A single-photon hyperspectral imaging method and system based on spectral compression sampling

Abstract

The present invention proposes a single-photon hyperspectral imaging method and system based on spectral compression sampling. In order to address the problem that hyperspectral compression imaging methods are difficult to apply to beam scanning detection systems, a spatial light modulator is used to efficiently and flexibly modulate the spectrum of the dispersed light source, and spatial information is acquired through point-by-point scanning, which makes the imaging method applicable to beam scanning detection systems. Then, the sparsity of spectral information is fully utilized to construct a hyperspectral reconstruction model, and finally the alternating direction multiplier method is used to iteratively solve the hyperspectral reconstruction model, thereby reconstructing the hyperspectral data of the target using the compressed sampling image. This method can reconstruct hyperspectral data using a small amount of compressed sampling observation data, greatly reducing the imaging time and the amount of imaging data, and providing convenience for hyperspectral imaging of beam scanning detection systems.

Description

Technical Field

[0001] The present invention belongs to the field of hyperspectral compression imaging, and relates to a spectral compression sampling method based on a liquid crystal spatial light modulator and a hyperspectral image reconstruction method based on tensor representation, which is suitable for hyperspectral imaging application scenarios of beam scanning detection systems. Background Art

[0002] Compared with traditional hyperspectral imaging, hyperspectral compression imaging technology uses the sparsity of signals to project high-dimensional information into low-dimensional space for measurement, which can greatly reduce the amount of data required for the collection, transmission and storage of spectral image data. It has been applied in fields such as biomedicine and remote sensing detection.

[0003] In traditional hyperspectral imaging technology, the acquisition of multi-band spectral information is crucial. Traditional spectrometers obtain information from different spectral bands by spectral band separation, but this method results in a huge amount of data and severely limits the imaging speed. Methods based on spectral separators can separate multiple spectra in parallel to reduce imaging time, but the spectral resolution of this spectral imaging method is limited. In order to more efficiently obtain rich spectral information, spectral modulation films and multi-segment color wheels are used for spectral intensity modulation, which increases the spectral imaging speed. However, these methods require multiple measurements to obtain spectral information, and spectral modulation films and multi-segment color wheels are not flexible in modulating spectral information.

[0004] In recent years, hyperspectral imaging technology based on compressed sensing has demonstrated significant advantages in imaging speed. Classic coded aperture spectral imaging methods can reconstruct three-dimensional hyperspectral data from a single compressed image. However, coded aperture spectral imaging methods require mixed modulation of spatial and spectral information, and can only acquire data using area array detectors, making them unsuitable for beam scanning detection systems, such as lidar imaging systems. To address these challenges, a hyperspectral imaging method suitable for beam scanning detection systems is needed.

[0005] Single-photon hyperspectral imaging methods based on spectral compression sampling utilize a spatial light modulator to efficiently and flexibly modulate the spectrum of a dispersed light source and acquire spatial information through point-by-point scanning. Then, taking full advantage of the sparsity of spectral information, a tensor-based reconstruction method is used to recover the target's hyperspectral data from a small number of compressed observation images, thereby achieving high-quality hyperspectral compression imaging. This type of method significantly improves imaging speed, but cannot be applied to beam scanning detection systems. Therefore, how to achieve active spectral modulation of the illumination source and how to exploit the sparsity of information to reconstruct high-quality hyperspectral information are key issues in single-photon hyperspectral imaging methods based on spectral compression sampling. Summary of the Invention

[0006] In view of the shortcomings of the existing technology, the present invention utilizes a scanning imaging method based on spectral compression sampling to reconstruct hyperspectral data from a small amount of compressed observation images, and provides a single-photon hyperspectral imaging method based on spectral compression sampling.

[0007] The technical solution adopted by the present invention is: using a prism to expand the spectrum of a white light source in the horizontal direction of space, and then using a spatial light modulator to randomly sample the spectrum. The sampled light beam is passed through a two-dimensional galvanometer to perform spatial point scanning on the target, and a single-pixel photon counter is used to collect signals. Furthermore, a hyperspectral reconstruction model is constructed, and a fidelity term based on tensor representation is first established according to the spectral compression sampling process, and then a priori constraints are introduced according to the signal characteristics. In the spatial dimension of tensor expansion, the block clustering method is used to describe its spatial similarity. In the spectral dimension of tensor expansion, dictionary learning and sparse constraints are used to describe spectral similarity. Finally, the alternating direction multiplier method is used to iteratively solve the hyperspectral reconstruction model, thereby using the compressed sampling image to reconstruct the target's hyperspectral data. The schematic diagram of its imaging system device is shown in the attached figure. Figure 1 The method comprises the following steps:

[0008] Step 1: Build the optical path of the imaging system. The white light source is spectrally expanded in the horizontal direction of space through a prism. After the expanded light beam passes through the lens, it passes through the spectrum modulation module in parallel, including the polarizer, spatial light modulator, and analyzer. The modulation surface of the spatial light modulator is a 380nm-780nm spectrum from right to left. The lens is then used to converge the spectrally modulated light beam onto a two-dimensional galvanometer. The light beam scans the target through the galvanometer, and the reflected light from the target surface is received by a single-pixel photon counter.

