Spectral reconstruction method for channel type polarization spectrometer based on adaptive sparse basis

Abstract

This invention discloses a spectral reconstruction method for a channel-type polarization spectrometer based on adaptive sparse bases, comprising the following steps: 1. Input data: Obtain the measured spectrum through a CSP modulation system; 2. Obtain the preliminary reconstructed spectrum: Input a sparse basis matrix composed of a traditional Legendre polynomial and a DCT basis, and obtain an approximate spectral solution using compressed channel polarization technology; 3. Form an adaptive sparse basis matrix and iteratively solve for the reconstructed spectrum: By removing "useless atoms" from the original sparse basis and adding "sub-subdivision atoms" to the remaining effective atomic functions, an adaptive sparse basis matrix is ​​formed. The adaptive sparse basis matrix is ​​then iteratively solved to obtain a better reconstructed spectrum. This invention improves the reconstruction effect of traditional compressed channel polarization methods for high-frequency spectral signals and those with multiple absorption peaks, further enhancing the reconstruction accuracy of high-frequency complex spectra.

Description

Technical Field

[0001] This invention relates to the field of channel-type polarization spectroscopy measurement technology and the field of spectral reconstruction based on compressed sensing. Background Technology

[0002] In recent years, channel polarization spectroscopy has been widely used in atmospheric aerosol characterization, target identification, and remote sensing, thus attracting research attention in the field of polarization spectral reconstruction. Accurate reconstruction of Stokes parameters is crucial in this snapshot technique. The most advanced algorithms utilize Fourier transform to extract Stokes parameters from the channels in the Fourier domain, but this method is highly sensitive to noise and channel crosstalk.

[0003] Compressive sensing (CS) is an emerging sampling method that reduces coding complexity by simultaneously sampling and compressing through linear projection. It captures sparse or compressible signals as compressed signals through linear projection, allowing the original complete signal to be recovered from a small amount of compressed signal. Recently, a compressed channel polarization spectroscopy technique was proposed. Reconstruction in channel spectropolarimetry is an underdetermined problem; 3N unknown Stokes parameters can be solved by performing N measurements. Inspired by compressed sensing, an optimization problem is proposed by creating a mathematical model of a channel spectropolarimeter. This method addresses some shortcomings of the traditional Fourier transform method and exhibits higher noise robustness and reconstruction accuracy. However, some problems still exist.

[0004] 1. This method only reconstructs the linear polarization components, thus losing the circular polarization information.

[0005] 2. This method cannot achieve good polarization spectrum reconstruction results when dealing with high-frequency spectral signals and spectral signals with multiple absorption peaks. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a spectral reconstruction method for a channel-type polarization spectrometer based on adaptive sparse bases, aiming to improve the reconstruction effect of high-frequency spectral signals and those with multiple absorption peaks, thereby enhancing the reconstruction accuracy of high-frequency complex spectra.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] The spectral reconstruction method for a channel-type polarization spectrometer based on adaptive sparse bases of the present invention is characterized by comprising the following steps:

[0009] Step 1: Obtain the output measurement spectrum as shown in equation (1) using the CSP modulation system:

[0010]

[0011] In equation (1), y measured The output measured spectrum intensity is represented by λ, where λ is the wavelength, and S0, S1, S2, and S3 represent the four Stokes parameters of the input light of the CSP modulation system. This indicates the phase delay corresponding to the first multi-stage waveplate. Let represent the phase delay corresponding to the second multi-level waveplate, and we have:

[0012]

[0013] In equation (2), d1 and d2 are the thicknesses of the first and second multi-stage waveplates, respectively, and n o ,n e These are the refractive indices corresponding to the ordinary and unusual rays in the waveplate, respectively;

[0014] Step 2, obtain the preliminary reconstructed spectrum:

[0015] Step 2.1, construct the regularization function using equation (3). Then, the compressed channel spectral polarization method was used to solve equation (3) to obtain the optimized four sparse basis coefficients.

