Spectral Reconstruction Calculation Method and Spectral System Based on Adaptive Optimization of Sparse Dictionary

Abstract

The present invention relates to a spectral reconstruction calculation method and a spectral system based on an adaptive optimized sparse dictionary. This method uses a conventional basis function sparse dictionary for spectral reconstruction calculation to obtain an approximately optimal solution of the spectral signal. Taking the approximately optimal solution of the spectral signal as prior information, the construction process of the basis function sparse dictionary is optimized specifically. During the optimization process, first, the sparse basis functions are located, and all the remaining invalid sparse basis functions are deleted. Incomplete sparse basis functions are found and subdivision sparse basis functions are added to the incomplete sparse basis functions to obtain an optimized sparse dictionary. The optimized sparse dictionary is used to perform spectral reconstruction calculation again to obtain an optimized reconstructed spectral solution. The spectral signal approximately optimal solution is updated with the optimized reconstructed spectral solution, and the iteration is repeated until the termination condition is satisfied, and the spectral reconstruction result is output. This method can reduce the constraint of the basis function sparse dictionary on the spectral reconstruction calculation process, thereby improving the fidelity of the reconstructed spectrum, and at the same time can improve the calculation speed of the reconstructed spectrum.

Description

Technical Field

[0001] The present invention relates to the technical field of spectral reconstruction, and particularly to a spectral reconstruction calculation method and a spectral system based on an adaptive optimized sparse dictionary. Background Art

[0002] The spectral measurement method based on broadband filtering coding and computational reconstruction principle is a new type of spectral measurement technology, which has the advantages of high optical flux and compact structure, and is easy to be combined with various micro-nano spectral filtering devices to realize miniaturized spectral measurement or spectral imaging instruments; at the same time, it can also be combined with various spectral coding modulation devices (such as Fabry-Perot interferometric cavities, electro-optic modulation crystals, etc.) to realize high-throughput spectral imaging remote sensing. Therefore, it is a new type of spectral measurement technology with great application potential.

[0003] For a computational spectral measurement system, the encoding and decoding (i.e., spectral reconstruction) of the system is one of the core issues. At present, based on the design theory basis of broadband spectral coding, for a spectral measurement or spectral imaging system based on spectral dimension broadband filtering coding and computational reconstruction (hereinafter referred to as a broadband coding reconstruction spectral measurement system), it can be mainly divided into three categories: 1. The broadband spectral coding is not specially designed, and such systems mostly use l2 norm optimization algorithms for spectral reconstruction; 2. The broadband spectral coding is designed based on the compressed sensing theory, and such systems mostly use sparse representation methods combined with l1 norm optimization algorithms for spectral reconstruction; 3. The broadband spectral coding is designed based on machine learning methods, and such systems can directly complete spectral reconstruction using machine learning models.

[0004] Since the spectral reconstruction process is a typical inverse problem solving process, the measurement error of the detector has a great influence on the accuracy of the reconstructed spectrum. Therefore, the current accuracy and resolution of the reconstructed spectrum are one of the main problems restricting the application of this technology. To solve this problem, in related research, it is proposed that designing the spectral filtering coding based on the compressed sensing theory and combining the sparse representation technology with the l1 norm optimization algorithm for spectral reconstruction calculation is one of the current mainstream solutions. This solution can not only effectively suppress the ill-posedness problem of inverse problem solving, but also utilize the advantages of the compressed sensing theory to reconstruct and recover more spectral band numbers than the number of spectral measurements, so it has great advantages and is one of the mainstream technical routes of the current broadband filtering coding reconstruction spectral technology.

[0005] The sparse representation methods adopted by the broadband coded reconstruction spectral measurement and spectral imaging system designed based on the compressed sensing theory can be mainly divided into two categories: one is to perform stretching and translation transformations on a certain basis function and then discretely arrange it in matrix form to form a basis function sparse dictionary (abbreviated as basis function dictionary). Common types of basis functions include Gaussian basis functions and various wavelet basis functions, etc.; the other is a learning dictionary (abbreviated as learning dictionary) constructed by using a supervised learning method for a certain spectral data set. Since the types and construction methods of the basis function sparse dictionary do not depend on the spectral data to be measured, it has better completeness in different application scenarios, but the fidelity of the reconstructed spectrum is relatively poor; while the construction process of the learning dictionary is highly related to the training data set, so it is difficult to guarantee completeness in a wide range of application scenarios, but generally has better spectral reconstruction effects for the training spectral data set. Summary of the Invention

[0006] Aiming at the problem that the existing spectral reconstruction methods using two sparse representation methods are difficult to be compatible, resulting in the inability to balance the accuracy and completeness of spectral reconstruction, the present invention proposes a spectral reconstruction calculation method and a spectral system based on an adaptive optimized sparse dictionary. On the basis of ensuring the advantages of the completeness of spectral reconstruction of the basis function sparse dictionary, the method and the spectral system improve the resolution and accuracy of the reconstructed spectrum; at the same time, by defining the adaptive optimization construction process of the sparse dictionary, it can also play a role in reducing the complexity of the sparse dictionary and thus improving the speed of spectral reconstruction.