[0009] Step 2: Import the spatial light modulator into the spectrum random sampling map. The sampling map is divided into λ equal parts along the horizontal direction, i.e., λ spectrum segments. Use the 0-1 modulation method to generate a 1×λ random sampling matrix, and generate a spectrum random sampling map based on the random sampling matrix to randomly select the λ spectrum segments. Figure 2 This is an example of a random sampling image generated by a random sampling matrix. The random sampling matrix size is 1×20, i.e., λ = 20, and spectral segments 3, 6, 15, and 20 are selected. During the imaging process, each compressed sampling corresponds to a spectral random sampling image. For N spectral compressed samplings, the total spectral random sampling matrix Ψ is N×λ and consists of N random sampling matrices.

[0010] Step 3: Construct a hyperspectral reconstruction model based on tensor representation. A fidelity term based on tensor representation is established according to the spectral compression sampling process, and then a priori constraints are introduced based on signal characteristics. In the spatial dimension of the tensor expansion, a block clustering method is used to describe its spatial similarity. In the spectral dimension of the tensor expansion, dictionary learning and sparse constraints are used to describe spectral similarity.

[0011] Step 4: Using the observation data of N-times spectral compression sampling as input, the hyperspectral reconstruction model is iteratively solved using the alternating direction multiplier method to obtain the reconstructed hyperspectral data;

[0012] Furthermore, the specific implementation of step 3 includes the following sub-steps:

[0013] Step 3.1: For the hyperspectral data to be restored, first represent it as a third-order tensor Among them, W×H represents the spatial resolution, W refers to the horizontal resolution of the hyperspectral data to be restored, H refers to the vertical resolution of the restored hyperspectral data, and λ represents the number of spectra. At the same time, the compressed observation data can also be represented as a third-order tensor The spectral compression imaging process can be described as follows:

[0014]

[0015] in, for The 3-mode expansion matrix, for The 3-mode expansion matrix, is the spectral random sampling matrix, is the spectral fuzzy matrix, represents the Frobenius norm.

[0016] Step 3.2: Hyperspectral data Perform spatial dimension expansion to obtain a 1-mode expansion matrix Use the block clustering method to describe its spatial similarity. Define f(H (1) ) is for H (1) Perform block clustering operation: H (1) Divide into L d r ×d c Then, the k-means clustering method is used to divide all the small blocks into K groups, where the kth group is represented by f (k) (H (1) ). Using the nuclear norm to constrain the similarity between blocks in each cluster group can be expressed as the following constraint terms:

[0017]

[0018] Where λ1 is the equilibrium parameter, ||·|| * represents the nuclear norm.

[0019] Step 3.3: Hyperspectral data Perform spectral dimension expansion to obtain the 3-mode expansion matrix H (3), using dictionary learning method to constrain the sparsity of spectral information. (3) Decompose into dictionary matrix and coefficient matrix And taking advantage of the sparsity of the L1 norm constraint coefficient matrix, it can be expressed as the following constraint terms:

[0020]

[0021] Here, λ2 and λ3 are balance parameters, and ||·||1 represents the L1 norm.

[0022] In step 3.4, based on formula (1-3), the hyperspectral reconstruction model can be obtained:

[0023]

[0024] Furthermore, the specific implementation of step 4 includes the following sub-steps:

[0025] Step 4.1, use the alternating direction multiplier method to iteratively solve the hyperspectral reconstruction model. For formula (4), let U = H (3) B, P (k) =f (k) (H (1) ), Q=C, and the following formula is obtained:

[0026]

[0027] Among them, Y1, Y2, and Y3 are Lagrangian operators, and μ1, μ2, and μ3 are equilibrium operators. C is the variable to be solved, but in the model, C is constrained by two constraints (the last two terms in Formula 4), making it difficult to solve directly. Therefore, the Lagrangian operator Q is introduced, and Q = C is set. Then, C in one of the constraints can be replaced by Q, and the subproblem can be solved step by step using the Q subproblem and the C subproblem respectively. After introducing the Lagrangian operator Q, the Q subproblem and the C subproblem correspond to different constraints respectively. First, solve Q based on the first constraint, and then solve C based on the second constraint.

[0028] Step 4.2: Decompose formula (5) into 7 sub-problems and solve them iteratively.

[0029] U subproblem: Solve U from the following formula t+1

[0030]

[0031] Available

[0032]

[0033] in, is the identity matrix, and the superscript t indicates the t-th iteration.

[0034] Q subproblem: Solve Q from the following formula t+1

[0035]

[0036] Using the threshold shrinkage algorithm, we can get

[0037]

[0038] P (k) Sub-problem: Using the singular value shrinkage method, we can solve [P (k) ] t+1

[0039]

[0040] Subproblem D: Solve D from the following formula t+1

[0041]

[0042] Available

[0043]

[0044] Subproblem C: Solve C from the following formula t+1

[0045]

[0046] Available

[0047]

[0048] in, is the identity matrix.