[0016]

[0017]

[0018] In equation (3), Denotes the i-th Stokes parameter s i The j-th sparse basis coefficients of the Discrete Cosine Transform (DCT) basis, τ is the threshold, and st represents the constraint condition; y model The intensity of the output measured spectrum obtained by the compressed channel spectral polarization method is represented by β, where β represents the regularization weight and R represents the regularization term.

[0019] Step 2.2: Define the current iteration number as k and initialize k = 1; set the optimized four sparse basis coefficients... The four sparse basis coefficients for the (k-1)th iteration

[0020] Step 2.3: Obtain the spectral approximation solution for the (k-1)th iteration using equation (4).

[0021]

[0022] In equation (4), Let represent the sparse basis matrix for the (k-1)th iteration. When k = 1, let M is a sparse basis matrixsupport ; This represents the i-th Stokes parameter in the (k-1)-th iteration. Represents the ith sparse basis coefficient in the (k-1)th iteration;

[0023] Step 3: Iteratively calculate the reconstructed polarization spectrum;

[0024] Step 3.0: Delete the sparse basis matrix of the (k-1)th iteration. After removing atoms whose sparse basis coefficients are less than the threshold δ, the processed sparse basis matrix after the (k-1)th iteration is obtained.

[0025] Step 3.1: Find the sparse basis matrices respectively. The sparse basis coefficients of the Legendre polynomial and the atoms in the sparse basis corresponding to the sparse basis coefficients in the Discrete Cosine Transform (DCT) basis that are greater than a certain threshold μ are considered as effective atoms.

[0026] Step 3.2, use equation (5) to calculate the nth subdivision Legendre polynomial P added near the effective atom. n M′ (x) and the element M′ in the m-th row and n-th column of the added subdivision Discrete Cosine Transform (DCT) basis. dct (m,n), thus forming the refined sparse basis matrix of the (k-1)th iteration composed of all added Legendre polynomials and discrete cosine transform bases.

[0027]

[0028] In equation (5), n represents the number of Legendre polynomials, x is the number of uniform samples in the interval (-1, 1), a is the number of cyclic summations in the Legendre polynomials, i represents the amount of subdivision added in the interval (-0.5, 0.5), N is the number of sampling points, and S is the number of added Discrete Cosine Transform (DCT) sparse bases.

[0029] Step 3.4: Use equation (6) to obtain the adaptive sparse basis matrix for the k-th iteration.

[0030]

[0031] In equation (6), W represents the total number of sparse bases added;

[0032] Step 3.5: Construct the regularization function for the k-th iteration using equation (7).

[0033]

[0034] In equation (7), Let y′ be the coefficients of the four sparse basis functions in the k-th iteration.model The intensity of the measured spectrum is output for the target; in step 3.6, the optimal spectral solution for the k-th iteration is obtained using equation (8).

[0035]

[0036] In equation (8), This represents the i-th reconstructed Stokes parameter in the k-th iteration. Represents the i-th sparse basis coefficient in the k-th iteration;

[0037] Step 3.7: Use equation (9) to obtain the adaptive sparse basis matrix for the (k+1)th iteration.

[0038]

[0039] Step 3.8: Use equation (10) to obtain the four reconstructed Stokes parameters for the (k+1)th iteration.

[0040]

[0041] In equation (10), Represents the ith sparse basis coefficient in the (k+1)th iteration;

[0042] Step 3.9: Determine whether equation (11) is true. If it is true, the iteration stops and the spectral optimization solution of the (k+1)th iteration is output. And use it as the reconstructed polarization spectrum; otherwise, assign k+1 to k and return to step 3 for sequential execution:

[0043]

[0044] In equation (11), i = 0, 1, 2, 3, and ε is the stop threshold.

[0045] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the spectral reconstruction method of the channel polarization spectrometer, and the processor is configured to execute the program stored in the memory.

