A spectral reconstruction method, system, and computer-readable storage medium based on coded filters.

Abstract

The present invention discloses a spectrum reconstruction method, system and computer-readable storage medium based on a codeable filter, the method comprising: obtaining the transmittance curve of m coding channels of the codeable filter and performing denoising processing; modulating the spectrum information F(λ) of the target to be measured received by m different coding channels of the codeable filter, the detector converting the modulated spectrum information F(λ) of the target to be measured into an electrical signal, reconstructing the spectrum using a ridge regression algorithm based on L2 regularization, and adding a non-negative constraint st0≤α to achieve reconstruction of the spectrum of the target to be measured. The present invention successfully solves the problems of spatial resolution, spectral resolution and signal-to-noise ratio constraints, large system volume, insufficient noise resistance and high data storage and transmission pressure existing in traditional spectral imaging technology through an innovative spectrum reconstruction method.

Description

Technical Field

[0001] The present invention relates to the technical field of spectral imaging, and in particular to a spectrum reconstruction method, system, and computer-readable storage medium based on a codeable filter. Background Art

[0002] Traditional infrared detector technology mainly detects the intensity of infrared signals radiated by target objects, while infrared spectroscopy combined with spectral imaging technology has significant advantages in target identification applications based on "fingerprint recognition". Mid-infrared spectroscopy is an important means of analyzing the chemical composition and structure of substances by detecting the absorption or emission spectrum of substances in the mid-infrared band. Due to the characteristics of molecular vibration and rotation energy levels, mid-infrared spectroscopy can provide rich molecular information, and is particularly suitable for component analysis of organic, inorganic, gas and complex materials. For high-precision material analysis and detection, spectral resolution is one of the important factors affecting the accuracy and reliability of the results. The mid-infrared band contains a large number of characteristic absorption peaks of molecules, especially the vibration frequencies of chemical bonds, which makes this band widely used in material analysis, environmental monitoring, gas detection and other fields.

[0003] Spectral resolution is the minimum difference between two adjacent wavelengths or wavenumbers that a spectrometer can distinguish. It directly affects the distinguishability of different absorption peaks in the spectrum. As the wavelength increases, the demand for wavelength resolution also increases, but the wavenumber resolution remains the same. In mid-infrared spectroscopy, the distances between the characteristic absorption peaks of many molecules are very close, so high-resolution spectral data is essential for accurate molecular structure analysis. In the mid-infrared band, the wavenumber resolution usually required is 0.5 cm -1 Up to 4 cm -1 The specific requirements depend on the application scenario: for applications that require precise resolution of molecular vibration modes (such as gas detection or analysis of complex organic matter), higher resolution (0.5 cm -1 - 1 cm -1 ) is necessary in order to distinguish very close absorption peaks. In routine material analysis (such as most polymers or inorganic materials), a resolution of 2 cm -1 Up to 4 cm -1 Sufficient to distinguish the characteristic absorption of different chemical groups.

[0004] The mutual constraints between spatial resolution, spectral resolution and signal-to-noise ratio in traditional spectral imaging technology are the main contradictions. How to resolve this contradiction has always been a technical problem in the field of spectral imaging. With the advancement of detector technology and the development of data processing technology, the introduction of computational methods in the process of optical imaging and spectral acquisition can effectively resolve the contradiction between spatial resolution, spectral resolution and signal-to-noise ratio. The mid-infrared spectral reconstruction system will be able to achieve higher spectral resolution while maintaining a high signal-to-noise ratio.

[0005] Unlike traditional spectral imaging technology that performs full sampling in spatial and spectral dimensions, computational spectral imaging technology is based on the sparsity of the target spectral image. It reduces the focal area occupied by spectral acquisition through projection, compression, and encoding. At the same time, it collects aliased broadband spectra, increases the luminous flux incident on a single pixel, and improves the detection signal-to-noise ratio.

[0006] In addition, the narrowband spectroscopy and Nyquist sampling strategies of traditional spectral imaging technology lead to a large system size and low light energy utilization. The spectral imaging technology based on spectral coding in this study uses a dynamically tunable filter that encodes the spectrum integrated with the detector to achieve spectral information compression, and combines the software spectral reconstruction algorithm to achieve the miniaturization of the spectral detection system. At the same time, the spectral encoding and decoding spectral imaging technology based on wavelength coding only encodes the spectral dimension, keeping the geometric position of the spatial dimension unchanged. The complexity of the reconstruction calculation is much lower than that of amplitude coding and phase coding. It is a new spectral imaging technology that is currently developing rapidly and is expected to be maturely applied in recent years.