[0049] Sub-problem: Solve the following equations separately and

[0050]

[0051] Available

[0052]

[0053]

[0054] in, is the identity matrix.

[0055] can be and Obtain

[0056]

[0057] Finally, the Lagrangian operators Y1, Y2, and Y3 can be updated by

[0058]

[0059] After t iterations This is the reconstructed hyperspectral data.

[0060] The present invention also provides a single-photon hyperspectral imaging system based on spectral compression sampling, comprising the following modules:

[0061] The imaging system building module is used to build the imaging system optical path. The white light source is spectrally expanded horizontally in space by a prism. After passing through a lens, the expanded light beam passes parallel to the spectrum modulation module, including a polarizer, a spatial light modulator, and an analyzer. The modulation plane of the spatial light modulator covers the 380nm-780nm spectrum from right to left. The lens is then used to converge the spectrally modulated light beam onto a two-dimensional galvanometer. The light beam scans the target through the galvanometer, and the reflected light from the target surface is received by a single-pixel photon counter.

[0062] The random sampling map generation module is used to import the spatial light modulator into the spectral random sampling map. The sampling map is divided into λ equal parts along the horizontal direction, that is, λ spectral segments. A 1×λ random sampling matrix is ​​generated using a 0-1 modulation method. The spectral random sampling map generated based on the random sampling matrix is ​​randomly selected to select the λ spectral segments. During the imaging process, each compressed sampling corresponds to a spectral random sampling map. For N spectral compressed samplings, the total spectral random sampling matrix Ψ is N×λ and is composed of N random sampling matrices.

[0063] The hyperspectral reconstruction model construction module is used to construct a hyperspectral reconstruction model based on tensor representation. According to the spectral compression sampling process, a fidelity term based on tensor representation is established. Then, a priori constraints are introduced based on signal characteristics. In the spatial dimension of the tensor expansion, the block clustering method is used to describe its spatial similarity. In the spectral dimension of the tensor expansion, the spectral similarity is described using dictionary learning and sparse constraints.

[0064] The solution module is used to take the observation data of N-times spectral compression sampling as input, and iteratively solve the hyperspectral reconstruction model using the alternating direction multiplier method to obtain reconstructed hyperspectral data.

[0065] Furthermore, the specific implementation of the hyperspectral reconstruction model construction module is as follows;

[0066] Step 3.1: For the hyperspectral data to be restored, first represent it as a third-order tensor Among them, W×H represents the spatial resolution, W refers to the horizontal resolution of the hyperspectral data to be restored, H refers to the vertical resolution of the restored hyperspectral data, and λ represents the number of spectra; at the same time, the compressed observation data can also be represented as a third-order tensor The spectral compression imaging process can be described as follows:

[0067]

[0068] in, for The 3-mode expansion matrix, for The 3-mode expansion matrix, is the spectral random sampling matrix, is the spectral fuzzy matrix, represents the Frobenius norm;

[0069] Step 3.2: Hyperspectral data Perform spatial dimension expansion to obtain a 1-mode expansion matrix Use the block clustering method to describe its spatial similarity and define f(H (1) ) is for H (1) Perform block clustering operation: H (1) Divide into L d r ×d c Then, the k-means clustering method is used to divide all the small blocks into K groups, where the kth group is represented by f (k) (H (1) ), the nuclear norm is used to constrain the similarity between blocks in each cluster group, which can be expressed as the following constraint terms:

[0070]

[0071] Where λ1 is the equilibrium parameter, ||·|| * represents the nuclear norm;

[0072] Step 3.3: Hyperspectral data Expand the spectrum dimension and obtain the 3-mode expansion matrix H (3) , using dictionary learning method to constrain the sparsity of spectral information, H (3) Decompose into dictionary matrix and coefficient matrix And taking advantage of the sparsity of the L1 norm constraint coefficient matrix, it can be expressed as the following constraint terms:

[0073]

[0074] Among them, λ2 and λ3 are balance parameters, ||·||1 represents the L1 norm;

[0075] Step 3.4, based on formula (1-3), obtain the hyperspectral reconstruction model:

[0076]

[0077] Furthermore, the specific implementation of the solution module is as follows;

[0078] Step 4.1, use the alternating direction multiplier method to iteratively solve the hyperspectral reconstruction model. For formula (4), let U = H (3) B, P (k) =f (k) (H (1) ), Q=C, and the following formula is obtained:

[0079]

[0080] Among them, Y1, Y2 and Y3 are Lagrangian operators, μ1, μ2 and μ3 are equilibrium operators;

[0081] Step 4.2, decompose formula (5) into 7 sub-problems and solve them iteratively;

[0082] U subproblem: Solve U from equation (6) t+1

[0083]

[0084] Available

[0085]