[0007] The present invention adopts the following technical solutions:

[0008] A spectral reconstruction calculation method based on an adaptive optimized sparse dictionary, comprising the following steps:

[0009] Step 1, determine the input parameters, where the input parameters include the target spectral range, the number of reconstructed spectral bands, the spectral response matrix, the measurement signal vector, the regularization parameter, and the subdivision basis function determination threshold;

[0010] Step 2, perform spectral reconstruction calculation using a conventional basis function sparse dictionary to obtain an approximate optimal solution of the spectral signal;

[0011] Step 3, judge whether the spectral reconstruction calculation process terminates according to the approximate optimal solution of the spectral signal and the preset algorithm termination condition. If so, output the reconstructed spectrum; if not, execute Step 4;

[0012] Step 4, use the approximate optimal solution of the spectral signal as the prior information to specifically optimize the construction process of the basis function sparse dictionary to obtain an optimized sparse dictionary;

[0013] When specifically optimizing the construction process of the basis function sparse dictionary, first find all the quantities greater than the threshold in the reconstructed spectral sparse representation vector, locate the corresponding sparse basis functions of these quantities, and delete all the remaining invalid sparse basis functions; find the incomplete sparse basis functions among all the remaining sparse basis functions; locate the central wavelengths of all the incomplete sparse basis functions, and add finer sparse basis functions with a narrower full width at half maximum and a smaller central wavelength interval near these central wavelengths; the added finer sparse basis functions and the conventional basis function sparse dictionary after deleting the invalid sparse basis functions together constitute the optimized sparse dictionary;

[0014] Step 5: Use the optimized sparse dictionary to perform spectral reconstruction calculation again to obtain the optimized reconstructed spectral solution;

[0015] Step 6: Update the spectral signal approximate optimal solution with the optimized reconstructed spectral solution, repeat the iterative steps from Step 3 to Step 5 until the preset algorithm termination condition is met, then end the spectral reconstruction calculation process, and output the finally obtained optimized reconstructed spectral solution as the spectral reconstruction result.

[0016] The present invention also proposes a spectral system, including:

[0017] A spectral modulation and encoding device for modulating and encoding the spectral of the target to be measured;

[0018] An optical signal acquisition system for receiving the encoded spectral of the target to be measured and completing the photoelectric signal conversion;

[0019] A backend signal processing system for receiving the detector signal output by the signal acquisition system and performing spectral reconstruction calculation according to the aforementioned spectral reconstruction calculation method based on the adaptive optimized sparse dictionary to obtain the reconstructed spectrum.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] (1) The spectral reconstruction method proposed by the present invention is based on the construction of the basis function sparse dictionary, so it can ensure the completeness of the spectral measurement system in different application scenarios; at the same time, by adding finer basis functions, the accuracy and resolution of the reconstructed spectrum can be improved on the basis of the existing basis function sparse dictionary construction method;

[0022] (2) The spectral reconstruction method proposed by the present invention, by adding the adaptive iterative optimization process of the basis function sparse dictionary, can, on the basis of ensuring the strong spectral reconstruction robustness of the existing sparse representation method, take into account the high-precision reconstruction of the finer basis function sparse dictionary for high-frequency spectral signals, and improve the problem that the existing methods cannot take into account both the high-frequency and low-frequency parts of the reconstructed spectral signals at the same time;

[0023] (3) The spectral reconstruction method proposed by the present invention can, while ensuring the above advantages, reduce the storage resource consumption of a large-scale over-complete dictionary and improve the spectral reconstruction calculation speed by setting an adaptive optimization process for the basis function sparse dictionary. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is a flowchart of the spectral reconstruction calculation method based on an adaptively optimized sparse dictionary according to the present invention;

[0025] Figure 2 is a schematic diagram of a feasible Gaussian function sparse solution space;

[0026] Figure 3 is a schematic diagram of the principle of a passive and active broadband filtering coded reconstruction spectral measurement system;

[0027] Figure 4 is a flowchart of numerical simulation;

[0028] Figure 5 is a comparison chart of the reconstruction performance simulation results of a given complex spectral signal using the traditional Normal SD, the subdivision sparse dictionary SSD, and the AOSDSR method. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0029] The present invention aims to propose a spectral reconstruction calculation method based on an adaptively optimized sparse dictionary. On the basis of the conventional basis function sparse dictionary construction method, by setting an adaptive iterative optimization process for the basis function sparse dictionary, the present invention can reduce the constraint of the basis function sparse dictionary on the spectral reconstruction calculation process, thereby improving the fidelity of the reconstructed spectrum; at the same time, the adaptive optimization process of the sparse dictionary can also improve the spectral reconstruction calculation speed when using a large-scale sparse dictionary. The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments.