[0007] The infrared spectral imaging chip based on the codeable filter can modulate the light signal received by the sensor to form a modulated electrical signal containing spectral information, and then reconstruct the infrared spectral curve using an algorithm.

[0008] The spectral signal of the target is modulated by a dynamically tunable filter and then collected by the detector. It is then transmitted to the data processing system in the form of an electrical signal to obtain a modulated signal, which represents the integral of the product of the incident spectrum and the transmittance modulation signal. The spectral transfer process of the spectral imaging chip is an ill-conditioned equation, and there are disturbances that are difficult to eliminate, including but not limited to measurement deviations, structural processing deviations, sensor noise, etc. The disturbances will be amplified in the ill-conditioned matrix, making it very easy to overfit the reconstructed data. Therefore, the results are often approximated based on regularized optimization algorithms, such as compressed sensing. This type of method can reconstruct the spectral curve more accurately, but the reconstruction speed is slow.

[0009] Therefore, technical personnel in this field urgently need to develop a spectral reconstruction method with short time consumption, strong noise resistance, high resolution, high fidelity, high signal-to-noise ratio, small amount of data storage and transmission, simple structure, compact size, and flexible encoding method. This is very critical for the development of future spectral imaging chips in the fields of earth remote sensing, medical diagnosis, environmental monitoring, life sciences, color information processing, precision agriculture, etc. Summary of the invention

[0010] The invention discloses a spectrum reconstruction method and system based on a codable filter, which significantly improve the accuracy of spectrum reconstruction and the anti-noise performance of the system.

[0011] The technical solution of the present invention is as follows:

[0012] A spectrum reconstruction method based on a codeable filter, comprising:

[0013] (1) Obtaining the transmittance curves of the m coding channels of the codeable filter;

[0014] (2) The transmittance curve is denoised using the wavelet threshold denoising method to obtain the denoised transmittance curves corresponding to different coding channels, and the transmittance matrix T(λ) of the codable filter is constructed;

[0015] (3) The spectral information F(λ) of the target to be measured received by the m different coding channels of the codeable filter is modulated, and the detector converts the modulated spectral information F(λ) of the target to be measured into an electrical signal. The intensity of the electrical signal is I i for:

[0016] ;

[0017] Among them, the lower limit and upper limit of the wavelength λ are the lower limit and upper limit of the detectable bandwidth of the detector respectively; T i (λ) is the number of encodable filters i Transmittance curves of the coded channels; η i Indicates the encodable filter i The noise of the coding channel;

[0018] (4) Linearly expand the continuous target spectral information F(λ) using the Gaussian basis function φ j (λ) and weight coefficient α j To express:

[0019] ;

[0020] (1)

[0021] Where: σis the standard deviation, the half-height full width of the Gaussian function is; λ represents the wavelength of the Gaussian basis function; λ j Indicates j The central wavelength of the Gaussian basis function; n is the number of Gaussian basis functions;

[0022] Then the intensity I of the electrical signal is transformed into:

[0023] ;

[0024] ;

[0025] Where: T i (λ) represents the i The filter of the coding channel is j The transmittance at the central wavelength of the Gaussian basis function; A represents T(λ) φ (λ); α represents the weight coefficient of the Gaussian basis function; η Indicates noise;

[0026] (5) The spectrum is reconstructed using the ridge regression algorithm based on L2 regularization, and the non-negative constraint st0≤α is added to obtain the optimization equation:

[0027] (2)

[0028] Where β is the regularization parameter;

[0029] The weight coefficient α of the target spectrum to be measured is obtained by solving equation (2), and the reconstruction of the target spectrum to be measured is realized according to equation (1).

[0030] The coded filter is a static voltage tunable filter. The coded filter has different transmittance curves under different voltages, and one voltage corresponds to one transmittance curve and one coding channel.

[0031] The invention uses static voltage to tune the transmittance curve of the filter, so that the filter can accurately select and transmit spectral signals in different wavelength ranges. This method avoids the use of mechanical moving parts, significantly improves the stability and reliability of the system, and reduces the space occupation of the system.

[0032] In step (2), the denoising process of the transmittance curve using the wavelet threshold denoising method includes:

[0033] (2-1) Perform wavelet decomposition on the transmittance curve;

[0034] (2-2) Perform hard threshold processing on each coefficient of wavelet decomposition to obtain the estimated value of the wavelet coefficient;

[0035] (2-3) Perform inverse wavelet transform on the wavelet coefficients after hard threshold processing to obtain the denoised transmittance curve.