[0086] in, is the identity matrix, and the superscript t indicates the tth iteration;

[0087] Q subproblem: Solve Q from equation (8) t+1

[0088]

[0089] Using the threshold shrinkage algorithm, we can get

[0090]

[0091] P (k) Sub-problem: Use the singular value contraction method to solve [P (k) ] t+1

[0092]

[0093] D subproblem: Solve D from equation (11) t+1

[0094]

[0095] Available

[0096]

[0097] C subproblem: Solve C from equation (13) t+1

[0098]

[0099] Available

[0100]

[0101] in, is the identity matrix;

[0102] Sub-problem: Solve the equation (15) and

[0103]

[0104] Available

[0105]

[0106]

[0107] in, is the identity matrix;

[0108] can be and to obtain;

[0109]

[0110] Finally, the Lagrangian operators Y1, Y2, and Y3 can be updated by equation (19):

[0111]

[0112] After t iterations This is the reconstructed hyperspectral data.

[0113] Compared with the prior art, the advantages of the present invention are as follows: the present invention uses a spatial light modulator to perform efficient and flexible spectral modulation on the dispersed light source, and obtains spatial information by scanning point by point. The proposed hyperspectral compression imaging method can be applied to the beam scanning detection system. Then, the sparsity of the spectral information is fully utilized to construct a hyperspectral reconstruction model. In the spatial dimension of the hyperspectral tensor, the block clustering method is used to describe its spatial similarity. In the spectral dimension of the hyperspectral tensor, dictionary learning and sparse constraints are used to describe the spectral similarity. Finally, the alternating direction multiplier method is used to iteratively solve the hyperspectral reconstruction model, thereby using the compressed sampling image to reconstruct the target's hyperspectral data. Compared with the prior art, the present invention can reconstruct higher quality hyperspectral data based on less spectral compression observation data, and can be applied to the beam scanning detection system. BRIEF DESCRIPTION OF THE DRAWINGS

[0114] Figure 1 This is a schematic diagram of a single-photon hyperspectral imaging method based on spectral compression sampling.

[0115] Figure 2 is an example of a randomly sampled graph.

[0116] Figure 3 20 spectrum scanning images of the embodiment.

[0117] Figure 4 20 spectrum bands reconstructed image of the embodiment. DETAILED DESCRIPTION

[0118] In order to facilitate those skilled in the art to understand and implement the present invention, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0119] The present invention mainly addresses the problem that the hyperspectral compression imaging method is difficult to apply to the light beam scanning detection system, and proposes a single-photon hyperspectral imaging method based on spectral compression sampling. A spatial light modulator is used to perform random compression sampling on the spectrum of the illumination light source, and the modulated light beam is passed through a two-dimensional galvanometer to scan the target for spatial point imaging, and a single-pixel photon counter is used to receive the target's reflected signal. Then, the hyperspectral data of the target is reconstructed from the compressed observation data through a hyperspectral reconstruction model based on tensor representation. In contrast, the above-mentioned imaging system is used to individually select each spectral band to obtain the scanning image of each spectral band of the target, as shown in the attached figure. Figure 3 shown.

[0120] This embodiment provides a single-photon hyperspectral imaging method based on spectral compression sampling to perform hyperspectral compression imaging, which specifically includes the following steps:

[0121] Step 1: Build the optical path of the imaging system. The white light source is spectrally expanded in the horizontal direction of space through a prism. After the expanded light beam passes through the lens, it passes through the spectral modulation module in parallel, including a polarizer, a spatial light modulator, and an analyzer. The modulation surface of the spatial light modulator is a 780nm-380nm spectrum from left to right. The lens is then used to converge the spectrally modulated light beam onto a two-dimensional galvanometer. The light beam scans the target through the galvanometer, and the reflected light from the target surface is received by a single-pixel photon counter. The imaging time for a single scan is 10s, and 100×100 spatial pixels are collected;

[0122] Step 2: Import the spatial light modulator into the spectral random sampling map. The sampling map is divided into 20 equal parts horizontally, that is, into 20 spectral segments. A 1×20 random sampling matrix is ​​generated using the 0-1 modulation method, and a spectral random sampling map is generated based on the random sampling matrix to randomly select the 20 spectral segments. This embodiment performs two spectral compression samplings, and each spectral compression sampling corresponds to a spectral random sampling map. The size of the spectral random sampling matrix Ψ is 2×20 and is composed of two random sampling matrices;

[0123] Step 3: Construct a hyperspectral reconstruction model based on tensor representation. A fidelity term based on tensor representation is established according to the spectral compression sampling process, and then a priori constraints are introduced based on signal characteristics. In the spatial dimension of the tensor expansion, a block clustering method is used to describe spatial similarity. In the spectral dimension of the tensor expansion, dictionary learning and sparse constraints are used to describe spectral similarity. The specific implementation includes the following sub-steps:

[0124] Step 3.1: For the hyperspectral data to be restored, first represent it as a third-order tensor form At the same time, the compressed observation data can also be represented as a third-order tensor The spectral compression imaging process can be described as follows:

[0125]

[0126] in, for The 3-mode expansion matrix, for The 3-mode expansion matrix, is the spectral random sampling matrix, is the spectral fuzzy matrix.

