0004084898970000028
Is a spectrum fuzzy matrix>
Figure FDA0004084898970000029
Representing the Frobenius norm;
step 3.2 for hyperspectral data
Figure FDA00040848989700000210
Performing spatial dimension expansion to obtain 1-mode expansion matrix +.>
Figure FDA00040848989700000211
Spatial similarity is described by using a method of block clustering, and f (H () ) To H () And performing block clustering operation: will H () Divided into L d r ×d c Then all the patches are divided into K groups by a K-means clustering method, wherein the K-th group is denoted as f () (H () ) The inter-block similarity within each cluster group is constrained by a kernel norm, which can be represented by the following constraint terms:
Figure FDA00040848989700000212
wherein ,λ1 Is balance parameter II * Representing a kernel norm;
step 3.3 for hyperspectral data
Figure FDA00040848989700000213
Performing spectrum dimension expansion to obtain a 3-mode expansion matrix H () Constraint of sparsity of spectrum information by dictionary learning method, and H is as follows () Decomposition into dictionary matrix->
Figure FDA00040848989700000214
Sum coefficient matrix->
Figure FDA00040848989700000215
And the sparsity of the coefficient matrix is constrained by using the L1 norm, which can be represented by the following constraint terms:
Figure FDA00040848989700000216
wherein ,λ2 and λ3 Is balance parameter II 1 Represents an L1 norm;
step 3.4, obtaining a hyperspectral reconstruction model based on the formula (1-3):
Figure FDA00040848989700000217
4. a single photon hyperspectral imaging method based on spectral compression sampling as claimed in claim 3 wherein: the specific implementation of the step 4 comprises the following substeps;
step 4.1, iteratively solving the hyperspectral reconstruction model by using an alternate direction multiplier method, wherein for formula (4), let u=h (3) B，P (k) ＝ (k) (H (1) ) Q=c, giving the following formula:
Figure FDA00040848989700000218
wherein ,Y1 、Y 2 and Y3 For Lagrangian, μ 1 、μ 2 and μ3 Is a balance operator;
step 4.2, decomposing the formula (5) into 7 sub-problems for iterative solution;
u sub-problem: solving for U from equation (6) t+1
Figure FDA0004084898970000031
Is available in the form of
Figure FDA0004084898970000032
wherein ,
Figure FDA0004084898970000033
the upper mark t represents the t-th iteration;
q sub-problem: solving for Q from equation (8) t+1
Figure FDA0004084898970000034
Using a threshold shrink algorithm, it is possible to obtain
Figure FDA0004084898970000035
P (k) Sub-problems: solving [ P ] from formula (10) by singular value reduction (k) ] t+1
Figure FDA0004084898970000036
D sub-problem: solving for D from equation (11) t+1
Figure FDA0004084898970000037
Is available in the form of
Figure FDA0004084898970000038
C sub-problem: solving for C from equation (13) t+1
Figure FDA0004084898970000039
Is available in the form of
Figure FDA00040848989700000310
wherein ,
Figure FDA00040848989700000311
is a unit matrix;
Figure FDA00040848989700000312
sub-problems: solving for +.>
Figure FDA00040848989700000313
and />
Figure FDA00040848989700000314
Figure FDA00040848989700000315
Is available in the form of
Figure FDA00040848989700000316
Figure FDA00040848989700000317
wherein ,
Figure FDA00040848989700000318
is a unit matrix;
Figure FDA0004084898970000041
can be by->
Figure FDA0004084898970000042
and />
Figure FDA0004084898970000043
Obtaining;
Figure FDA0004084898970000044
finally, lagrangian operator Y 1 、Y 2 and Y3 Can be updated by (19)
Figure FDA0004084898970000045
After t iterations
Figure FDA0004084898970000046
I.e. reconstructed hyperspectral data.
5. A single photon hyperspectral imaging method based on spectral compression sampling as claimed in claim 2 wherein: in the step 1, the imaging time of a single scanning is 10s, and 100×100 spatial pixel points are acquired.
6. A single photon hyperspectral imaging method based on spectral compression sampling as claimed in claim 2 wherein: λ=20.
7. A single photon hyperspectral imaging method based on spectral compression sampling as claimed in claim 4 wherein: parameter lambda 1 ＝0.55，λ 2 ＝0.3，λ 3 ＝0.15，μ 1 ＝0.03，μ 2 ＝0.1，μ 3 ＝0.08。
8. A single photon hyperspectral imaging system based on spectral compressive sampling, comprising the following modules:
the imaging system building module is used for building an imaging system light path; the white light source performs spectrum expansion in the horizontal direction of space through a triple prism, the expanded light beams pass through a lens and then pass through a spectrum modulation module in parallel, the spectrum modulation module comprises a polarizer, a spatial light modulator and an analyzer, the spectrum of the light beams is 380nm-780nm from right to left on the modulation surface of the spatial light modulator, then the light beams subjected to spectrum modulation are converged on a two-dimensional vibrating mirror through the lens, the light beams pass through the vibrating mirror to scan a target, and reflected light on the surface of the target is received by a single-pixel photon counter;
the random sampling diagram generation module is used for leading the spatial light modulator into a spectrum random sampling diagram, dividing the sampling diagram by lambda along the horizontal direction, namely lambda spectral fragments, generating a 1 x lambda random sampling matrix by using a 0-1 modulation method, and generating the spectrum random sampling diagram according to the random sampling matrix to randomly gate the lambda spectral fragments; in the imaging process, each compressed sampling corresponds to a spectrum random sampling graph, and for N times of spectrum compressed sampling, the total spectrum random sampling matrix ψ is N multiplied by lambda and is composed of N random sampling matrixes;
the hyperspectral reconstruction model construction module is used for constructing a hyperspectral reconstruction model based on tensor characterization, establishing a fidelity item based on tensor characterization according to a spectrum compression sampling process, introducing priori constraint based on signal characteristics, describing spatial similarity by using a block clustering method on the spatial dimension of tensor expansion, and describing spectral similarity by using dictionary learning and sparse constraint on the spectral dimension of tensor expansion;
and the solving module is used for taking the observation data of N times of spectrum compression sampling as input, and carrying out iterative solving on the hyperspectral reconstruction model by using an alternating direction multiplier method so as to obtain reconstructed hyperspectral data.