[0046] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs the steps of the channel polarization spectrometer spectral reconstruction method.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] 1. Compared with traditional compressed channel polarization spectroscopy, the spectral reconstruction method of this invention provides reconstruction of all Stokes components. Furthermore, it uses traditional methods as prior information to optimize adaptive sparse bases, improving the sparse representation capability of the sparse bases. It significantly improves the reconstruction effect for high-frequency spectra with multiple absorption peaks, reduces edge effects and high-frequency details in spectral reconstruction, and enhances the overall reconstruction accuracy.

[0049] 2. This invention obtains the measured spectrum through a CSP modulation system; then, it inputs a sparse basis matrix composed of a traditional Legendre polynomial and a DCT basis, and uses compressed channel spectral polarization technology to obtain an approximate solution for the spectrum; next, it removes "useless atoms" from the original sparse basis and adds "subdivision atoms" to the remaining effective atomic functions to form an adaptive sparse basis matrix, and uses the adaptive sparse basis matrix to solve for the reconstructed spectrum; finally, by repeating the above process, a better spectrum reconstruction effect is obtained. Attached Figure Description

[0050] Figure 1 This is a flowchart of the spectral reconstruction method for a channel polarization spectrometer based on adaptive sparse bases in this invention;

[0051] Figure 2 This is a system structure diagram of the measurement spectrum obtained by the CSP modulation system in this invention;

[0052] Figure 2 In the diagram: R1 and R2 are multi-level waveplates with thicknesses d1 and d2, respectively, with their fast axes at 0 degrees and 45 degrees relative to the horizontal direction. A is a polarizer with its fast axis at 0 degrees.

[0053] Figure 3 This is a preliminary spectral reconstruction diagram of the traditional compressed channel spectral polarization technique in this invention;

[0054] Figure 4 This is the final optimized spectral reconstruction diagram of the channel polarization spectrometer spectral reconstruction method based on adaptive sparse basis in this invention;

[0055] Figure 3 and Figure 4 S0 in the equation represents the solar spectral signal, S1 is 0.5 times S0, S2 is 0.3 times S0, and S3 is 0.2 times S0. Detailed Implementation

[0056] In this implementation example, such as Figure 1 As shown, a spectral reconstruction method for a channel-type polarization spectrometer based on adaptive sparse bases includes the following steps:

[0057] Step 1, Input Data: Obtain the output measurement spectrum as shown in Equation (4) through the CSP (Channeled Spectropolarimetry) modulation system:

[0058] Through such Figure 2 The measurement spectrum obtained by the CSP modulation system shown is obtained as follows:

[0059] Input Stokes vector: S in (λ)=[S0(λ),S1(λ),S2(λ),S3(λ)] T (1)

[0060] The Mueller matrix of the CSP optical system is:

[0061]

[0062] The output after passing through the optical system is: S out (λ)=M(λ)·S in (λ)(3)

[0063] The output measurement spectrum is:

[0064] In equation (4), y measured The value represents the intensity of the measured output spectrum, λ is the wavelength ranging from 500-800 nm, and S0, S1, S2, and S3 represent the four Stokes parameters of the input light of the CSP modulation system. This indicates the phase delay corresponding to the first multi-stage waveplate. Let represent the phase delay corresponding to the second multi-level waveplate, and we have:

[0065]

[0066] In equation (5), d1 and d2 are the thicknesses of the first and second multi-level waveplates, respectively, and are 0.58 cm and 1.16 cm. o ,n e Let n0-n be the refractive indices corresponding to the ordinary and unusual rays in the waveplate, respectively. e =0.0092;

[0067] Step 2, Obtain the preliminary reconstructed spectrum: Input a sparse basis matrix composed of a traditional Legendre polynomial and a DCT (Discrete Cosine Transform) basis, and use compressed channel spectral polarization technique to obtain an approximate spectral solution, as follows:

[0068] Legendre polynomials and DCT basis expressions are as follows:

[0069]

[0070] Among them, P n (x) represents the Legendre polynomial, n represents the number of Legendre polynomials, and a is the number of cyclic sums in the Legendre polynomial; M dct (m,n) represents the Discrete Cosine Transform (DCT) basis, where m and n represent the m-th row and n-th column, respectively; x is the uniform sampling number in (-1, 1), and N is the number of sampling points with a value of 600.