[0127] Step 3.2: Hyperspectral data Perform spatial dimension expansion to obtain a 1-mode expansion matrix Use the block clustering method to describe its spatial similarity. Define f(H (1) ) is for H (1)Perform block clustering operation: H (1) It is divided into 2000 7×15 small blocks, and then the k-means clustering method is used to divide all the small blocks into 20 groups, where the kth group is represented by f (k) (H (1) ). Using the nuclear norm to constrain the similarity between blocks in each cluster group can be expressed as the following constraint terms:

[0128]

[0129] Among them, λ1 is the equilibrium parameter.

[0130] Step 3.3: Hyperspectral data Expand the spectrum dimension and obtain the 3-mode expansion matrix H (3) , using dictionary learning method to constrain the sparsity of spectral information. (3) Decompose into dictionary matrix and coefficient matrix And taking advantage of the sparsity of the L1 norm constraint coefficient matrix, it can be expressed as the following constraint terms:

[0131]

[0132] Among them, λ2 and λ3 are balance parameters.

[0133] Step 3.4, obtain the hyperspectral reconstruction model:

[0134]

[0135] Step 4: Using the observation data of the second spectral compression sampling as input, the alternating direction multiplier method is used to iteratively solve the hyperspectral reconstruction model to obtain the reconstructed hyperspectral data. The specific implementation includes the following sub-steps:

[0136] Step 4.1, use the alternating direction multiplier method to iteratively solve the hyperspectral reconstruction model. For formula (4), let U = H (3) B, P (k) =f (k) (H (1) ), Q=C, and the following formula is obtained:

[0137]

[0138] Among them, Y1, Y2 and Y3 are Lagrangian operators, and μ1, μ2 and μ3 are equilibrium operators.

[0139] Step 4.2: Decompose the above equation into 7 sub-problems and solve them iteratively.

[0140] U subproblem: Solve U from the following formula t+1

[0141]

[0142] Available

[0143]

[0144] in, is the identity matrix, and the superscript t indicates the t-th iteration.

[0145] Q subproblem: Solve Q from the following formula t+1

[0146]

[0147] Using the threshold shrinkage algorithm, we can get

[0148]

[0149] P (k) Sub-problem: Using the singular value shrinkage method, we can solve [P (k) ] t+1

[0150]

[0151] Subproblem D: Solve D from the following formula t+1

[0152]

[0153] Available

[0154]

[0155] Subproblem C: Solve C from the following formula t+1

[0156]

[0157] Available

[0158]

[0159] in, is the identity matrix.

[0160] Sub-problem: Solve the following equations separately and

[0161]

[0162] Available

[0163]

[0164]

[0165] in, is the identity matrix.

[0166] can be and Obtain

[0167]

[0168] Finally, the Lagrangian operators Y1, Y2, and Y3 can be updated by

[0169]

[0170] After t iterations In this embodiment, the number of iterations t is 30, and the parameters λ1 = 0.55, λ2 = 0.3, λ3 = 0.15, μ1 = 0.03, μ2 = 0.1, and μ3 = 0.08.

[0171] Based on the above steps, the target’s hyperspectral data is obtained. Figure 4 The reconstructed image of the target's 20 spectral bands. Figure 3 Compared with the single spectral segment scanning image in the figure, it can be seen that the method proposed in the present invention can reconstruct a hyperspectral image of 20 spectral segments using only the observation data of two spectral compression imaging, realizing the reconstruction of high-quality hyperspectral data using a small amount of spectral compression observation data, and achieving high-quality hyperspectral compression imaging.

[0172] The present invention also provides a single-photon hyperspectral imaging system based on spectral compression sampling, comprising the following modules:

[0173] The imaging system building module is used to build the imaging system optical path. The white light source is spectrally expanded horizontally in space by a prism. After passing through a lens, the expanded light beam passes parallel to the spectrum modulation module, including a polarizer, a spatial light modulator, and an analyzer. The modulation plane of the spatial light modulator covers the 380nm-780nm spectrum from right to left. The lens is then used to converge the spectrally modulated light beam onto a two-dimensional galvanometer. The light beam scans the target through the galvanometer, and the reflected light from the target surface is received by a single-pixel photon counter.

[0174] The random sampling map generation module is used to import the spatial light modulator into the spectral random sampling map. The sampling map is divided into λ equal parts along the horizontal direction, that is, λ spectral segments. A 1×λ random sampling matrix is ​​generated using a 0-1 modulation method. The spectral random sampling map generated based on the random sampling matrix is ​​randomly selected to select the λ spectral segments. During the imaging process, each compressed sampling corresponds to a spectral random sampling map. For N spectral compressed samplings, the total spectral random sampling matrix Ψ is N×λ and is composed of N random sampling matrices.