[0036] In step (2-1), the wavelet layer number is selected as 3, the wavelet basis function is db4, and wavelet decomposition is performed to obtain a set of wavelet coefficients.

[0037] In step (2-2), the threshold T of hard threshold processing is given by the following formula:

[0038] ;

[0039] Where τ is the noise intensity and N is the length of the signal.

[0040] There are many ways to extract τ. In the simplest case, we can assume that the signal noise is Gaussian white noise and τ=1.

[0041] In step (5), the generalized cross-validation method is used to determine the regularization parameter β.

[0042] The present invention solves the mutual constraints among spatial resolution, spectral resolution and signal-to-noise ratio by combining ridge regression with generalized cross validation (GCV): by introducing the L2 regularized ridge regression algorithm, the correlation between data is reduced and the robustness of the model is improved. Furthermore, the optimal regularization parameter is automatically selected by GCV to ensure the accuracy and stability of the model on different data sets, thereby achieving a good balance between high resolution and high signal-to-noise ratio.

[0043] The codeable filter based on spectral coding can realize the miniaturization of the system and improve the utilization rate of light energy: using spectral coding technology, the codeable filter is integrated into the detector, and through spectral compression and modulation, the miniaturization of the system is realized, the utilization rate of light energy is improved, and the problems of bulky size and low light energy utilization of traditional systems are solved.

[0044] Enhance noise resistance through wavelet threshold reconstruction denoising algorithm: The introduction of wavelet threshold denoising algorithm effectively reduces the impact of measurement noise and interference, ensures the stability and accuracy of reconstructed data, and solves the overfitting problem that is prone to occur in traditional methods.

[0045] The present invention also provides a spectrum reconstruction system based on a codeable filter, comprising a codeable filter, a detector, a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the spectrum reconstruction method when executing the computer program.

[0046] The spectral reconstruction system also includes a GUI interface, which can input the working wavelength range, the FWHM of the spectrum, the number of target spectra to be measured, the number of encoding channels and encoding data, electrical signal intensity data, reference incident spectrum data files, etc., and output the MSE of the reconstructed spectrum and the reference spectrum, as well as images of the reconstructed spectrum and the reference spectrum.

[0047] The GUI interface realizes the integrated operation of parameter input, result output and data visualization of the spectrum reconstruction system. The interface supports multi-parameter debugging and real-time feedback, and automatically generates the error and comparison images of the reconstructed spectrum and the reference spectrum, which significantly improves the ease of use of the system, data analysis efficiency and result interpretation, making the spectrum reconstruction process more efficient, intuitive and user-friendly.

[0048] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is processed and executed, the steps of the spectrum reconstruction method are implemented.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] (1) Compared with the traditional spectrometer, the spectrum reconstruction method adopted by the present invention omits moving parts, reduces the mechanical complexity of the system, and reduces the space occupied by the entire system. Compared with the traditional narrow-band spectrometer, the system of the present invention is smaller in size.

[0051] (2) The present invention solves the huge data storage and transmission pressure caused by full spectral and spatial sampling in traditional methods by improving the encoding method and spectral reconstruction technology. This optimization enables the system of the present invention to efficiently process spectral data while reducing the requirements for data storage and transmission.

[0052] (3) The present invention innovatively introduces a wavelet threshold reconstruction denoising algorithm, which can effectively separate the signal and noise in the spectral reconstruction process. By performing wavelet decomposition on the coded signal and setting thresholds at different wavelet scales, the decomposed coefficients are selectively processed to suppress noise and retain useful signals. Compared with traditional reconstruction methods, this technology not only effectively removes noise, but also retains the detailed features of the coded signal, significantly improving the accuracy of spectral reconstruction and the anti-noise performance of the system.

[0053] (4) The present invention introduces ridge regression, generalized cross validation (GCV) and non-negative constraints into the spectral data reconstruction algorithm, further improving the accuracy, stability and physical consistency of the model. These methods, through regularization processing and automated parameter selection, enable the present invention to show significant advantages in processing complex spectral data, successfully solve the multicollinearity, regularization parameter selection and physical consistency problems in spectral data reconstruction, and provide more accurate and reliable spectral reconstruction results in complex scenarios.