[0071] The sparse basis matrix formed by them is:

[0072]

[0073] In equation (7), L is the number of Legendre polynomials, which takes the value of 5, and M... support It is a sparse basis matrix.

[0074] Stokes vectors can be represented by sparse basis matrices as follows:

[0075] S i =M support s i (8)

[0076] Among them, s i Denotes the sparse basis coefficients and has the following:

[0077]

[0078] The intensity of the output measured spectrum obtained by the compressed channel spectral polarization method is:

[0079]

[0080] in:

[0081]

[0082] The regularization function is:

[0083]

[0084] Step 2.1, construct the regularization function using equation (13). The compressed channel spectral polarization method was used to solve equation (13) to obtain the optimized four sparse basis coefficients.

[0085]

[0086]

[0087] In equation (13), Denotes the i-th Stokes parameter s iThe j-th sparse basis coefficients of the Discrete Cosine Transform (DCT) basis, where τ is the threshold value of 180, and st represents the constraint condition; y model The intensity of the output measured spectrum obtained by the compressed channel spectral polarization method is represented by β, which represents the regularization weight with a value of 0.001, and R represents the regularization term. The optimization constraint is to set the DCT basis coefficient components that are greater than a certain threshold to zero in order to avoid high-frequency oscillations.

[0088] Step 2.2: Define the current iteration number as k and initialize k = 1; set the optimized four sparse basis coefficients... The four sparse basis coefficients for the (k-1)th iteration

[0089] Step 2.3: Obtain the spectral approximation solution for the (k-1)th iteration using equation (14).

[0090]

[0091] In equation (14), Let represent the sparse basis matrix for the (k-1)th iteration. When k = 1, let M is a sparse basis matrix support ; This represents the i-th Stokes parameter in the (k-1)-th iteration. Represents the ith sparse basis coefficient in the (k-1)th iteration;

[0092] like Figure 3 The figure shows the spectrum of the spectral approximation solution. It can be seen from the figure that the reconstructed spectrum obtained by the traditional compressed channel polarization spectroscopy method is not very good for this spectrum with high frequency and multiple absorption peaks. The edge effect is more obvious, and the reconstruction effect of S2 and S3 is poor.

[0093] Step 3: By removing the "useless atoms" in the original sparse basis and adding "subdivision atoms" to the remaining effective atomic functions, an adaptive sparse basis matrix is ​​formed. The reconstructed polarization spectrum is then calculated iteratively using the adaptive sparse basis matrix.

[0094] Step 3.0: Delete the sparse basis matrix of the (k-1)th iteration. After identifying atoms with sparse basis coefficients less than the threshold δ = 0.001, the processed sparse basis matrix is ​​obtained in the (k-1)th iteration.

[0095] Secondly, atomic functions are identified from the remaining effective atoms according to certain criteria. This invention extracts all reconstructed sparse spectral components corresponding to the Legendre polynomials and the atomic function sequences in the DCT basis that exceed a certain threshold. Here, we can call these extracted atoms "incomplete atoms," meaning that high-frequency signals may have incomplete sparse representations. If high-frequency information exists somewhere in the spectral signal, it is most likely to be sparsely represented by atomic functions of larger reconstructed sparse components in the sparse basis. Therefore, high-frequency spectral signals that cannot be precisely represented should exist near "incomplete atoms." Thus, by adding refined atomic functions near "incomplete atoms," adaptive optimization of the sparse basis can be achieved. In this invention, refined atomic functions are inserted into the Legendre polynomials representing low-frequency signals and the DCT basis representing high-frequency signals, respectively, to form adaptive sparse bases.