[0175] The hyperspectral reconstruction model construction module is used to construct a hyperspectral reconstruction model based on tensor representation. According to the spectral compression sampling process, a fidelity term based on tensor representation is established. Then, a priori constraints are introduced based on signal characteristics. In the spatial dimension of the tensor expansion, the block clustering method is used to describe its spatial similarity. In the spectral dimension of the tensor expansion, the spectral similarity is described using dictionary learning and sparse constraints.

[0176] The solution module is used to take the observation data of N-times spectral compression sampling as input, and iteratively solve the hyperspectral reconstruction model using the alternating direction multiplier method to obtain reconstructed hyperspectral data.

[0177] Furthermore, the specific implementation of the hyperspectral reconstruction model construction module is as follows;

[0178] Step 3.1: For the hyperspectral data to be restored, first represent it as a third-order tensor Among them, W×H represents the spatial resolution, W refers to the horizontal resolution of the hyperspectral data to be restored, H refers to the vertical resolution of the restored hyperspectral data, and λ represents the number of spectra; at the same time, the compressed observation data can also be represented as a third-order tensor The spectral compression imaging process can be described as follows:

[0179]

[0180] in, for The 3-mode expansion matrix, for The 3-mode expansion matrix, is the spectral random sampling matrix, is the spectral fuzzy matrix, represents the Frobenius norm;

[0181] Step 3.2: Hyperspectral data Perform spatial dimension expansion to obtain a 1-mode expansion matrix Use the block clustering method to describe its spatial similarity and define f(H (1) ) is for H (1)Perform block clustering operation: H (1) Divide into L d r ×d c Then, the k-means clustering method is used to divide all the small blocks into K groups, where the kth group is represented by f (k) (H (1) ), the nuclear norm is used to constrain the similarity between blocks in each cluster group, which can be expressed as the following constraint terms:

[0182]

[0183] Where λ1 is the equilibrium parameter, ||·|| * represents the nuclear norm;

[0184] Step 3.3: Hyperspectral data Perform spectral dimension expansion to obtain the 3-mode expansion matrix H (3) , using dictionary learning method to constrain the sparsity of spectral information, H (3) Decompose into dictionary matrix and coefficient matrix And taking advantage of the sparsity of the L1 norm constraint coefficient matrix, it can be expressed as the following constraint terms:

[0185]

[0186] Among them, λ2 and λ3 are balance parameters, ||·||1 represents the L1 norm;

[0187] Step 3.4, based on formula (1-3), obtain the hyperspectral reconstruction model:

[0188]

[0189] Furthermore, the specific implementation of the solution module is as follows;

[0190] Step 4.1, use the alternating direction multiplier method to iteratively solve the hyperspectral reconstruction model. For formula (4), let U = H (3) B, P (k) =f (k) (H (1) ), Q=C, and the following formula is obtained:

[0191]

[0192] Among them, Y1, Y2 and Y3 are Lagrangian operators, μ1, μ2 and μ3 are equilibrium operators;

[0193] Step 4.2, decompose formula (5) into 7 sub-problems and solve them iteratively;

[0194] U subproblem: Solve U from equation (6) t+1

[0195]

[0196] Available

[0197]

[0198] in, is the identity matrix, and the superscript t indicates the tth iteration;

[0199] Q subproblem: Solve Q from equation (8) t+1

[0200]

[0201] Using the threshold shrinkage algorithm, we can get

[0202]

[0203] P (k) Sub-problem: Use the singular value contraction method to solve [P (k) ] t+1

[0204]

[0205] D subproblem: Solve D from equation (11) t+1

[0206]

[0207] Available

[0208]

[0209] C subproblem: Solve C from equation (13) t+1

[0210]

[0211] Available

[0212]

[0213] in, is the identity matrix;

[0214] Sub-problem: Solve the equation (15) and

[0215]

[0216] Available

[0217]

[0218]

[0219] in, is the identity matrix;

[0220] can be and to obtain;

[0221]

[0222] Finally, the Lagrangian operators Y1, Y2, and Y3 can be updated by equation (19):

[0223]

[0224] After t iterations This is the reconstructed hyperspectral data.

[0225] It should be understood that parts not elaborated in detail in this specification belong to the prior art.

[0226] It should be understood that the above description of the embodiments is relatively detailed and cannot be regarded as limiting the scope of protection of the patent of the present invention. Under the guidance of the present invention, ordinary technicians in this field can also make substitutions or modifications without departing from the scope of protection of the claims of the present invention, which all fall within the scope of protection of the present invention. The scope of protection requested by the present invention shall be based on the attached claims.