[0030] As Figure 1 shown, the present invention provides a spectral reconstruction calculation method based on an adaptively optimized sparse dictionary (adaptively optimized sparse dictionary-based spectral reconstruction, AOSDSR), which specifically includes the following steps:

[0031] The implementation method of the present invention is described by taking a common Gaussian basis sparse dictionary as an example.

[0032] Step 1, algorithm initialization:

[0033] Determine the input parameters, including basic parameters such as the target spectral range, the number of reconstructed spectral bands, the spectral response matrix, the measured signal vector, the regularization parameter τ, and the subdivision basis function determination threshold s.

[0034] Step 2: Perform spectral reconstruction calculation using a conventional basis function sparse dictionary to obtain an approximately optimal solution of the spectral signal.

[0035] In this step, when performing spectral reconstruction calculation using a conventional basis function sparse dictionary, it can be implemented by using passive broadband filtering coding calculation spectral measurement technology or active broadband filtering coding calculation spectral measurement technology. The reconstruction algorithms used can adopt various l1 optimization algorithms or other compressive sensing reconstruction algorithms. The conventional basis function sparse dictionary in this embodiment can use a Gaussian function as the basis function, or other various wavelet basis functions or discrete cosine transform bases to sparsely represent the spectral signal to be measured, and their basic principles and effects are similar.

[0036] Step 3: Determine whether the spectral reconstruction calculation process terminates according to the approximately optimal solution of the spectral signal and the preset algorithm termination condition. If so, output the reconstructed spectrum; if not, execute Step 4.

[0037] According to the preset algorithm termination condition, determine whether the spectral reconstruction is completed. The preset algorithm termination condition is that the approximately optimal solution of the spectral signal satisfies any one of the following conditions (1), (2), and (3):

[0038] According to user requirements or calculation resource limitations, when the reconstructed spectrum reaches a certain preset resolution level (i.e., the width of the narrowest sparse basis function in the sparse dictionary reaches a certain preset level), the process terminates. Therefore, condition (1) is that the resolution of the approximately optimal solution of the spectral signal reaches the preset resolution level:;

[0039] According to the limitations of compressive sensing theory, the highest resolution of the reconstructed spectrum should theoretically be lower than the numerical discretization scale of the spectral response matrix. Therefore, condition (2) is: the highest resolution of the approximately optimal solution of the spectral signal is higher than the numerical discretization scale of the spectral response matrix;

[0040] According to the noise level limitation, if the measurement noise is large, then an excessively high resolution level (too narrow sparse basis function) will reduce the robustness of the reconstructed spectrum and cause overfitting problems. Therefore, for a higher measurement noise level, the narrowest sparse basis frequency level of the adaptive optimized sparse dictionary should be correspondingly reduced to ensure robustness. Therefore, condition (3) is: the resolution level of the approximately optimal solution of the spectral signal is higher than the set noise threshold.

[0041] Step 4: Adaptive optimization of the basis function sparse dictionary

[0042] In this step, using the approximately optimal solution of the spectral signal as prior information, specifically optimize the construction process of the basis function sparse dictionary to obtain an optimized sparse dictionary to improve the spectral reconstruction accuracy.

[0043] If the reconstructed spectral signal does not meet the calculation termination condition, the adaptive optimization construction step of the basis function sparse dictionary is started, which specifically includes: First, find all the quantities greater than the threshold in the sparse representation vector x of the reconstructed spectrum, and locate the corresponding sparse basis functions of these quantities, and delete all the remaining invalid sparse basis functions (the components corresponding to the sparse representation vector x of the reconstructed spectrum are equal to 0 or less than the threshold, and the sparse basis less than this threshold is considered to have little impact on the sparse representation of the target spectral signal); Search for incomplete sparse basis functions among all the remaining sparse basis functions. The so-called "incomplete sparse basis functions" means that these sparse bases may contain incomplete representations of high-frequency spectral signals. When searching for incomplete sparse basis functions, a hard threshold determination method can be used, that is, search for the narrowest and the second narrowest (i.e., the full width at half maximum (FWHM) is the smallest and the second smallest) sparse basis functions corresponding to the absolute value of the reconstructed sparse signal being greater than the subdivision basis function determination threshold s set during the algorithm initialization, or use a soft threshold method or a frequency amplitude screening method based on wavelet analysis to search for incomplete sparse basis functions among all the remaining sparse basis functions, and name these sparse basis functions as "incomplete sparse bases"; Then, combined with the construction method of the basis function sparse dictionary, locate the central wavelengths of all the incomplete sparse basis functions, and add subdivision sparse basis functions with a narrower FWHM and a smaller central wavelength interval near these central wavelengths; Finally, together with these added subdivision sparse basis functions and the conventional basis function sparse dictionary after deleting the invalid sparse basis functions, a new optimized sparse dictionary can be formed with the approximate optimal solution of the spectral signal obtained from the conventional basis function sparse dictionary as the prior information.