[0054] Through an innovative spectral reconstruction method, the present invention successfully solves the problems of spatial resolution, spectral resolution and signal-to-noise ratio constraints, large system size, insufficient noise resistance, and high data storage and transmission pressure in traditional spectral imaging technology, providing key technical support for the development of efficient and stable miniaturized spectral imaging systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a schematic diagram of the spectrum reconstruction principle of the spectrum reconstruction system;

[0056] Figure 2 It is a flowchart of the spectrum reconstruction method;

[0057] Figure 3 It is a flowchart of the wavelet threshold denoising method;

[0058] Figure 4 The transmittance curves before and after denoising using the wavelet threshold denoising method in Example 1;

[0059] Figure 5 This is the result diagram of the double peak spectrum reconstruction of Example 1;

[0060] Figure 6 This is the reconstructed spectrum result diagram before and after denoising using the wavelet threshold denoising method in Example 2. DETAILED DESCRIPTION

[0061] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be pointed out that the embodiments described below are intended to facilitate the understanding of the present invention and do not have any limiting effect on the present invention.

[0062] The spectrum reconstruction system of the present invention includes two modules: hardware encoding and software decoding.

[0063] The hardware encoding module integrates a dynamically tunable filter and a detector. The dynamically tunable filter has a voltage-tuned encoding channel with different spectral transmittance curves to perform hardware encoding on unknown spectra. The software decoding module reconstructs the unknown incident spectrum with the help of software algorithms. Figure 1 shown.

[0064] like Figure 2 As shown, the spectrum reconstruction method of the present invention comprises:

[0065] Step 1: Use a FTIR (Fourier Transform Infrare) spectrometer to obtain the transmittance curves of the dynamically tunable filter under different voltage controls. One voltage corresponds to one transmittance curve and one coding channel.

[0066] (1-1) Instrument preparation

[0067] Turn on the FTIR spectrometer and preheat the equipment to stabilize the light source and interferometer. Check whether the MCT detector is working properly and ensure that it covers the 3-5μm band;

[0068] Calibrate the FTIR system including the light source, interferometer and detector to ensure accurate measurements.

[0069] (1-2) Background spectrum measurement

[0070] Leave the sample compartment empty and make sure that no filters or other objects interfere with the light path.

[0071] Run the FTIR spectrometer and measure the background spectrum. Record the background spectrum for subsequent transmittance calculation.

[0072] Save the background spectrum data to ensure that the sample measurements are performed under the same conditions.

[0073] (1-3) Sample installation and initial measurement

[0074] Install the tunable filter in the light path of the sample compartment, making sure the filter is perpendicular to the beam path and firmly fixed.

[0075] Set the initial voltage (0V), connect the voltage source and apply this voltage to the filter.

[0076] Run the FTIR spectrometer to measure the transmission spectrum of the filter at this voltage and record the spectral data.

[0077] (1-4) Measurements at different voltages

[0078] According to the experimental design, the voltage applied to the filter is adjusted step by step.

[0079] For each voltage value, repeat the following steps:

[0080] ① Set the new voltage and wait for the filter to stabilize;

[0081] ② Use FTIR spectrometer to measure the transmission spectrum of the filter at this voltage;

[0082] ③Record and save the spectral data of each measurement.

[0083] (1-5) Transmittance calculation

[0084] For each voltage spectrum, the transmittance is calculated using the previously measured background spectrum:

[0085] ;

[0086] in, T ( λ,V ) is the transmittance at wavelength λ under voltage V, I sample ( λ,V ) is the spectral intensity of the sample (filter) at this voltage, I background ( λ ) is the background spectrum intensity.

[0087] Step 2: According to step 1, the transmittance curves of m filter channels are obtained, and the hardware encoding matrix T of the spectral imaging chip is constructed; the element t of the matrix T is ij For the i Encoding channel j The transmittance of the sampling point at each wavelength.

[0088] The wavelet threshold denoising method is used to remove the measurement noise and improve the reconstruction effect on the filter transmittance curve.

[0089] The process of wavelet threshold denoising on the filter transmittance curve is as follows: Figure 3 As shown, including:

[0090] (2-1) Perform wavelet decomposition on the noisy signal. Select the wavelet layer number as 3 and the wavelet basis function as db4, perform wavelet decomposition, and obtain a set of wavelet coefficients.

[0091] (2-2) Perform hard threshold processing on each coefficient of wavelet decomposition to obtain the estimated value of the wavelet coefficient.

[0092] The threshold is given by the following formula:

[0093] ;

[0094] Where τ is the noise intensity and N is the length of the signal.

[0095] There are many ways to extract τ. In the simplest case, we can assume that the signal noise is Gaussian white noise and τ=1.