[0096] Step 3.1: Find the sparse basis matrices respectively. The sparse basis coefficients of the Legendre polynomial and the atoms in the sparse basis corresponding to the sparse basis coefficients in the Discrete Cosine Transform (DCT) basis that are greater than a certain threshold μ = 0.15 are considered as effective atoms.

[0097] Step 3.2, use equation (15) to calculate the nth subdivision Legendre polynomial P added near the effective atom. n M′ (x) and the element M′ in the m-th row and n-th column of the added subdivision Discrete Cosine Transform (DCT) basis. dct (m,n), thus forming the refined sparse basis matrix of the (k-1)th iteration composed of all added Legendre polynomials and discrete cosine transform bases.

[0098]

[0099] In equation (15), S is the number of added Discrete Cosine Transform (DCT) sparse bases;

[0100] Step 3.4: Use equation (16) to obtain the adaptive sparse basis matrix for the k-th iteration.

[0101]

[0102] In equation (16), W represents the total number of sparse bases added;

[0103] Then the intensity of the target output measured spectrum at this time is:

[0104]

[0105] Finally, the polarization spectrum was reconstructed using the optimized sparse basis to obtain a more accurate reconstructed spectrum.

[0106] Step 3.5: Construct the regularization function for the k-th iteration using equation (18).

[0107]

[0108] In equation (18), Let y′ be the coefficients of the four sparse basis functions in the k-th iteration. model The intensity of the measured spectrum is output for the target; in step 3.6, the optimal spectral solution for the k-th iteration is obtained using equation (19).

[0109]

[0110] In equation (19), This represents the i-th reconstructed Stokes parameter in the k-th iteration. Represents the i-th sparse basis coefficient in the k-th iteration;

[0111] Step 3.7: Use equation (20) to obtain the adaptive sparse basis matrix for the (k+1)th iteration.

[0112]

[0113] Step 3.8: Use equation (21) to obtain the four reconstructed Stokes parameters for the (k+1)th iteration.

[0114]

[0115] In equation (21), Represents the ith sparse basis coefficient in the (k+1)th iteration;

[0116] Step 3.9: Determine whether equation (22) is true. If it is true, the iteration stops and the spectral optimization solution of the (k+1)th iteration is output. And use it as the reconstructed polarization spectrum; otherwise, assign k+1 to k and return to step 3 for sequential execution:

[0117]

[0118] In formula (22), i=0,1,2,3, ε=10 -4 This is the stop threshold.

[0119] like Figure 4 The image shows the reconstructed spectrum after iterative optimization. The comparison can be seen from the figure. Figure 3The reconstruction effect of traditional methods has been significantly improved. The reconstruction effect of high-frequency spectra with multiple absorption peaks has been significantly improved, the edge effect and high-frequency details of spectral reconstruction have been improved, and the overall reconstruction accuracy has been improved.

[0120] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0121] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