9. A single photon hyperspectral imaging system based on spectral compression sampling as claimed in claim 8 wherein: the specific implementation mode of the hyperspectral reconstruction model building module is as follows;
step 3.1, for the hyperspectral data to be recovered, characterizing it as a third-order tensor form
Figure FDA0004084898970000051
Wherein W×H represents spatial resolution, W represents horizontal resolution of hyperspectral data to be recovered, H represents vertical resolution of the hyperspectral data to be recovered, and lambda represents the number of spectra; at the same time, the compressed observation data can also be characterized as a third-order tensor +.>
Figure FDA0004084898970000052
The spectral compression imaging process can be described as the following fidelity term:
Figure FDA0004084898970000053
wherein ,
Figure FDA0004084898970000054
is->
Figure FDA0004084898970000055
3-mode expansion matrix of +.>
Figure FDA0004084898970000056
Is->
Figure FDA0004084898970000057
A 3-mode expansion matrix of (c) is provided,
Figure FDA0004084898970000058
for a spectrum random sampling matrix, < >>
Figure FDA0004084898970000059
Is a spectrum fuzzy matrix>
Figure FDA00040848989700000510
Representing the Frobenius norm;
step 3.2 for hyperspectral data
Figure FDA00040848989700000511
Performing spatial dimension expansion to obtain 1-mode expansion matrix +.>
Figure FDA00040848989700000512
Spatial similarity is described by using a method of block clustering, and f (H (1) ) To H (1) And performing block clustering operation: will H (1) Divided into L d r ×d c Then all the patches are divided into K groups by a K-means clustering method, wherein the K-th group is denoted as f (k) (H (1) ) The inter-block similarity within each cluster group is constrained by a kernel norm, which can be represented by the following constraint terms:
Figure FDA00040848989700000513
wherein ,λ1 Is balance parameter II * Representing a kernel norm;
step 3.3 for hyperspectral data
Figure FDA00040848989700000519
Performing spectrum dimension expansion to obtain a 3-mode expansion matrix H (3) Constraint of sparsity of spectrum information by dictionary learning method, and H is as follows (3) Is decomposed intoDictionary matrix->
Figure FDA00040848989700000514
Sum coefficient matrix->
Figure FDA00040848989700000515
And the sparsity of the coefficient matrix is constrained by using the L1 norm, which can be represented by the following constraint terms:
Figure FDA00040848989700000516
wherein ,λ2 and λ3 Is balance parameter II 1 Represents an L1 norm;
step 3.4, obtaining a hyperspectral reconstruction model based on the formula (1-3):
Figure FDA00040848989700000517
10. a single photon hyperspectral imaging system based on spectral compression sampling as claimed in claim 9 wherein: the specific implementation mode of the solving module is as follows;
step 4.1, iteratively solving the hyperspectral reconstruction model by using an alternate direction multiplier method, wherein for formula (4), let u=h (3) B，P (k) ＝f (k) (H (1) ) Q=c, giving the following formula:
Figure FDA00040848989700000518
wherein ,Y1 、Y 2 and Y3 For Lagrangian, μ 1 、μ 2 and μ3 Is a balance operator;
step 4.2, decomposing the formula (5) into 7 sub-problems for iterative solution;
u sub-problem: solving for U from equation (6) t+1
Figure FDA0004084898970000061
Is available in the form of
Figure FDA0004084898970000062
wherein ,
Figure FDA0004084898970000063
the upper mark t represents the t-th iteration;
q sub-problem: solving for Q from equation (8) t+1
Figure FDA0004084898970000064
Using a threshold shrink algorithm, it is possible to obtain
Figure FDA0004084898970000065
P (k) Sub-problems: solving [ P ] from formula (10) by singular value reduction (k) ] t+1
Figure FDA0004084898970000066
D sub-problem: solving for D from equation (11) t+1
Figure FDA0004084898970000067
Is available in the form of
Figure FDA0004084898970000068
C sub-problem: solving for C from equation (13) t+1
Figure FDA0004084898970000069
Is available in the form of
Figure FDA00040848989700000610
wherein ,
Figure FDA00040848989700000611
is a unit matrix; />
Figure FDA00040848989700000612
Sub-problems: solving for +.>
Figure FDA00040848989700000613
and />
Figure FDA00040848989700000614
Figure FDA00040848989700000615
Is available in the form of
Figure FDA0004084898970000071
Figure FDA0004084898970000072
wherein ,
Figure FDA0004084898970000073
is a unit matrix;
Figure FDA0004084898970000074
can be by->
Figure FDA0004084898970000075
and />
Figure FDA0004084898970000076
Obtaining;
Figure FDA0004084898970000077
finally, lagrangian operator Y 1 、Y 2 and Y3 Can be updated by (19)
Figure FDA0004084898970000078
After t iterations
Figure FDA0004084898970000079
I.e. reconstructed hyperspectral data. />
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