[0096] (2-3) The wavelet coefficients processed by threshold quantization are subjected to inverse wavelet transform to reconstruct the signal and obtain the denoised coded signal.

[0097] Step 3: modulate the spectral information F(λ) of the target to be measured received by the m different coding channels of the dynamically tunable filter, and the detector converts the modulated spectral information F(λ) of the target to be measured into an electrical signal, and the intensity of the electrical signal I i for:

[0098] ;

[0099] Among them, the lower and upper limits of the wavelength λ are the detectable bandwidth of the detector; T i (λ) is the dynamic tunable filter i Spectral transmittance curve of the coding channel; F(λ) represents the incident spectrum to be reconstructed; η i The dynamically tunable filter i The noise of the coding channel.

[0100] Step 4: Linearly expand the continuous spectrum F(λ) using the Gaussian basis function φ j (λ) and weight coefficient α j To express it, the entire reconstruction process is converted from the original integral process into a linear equation and expressed using matrix multiplication.

[0101] ;

[0102] (1)

[0103] Where: σ is the standard deviation, and the full width at half maximum of the Gaussian function is ;λ represents the wavelength of the Gaussian basis function;λ j Indicates j The central wavelength of the Gaussian basis function; F ^ (λ) represents the incident spectrum curve data estimated by linear summation of Gaussian functions (assuming that the incident spectrum is a superposition of a finite number of Gaussian basis functions with different weight coefficients and different central wavelengths); n is the number of Gaussian bases.

[0104] After the above linear expansion process, the integral of the encoded integral process becomes a discrete linear equation:

[0105] ;

[0106] ;

[0107] Where: T ij (λ) represents the i The filter of the coding channel is j The transmittance at the central wavelength of the Gaussian basis function; A represents T(λ) φ(λ); α represents the weight coefficient of the Gaussian basis function; η Indicates noise.

[0108] The matrix form of the encoding process is:

[0109] ;

[0110] m is the number of encoding channels; η i For noise.

[0111] After comprehensive analysis of various reconstruction methods, the ridge regression algorithm based on L2 regularization (i.e., Tikhonnov regularization, TR, Tikhonov regularization) is used to reconstruct the spectrum. L2 regularization technology is widely used to prevent overfitting. This algorithm is a linear regression algorithm that performs well in spectral reconstruction and has good noise stability. The reconstruction process is to solve a solution to an ill-conditioned inverse equation. Because of the presence of high-frequency noise signals, directly minimizing the residual norm will lead to instability of the solution. To solve this problem, L2 regularization (ridge regression) is used in the present invention to stabilize the minimization process. At the same time, according to the non-negative nature of the spectrum, a non-negative constraint NNLS (non-negative least squares) st0≤α is added, and finally the optimization equation is obtained by solving the ill-conditioned inverse equation:

[0112] (2)

[0113] In the formula, β is the regularization parameter.

[0114] The weight coefficient α of the unknown spectrum is obtained by minimizing the residual norm (square error), and the reconstruction of the unknown spectrum is achieved according to formula (1).

[0115] In formula (2), the regularization parameter changes with the encoding matrix of the system for the spectrum. The present invention uses the generalized cross validation GCV method to determine the regularization parameter.

[0116] Step 5: Use MSE (mean square error) and spectral resolution as the measurement indicators of reconstruction effect.

[0117] The spectral reconstruction system also has a GUI interface, which can input the working wavelength range, the FWHM (full width half maximum) of the spectrum, the number of spectra to be reconstructed, the encoding dimension (number of channels) and the encoding data (transmittance matrix), the observation value (electrical signal intensity) data, the reference incident spectrum data file, etc., and output the MSE of the reconstructed spectrum and the reference spectrum, as well as images of the reconstructed spectrum and the reference spectrum.

[0118] Example 1

[0119] Input the double-peak incident light to be reconstructed, with the center wavelength of the two peaks differing by 20nm. In the GUI interface, enter the minimum wavelength as 3000nm, the maximum wavelength as 5000nm, the number of incident lights as 1, and the number of encoding channels as 7 in the measurement number.

[0120] Figure 4 are the transmittance curves of the voltage dynamically tunable filter, where (a) is the transmittance curve without denoising using the wavelet threshold denoising method, and (b) is the transmittance curve after denoising using the wavelet threshold denoising method.

[0121] The reconstruction results of the coding matrix before and after denoising using the wavelet threshold denoising method are compared. Figure 5 As shown in the figure, the difference between the two peak center wavelengths of the incident spectrum to be reconstructed is 20nm. The dotted line is the reference incident spectrum, and the solid line is the reconstruction result. The double peaks can be distinguished. The spectral resolution can reach 20nm, and the corresponding wavenumber resolution is about 0.99 cm -1 . MSE is less than 0.01.