Claims

1. A single-photon hyperspectral imaging method based on spectral compression sampling, characterized in that: include: A prism is used to expand the spectrum of a white light source in the horizontal direction of space. The spectrum is then randomly sampled using a spatial light modulator. The sampled light beam passes through a two-dimensional galvanometer to scan the target in space, and a single-pixel photon counter is used to collect signals. Furthermore, a hyperspectral reconstruction model is constructed. First, a fidelity term based on tensor representation is established according to the spectral compression sampling process. Then, prior constraints are introduced according to the signal characteristics. In the spatial dimension of the tensor expansion, the block clustering method is used to describe its spatial similarity. In the spectral dimension of the tensor expansion, dictionary learning and sparse constraints are used to describe the spectral similarity. Finally, the alternating direction multiplier method is used to iteratively solve the hyperspectral reconstruction model, thereby reconstructing the hyperspectral data of the target using the compressed sampling image.

2. The single-photon hyperspectral imaging method based on spectral compression sampling according to claim 1, characterized in that: The specific steps include: Step 1: Build the optical path of the imaging system. A white light source is spectrally expanded horizontally in space through a prism. The expanded light beam passes through a lens and then passes parallel to a spectral modulation module, including a polarizer, a spatial light modulator, and an analyzer. The modulation plane of the spatial light modulator covers a 380nm-780nm spectrum from right to left. The spectrally modulated light beam is then converged onto a two-dimensional galvanometer using a lens. The light beam scans the target through the galvanometer, and the reflected light from the target surface is received by a single-pixel photon counter. Step 2: Import the spatial light modulator into the spectrum random sampling map, and the sampling map is carried out in the horizontal direction. Divide equally and obtain spectral segments, generated using the 0-1 modulation method The random sampling matrix is ​​used to generate the spectral random sampling map pair according to the random sampling matrix. Random selection of spectrum segments; During the imaging process, each compression sampling corresponds to a spectral random sampling map. For N times of spectral compression sampling, the total spectral random sampling matrix is The size is , consisting of N random sampling matrices; Step 3: Build a hyperspectral reconstruction model based on tensor representation. Establish a fidelity term based on tensor representation according to the spectral compression sampling process. Then, introduce prior constraints based on signal characteristics. In the spatial dimension of tensor expansion, use block clustering to describe spatial similarity. In the spectral dimension of tensor expansion, use dictionary learning and sparsity constraints to describe spectral similarity. In step 4, the observation data of N-times spectral compression sampling is used as input, and the hyperspectral reconstruction model is iteratively solved using the alternating direction multiplier method to obtain the reconstructed hyperspectral data.

3. The single-photon hyperspectral imaging method based on spectral compression sampling according to claim 2, characterized in that: The specific implementation of step 3 includes the following sub-steps: Step 3.1: For the hyperspectral data to be restored, first represent it as a third-order tensor ,in, Indicates spatial resolution, W refers to the horizontal resolution of the hyperspectral data to be restored, and H refers to the vertical resolution of the restored hyperspectral data. Represents the spectral number; at the same time, the compressed observation data is also represented as a third-order tensor , the spectral compression imaging process is described as the following fidelity terms: (1) in, for The 3-mode expansion matrix, for The 3-mode expansion matrix, is the spectral random sampling matrix, is the spectral fuzzy matrix, represents the Frobenius norm; Step 3.2: Hyperspectral data Perform spatial dimension expansion to obtain a 1-mode expansion matrix , using the block clustering method to describe its spatial similarity, defining For Perform block clustering operation: Split into indivual Then use k-means clustering method to divide all the small blocks into Group, of which Groups are represented as , the nuclear norm is used to constrain the similarity between blocks in each cluster group, which is expressed as the following constraint terms: (2) in, is the balance parameter, represents the nuclear norm; Step 3.3: Hyperspectral data Perform spectral dimension expansion to obtain a 3-mode expansion matrix , using dictionary learning method to constrain the sparsity of spectral information, Decompose into dictionary matrix and coefficient matrix , and use The norm constrains the sparsity of the coefficient matrix, expressed as the following constraints: (3) in, and is the balance parameter, represents the L1 norm; Step 3.4, based on formula (1-3), obtain the hyperspectral reconstruction model: (4)。 4. The single-photon hyperspectral imaging method based on spectral compression sampling according to claim 3, characterized in that: The specific implementation of step 4 includes the following sub-steps: Step 4.1, use the alternating direction multiplier method to iteratively solve the hyperspectral reconstruction model. For formula (4), let , , , we get the following formula: (5) in, 、 and is the Lagrangian operator, 、 and is the balance operator; Step 4.2, decompose formula (5) into 7 sub-problems and solve them iteratively; Sub-problem: Solve from formula (6) (6) have to (7) in, is the identity matrix, the superscript Indicates the iterations; Sub-problem: Solve from formula (8) (8) Using the threshold shrinkage algorithm, we get (9) Subproblem: Solve Equation (10) using the singular value contraction method (10) Sub-problem: Solve from formula (11) (11) have to (12) Sub-problem: Solve from formula (13) (13) have to (14) in, is the identity matrix; Sub-problem: Solve the equation (15) and (15) have to (16) (17) in, is the identity matrix; Depend on and to obtain; (18) Finally, the Lagrangian operator 、 and Updated by formula (19) (19) go through After iterations This is the reconstructed hyperspectral data.