Claims

1. A spectral reconstruction method for a channel-type polarization spectrometer based on adaptive sparse bases, characterized in that, Includes the following steps: Step 1: Obtain the output measurement spectrum as shown in equation (1) using the CSP modulation system: In equation (1), y measured The output measured spectrum intensity is represented by λ, where λ is the wavelength, and S0, S1, S2, and S3 represent the four Stokes parameters of the input light of the CSP modulation system. This indicates the phase delay corresponding to the first multi-stage waveplate. Let represent the phase delay corresponding to the second multi-level waveplate, and we have: In equation (2), d1 and d2 are the thicknesses of the first and second multi-stage waveplates, respectively, and n o ,n e These are the refractive indices corresponding to the ordinary and unusual rays in the waveplate, respectively; Step 2, obtain the preliminary reconstructed spectrum: Step 2.1, construct the regularization function using equation (3). Then, the compressed channel spectral polarization method was used to solve equation (3) to obtain the optimized four sparse basis coefficients. In equation (3), Denotes the i-th Stokes parameter s i The j-th sparse basis coefficients of the Discrete Cosine Transform (DCT) basis, τ is the threshold, and st represents the constraint condition; y model The intensity of the output measured spectrum obtained by the compressed channel spectral polarization method is represented by β, where β represents the regularization weight and R represents the regularization term. Step 2.2: Define the current iteration number as k and initialize k = 1; set the optimized four sparse basis coefficients... The four sparse basis coefficients in the (k-1)th iteration Step 2.3: Obtain the spectral approximation solution for the (k-1)th iteration using equation (4). In equation (4), Let represent the sparse basis matrix of the (k-1)th iteration. When k=1, let M is a sparse basis matrix support ; This represents the i-th Stokes parameter in the (k-1)-th iteration. Represents the ith sparse basis coefficient in the (k-1)th iteration; Step 3: Iteratively calculate the reconstructed polarization spectrum; Step 3.0: Delete the sparse basis matrix of the (k-1)th iteration. After removing atoms whose sparse basis coefficients are less than the threshold δ, the processed sparse basis matrix after the (k-1)th iteration is obtained. Step 3.1: Find the sparse basis matrices respectively. The sparse basis coefficients of the Legendre polynomial and the atoms in the sparse basis corresponding to the sparse basis coefficients in the Discrete Cosine Transform (DCT) basis that are greater than a certain threshold μ are considered as effective atoms. Step 3.2, use equation (5) to calculate the nth subdivision Legendre polynomial P added near the effective atom. n M′ (x) and the element M′ in the m-th row and n-th column of the added subdivision Discrete Cosine Transform (DCT) basis. dct (m,n), thus forming the refined sparse basis matrix of the (k-1)th iteration composed of all added Legendre polynomials and discrete cosine transform bases. In equation (5), n represents the number of Legendre polynomials, x is the number of uniform samples in the interval (-1, 1), a is the number of cyclic summations in the Legendre polynomials, i represents the amount of subdivision added in the interval (-0.5, 0.5), N is the number of sampling points, and S is the number of added Discrete Cosine Transform (DCT) sparse bases. Step 3.4: Use equation (6) to obtain the adaptive sparse basis matrix for the k-th iteration. In equation (6), W represents the total number of sparse bases added; Step 3.5: Construct the regularization function for the k-th iteration using equation (7). In equation (7), Let y′ be the coefficients of the four sparse basis functions in the k-th iteration. model Output the intensity of the measured spectrum for the target; Step 3.6: Use equation (8) to obtain the spectral optimization solution for the k-th iteration. In equation (8), This represents the i-th reconstructed Stokes parameter in the k-th iteration. Represents the i-th sparse basis coefficient in the k-th iteration; Step 3.7: Use equation (9) to obtain the adaptive sparse basis matrix for the (k+1)th iteration. Step 3.8: Use equation (10) to obtain the four reconstructed Stokes parameters for the (k+1)th iteration. In equation (10), Represents the ith sparse basis coefficient in the (k+1)th iteration; Step 3.9: Determine whether equation (11) is true. If it is true, the iteration stops and the spectral optimization solution of the (k+1)th iteration is output. And use it as the reconstructed polarization spectrum; otherwise, assign k+1 to k and return to step 3 for sequential execution: In equation (11), i = 0, 1, 2, 3, and ε is the stop threshold.

2. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the spectral reconstruction method of the channel polarization spectrometer according to claim 1, and the processor is configured to execute the program stored in the memory.

3. A computer-readable storage medium storing a computer program, characterized in that, The computer program, when run by the processor, executes the steps of the spectral reconstruction method of the channel polarization spectrometer as described in claim 1.

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