[0122] Example 2

[0123] Input the incident light to be reconstructed, the four center wavelengths are 3.4um, 3.8um, 4.2um, 4.6um, and the half-height full width is 100nm. The effect of reconstruction by the reconstruction method of the present invention is as follows: Figure 6 As shown in the figure, the dotted line is the reference incident spectrum, and the solid line is the reconstruction result. (a) is the reconstruction result before denoising, and (b) is the reconstruction result after denoising. The reconstruction effect is significantly improved. Compared with the reconstruction of transmittance without denoising, the MSE of the reconstruction of transmittance with denoising is improved, from 0.015 to 0.005.

[0124] The embodiments described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A spectrum reconstruction method based on a codable filter, characterized in that: include: (1) Obtaining the transmittance curves of the m coding channels of the codeable filter; (2) The transmittance curve is denoised using the wavelet threshold denoising method to obtain the denoised transmittance curves corresponding to different coding channels, and the transmittance matrix T(λ) of the codable filter is constructed; (3) The spectrum information F(λ) of the target to be measured received by the m different coding channels of the codeable filter is modulated, and the detector converts the modulated spectrum information F(λ) of the target to be measured into an electrical signal. i The intensity of the electrical signal of the coding channel I i for: ； Among them, the lower limit and upper limit of the wavelength λ are the lower limit and upper limit of the detectable bandwidth of the detector respectively; T i (λ) is the encodable filter i Transmittance curves of the coded channels; η i Represents the encodable filter i The noise of the coding channel; (4) Linearly expand the continuous target spectral information F(λ) and express it using Gaussian basis function and weight coefficient: ； （1） Where: σ is the standard deviation, and the half-height full width of the Gaussian basis function is ;λ represents the wavelength of the Gaussian basis function;λ j Indicates j The central wavelength of the Gaussian basis function; n is the number of Gaussian basis functions; φ j (λ) represents the j Gaussian basis function; α j Indicates the corresponding j Gaussian basis function φ j The weight coefficient of (λ); Then the intensity I of the electrical signal is transformed into: ； ； Where: T ij (λ) represents the i The filter of the coding channel is j The transmittance at the central wavelength of the Gaussian basis function; A represents T(λ) φ (λ), T(λ) represents the transmittance matrix of the codeable filter, φ (λ) represents the Gaussian basis function; α represents the weight coefficient of the Gaussian basis function; η Indicates noise; (5) The spectrum is reconstructed using the ridge regression algorithm based on L2 regularization, and the non-negative constraint st0≤α is added to obtain the optimization equation: （2） Where β is the regularization parameter; The weight coefficient α of the target spectrum to be measured is obtained by solving equation (2), and the reconstruction of the target spectrum to be measured is realized according to equation (1).

2. The spectrum reconstruction method based on a codeable filter according to claim 1, characterized in that: In step (2), the denoising process of the transmittance curve using the wavelet threshold denoising method includes: (2-1) Perform wavelet decomposition on the transmittance curve; (2-2) Perform hard threshold processing on each coefficient of wavelet decomposition to obtain the estimated value of the wavelet coefficient; (2-3) Perform inverse wavelet transform on the wavelet coefficients after hard threshold processing to obtain the denoised transmittance curve.

3. The spectrum reconstruction method based on a codeable filter according to claim 2, characterized in that: In step (2-1), the wavelet layer number is selected as 3, the wavelet basis function is db4, and wavelet decomposition is performed to obtain a set of wavelet coefficients.

4. The spectrum reconstruction method based on a codeable filter according to claim 2, characterized in that: In step (2-2), the threshold T of hard threshold processing is given by the following formula: ； Where τ is the noise intensity and N is the length of the signal.

5. The spectrum reconstruction method based on a codeable filter according to claim 4, characterized in that: The noise is Gaussian white noise and τ=1.

6. The spectrum reconstruction method based on a codeable filter according to claim 1, characterized in that: In step (5), the generalized cross-validation method is used to determine the regularization parameter β.

7. A spectrum reconstruction system based on a codeable filter, characterized in that: The invention comprises a codeable filter, a detector, a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the spectral reconstruction method according to any one of claims 1 to 6 when executing the computer program.

8. A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when processed and executed, implements the steps of the spectrum reconstruction method according to any one of claims 1 to 6.

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