5. The single-photon hyperspectral imaging method based on spectral compression sampling according to claim 2, characterized in that: In step 1, the single scanning imaging time is 10 s, and 100×100 spatial pixels are collected.

6. The single-photon hyperspectral imaging method based on spectral compression sampling according to claim 2, characterized in that: 。 7. The single-photon hyperspectral imaging method based on spectral compression sampling according to claim 4, characterized in that: parameter , , , , , .

8. A single-photon hyperspectral imaging system based on spectral compression sampling, characterized in that: Includes the following modules: The imaging system building module is used to build the imaging system optical path. The white light source is spectrally expanded horizontally in space by a prism. After passing through a lens, the expanded light beam passes parallel to the spectrum modulation module, including a polarizer, a spatial light modulator, and an analyzer. The modulation plane of the spatial light modulator covers the 380nm-780nm spectrum from right to left. The lens is then used to converge the spectrally modulated light beam onto a two-dimensional galvanometer. The light beam scans the target through the galvanometer, and the reflected light from the target surface is received by a single-pixel photon counter. Random sampling map generation module is used to import the spatial light modulator into the spectrum random sampling map, and the sampling map is carried out in the horizontal direction. Equally divided, that is spectral segments, generated using the 0-1 modulation method The random sampling matrix is ​​used to generate the spectral random sampling map pair according to the random sampling matrix. Random selection of spectrum segments; During the imaging process, each compression sampling corresponds to a spectral random sampling map. For N times of spectral compression sampling, the total spectral random sampling matrix is The size is , consisting of N random sampling matrices; The hyperspectral reconstruction model construction module is used to construct a hyperspectral reconstruction model based on tensor representation. According to the spectral compression sampling process, a fidelity term based on tensor representation is established. Then, a priori constraints are introduced based on signal characteristics. In the spatial dimension of the tensor expansion, the block clustering method is used to describe its spatial similarity. In the spectral dimension of the tensor expansion, the spectral similarity is described using dictionary learning and sparse constraints. The solution module is used to take the observation data of N-times spectral compression sampling as input and iteratively solve the hyperspectral reconstruction model using the alternating direction multiplier method to obtain the reconstructed hyperspectral data.

9. The single-photon hyperspectral imaging system based on spectral compression sampling according to claim 8, characterized in that: The specific implementation of the hyperspectral reconstruction model building module is as follows; Step 3.1: For the hyperspectral data to be restored, first represent it as a third-order tensor ,in, Indicates spatial resolution, W refers to the horizontal resolution of the hyperspectral data to be restored, and H refers to the vertical resolution of the restored hyperspectral data. Represents the spectral number; at the same time, the compressed observation data is also represented as a third-order tensor , the spectral compression imaging process is described as the following fidelity terms: (1) in, for The 3-mode expansion matrix, for The 3-mode expansion matrix, is the spectral random sampling matrix, is the spectral fuzzy matrix, represents the Frobenius norm; Step 3.2: Hyperspectral data Perform spatial dimension expansion to obtain a 1-mode expansion matrix , using the block clustering method to describe its spatial similarity, defining For Perform block clustering operation: Split into indivual Then use k-means clustering method to divide all the small blocks into Group, of which Groups are represented as , the nuclear norm is used to constrain the similarity between blocks in each cluster group, which is expressed as the following constraint terms: (2) in, is the balance parameter, represents the nuclear norm; Step 3.3: Hyperspectral data Perform spectral dimension expansion to obtain a 3-mode expansion matrix , using dictionary learning method to constrain the sparsity of spectral information, Decompose into dictionary matrix and coefficient matrix , and use The norm constrains the sparsity of the coefficient matrix, expressed as the following constraints: (3) in, and is the balance parameter, represents the L1 norm; Step 3.4, based on formula (1-3), obtain the hyperspectral reconstruction model: (4)。 10. The single-photon hyperspectral imaging system based on spectral compression sampling according to claim 9, characterized in that: The specific implementation of the solution module is as follows; Step 4.1, use the alternating direction multiplier method to iteratively solve the hyperspectral reconstruction model. For formula (4), let , , , we get the following formula: (5) in, 、 and is the Lagrangian operator, 、 and is the balance operator; Step 4.2, decompose formula (5) into 7 sub-problems and solve them iteratively; Sub-problem: Solve from formula (6) (6) have to (7) in, is the identity matrix, the superscript Indicates the iterations; Sub-problem: Solve from formula (8) (8) Using the threshold shrinkage algorithm, we get (9) Subproblem: Solve Equation (10) using the singular value contraction method (10) Sub-problem: Solve from formula (11) (11) have to (12) Sub-problem: Solve from formula (13) (13) have to (14) in, is the identity matrix; Sub-problem: Solve the equation (15) and (15) have to (16) (17) in, is the identity matrix; Depend on and to obtain; (18) Finally, the Lagrangian operator 、 and Updated by formula (19) (19) go through After iterations This is the reconstructed hyperspectral data.

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