[0044] Step 5: Use the optimized sparse dictionary obtained in Step 4 to perform spectral reconstruction calculation again to obtain the optimized reconstructed spectral solution;

[0045] Step 6: Use the optimized reconstructed spectral solution obtained in Step 5 to update and replace the approximate optimal solution of the spectral signal, and then repeat the iterative steps from Step 3 to Step 5 until the preset algorithm termination condition is met, and then end the spectral reconstruction calculation process, and output the finally obtained optimized reconstructed spectral solution as the spectral reconstruction result.

[0046] Further, when performing spectral reconstruction calculation in Step 2 and Step 5, within the framework of the compressive sensing principle, the discrete spectral distributions obtained from the active broadband filtering coded calculation spectral measurement system or the passive broadband filtering coded calculation spectral measurement system in Equations (4) and (6) can be regarded as the following convex optimization problem:

[0047]

[0048] where D is the spectral coding matrix. For the passive spectral measurement system, D = [R k (λ i )], R k (λi ) is the discrete value of the ideal spectral response function R(λ) at the k-th measurement. For the active spectral measurement system D = [R(λ i )E' k (λ i )], R(λ i ) is the discrete value of the ideal spectral response R(λ) of the sensor, and E' k (λ i ) is the discrete value of the ideal illumination spectral distribution E(λ) to be measured at the k-th measurement; ψ is the sparse dictionary, and Dψ is generally called the spectral observation matrix; x is the sparse representation vector, and ψx = E s ; S n is the measurement signal vector, and τ is the regularization parameter used to control the sparsity (and also the smoothness) of the solution.

[0049] The basic principle of the above-mentioned spectral reconstruction method based on the adaptive optimization of the sparse dictionary can be understood in two parts, which will be described separately below.

[0050] (1) The sparse representation ability of the spectral signal of the basis function sparse dictionary

[0051] Related research shows that natural spectral signals have piecewise continuous and smooth characteristics and can generally be sparsely represented in certain transform domains. Based on this basic characteristic, a large number of basis functions such as Gaussian basis functions or various wavelet basis functions are widely used in related research to sparsely represent spectral signals. The present invention takes the construction method of a conventional Gaussian basis function sparse dictionary as an example for illustration.

[0052] For a spectral imaging system with a measurement range from λ min to λ max and a spectral channel number of N, a Gaussian function with a center wavelength evenly distributed within the target spectral range and a full width at half maximum FWHM of (λ max - λ min ) / N is used as the basis function for constructing the sparse dictionary; after its center wavelength and FWHM are translated and stretched by an integer multiple, the transformed Gaussian basis function with a center wavelength in the range from λ min to λ max and (λ max - λ min ) / N ≤ FWHM ≤ (λ max - λ min ) is taken. After being numerically discretized into column vectors and combined and arranged into a matrix, it is the common fixed-parameter Gaussian basis function sparse dictionary, which will be called the Normal sparse dictionary, abbreviated as NormalSD, hereinafter.

[0053] Such as Figure 2Shown is a schematic diagram of the feasible sparse solution space of the Gaussian function. The two abscissas are respectively the full width at half maximum (FWHM) and the central wavelength of the Gaussian basis function, and the ordinate is the optimization function value. It can be seen that the conventional method for constructing the sparse dictionary of basis functions can be regarded as artificially dividing discrete grids in the feasible region of the Gaussian basis function for spectral reconstruction solutions. The optimized solution for reconstructing the spectrum can only be selected at the grid nodes of the divided grids. However, this division of the "grid" is actually artificially defined. For natural spectral signals, if Gaussian basis functions are used to optimally fit and represent them, these Gaussian basis functions often do not exactly lie on the divided "grids"; in other words, this common method for constructing the sparse dictionary of Gaussian basis functions actually limits the sparse representation ability of the Gaussian basis functions for the target spectrum. From this perspective, it can be known that improving the construction method of the sparse dictionary of basis functions can effectively enhance its sparse representation ability.

[0054] From Figure 2 Similarly, it can be simply seen that by only increasing the "grid" density, that is, adding more narrowband Gaussian basis functions with small central wavelength intervals in the sparse dictionary, the purpose of enhancing the sparse representation ability can be achieved. In the following text, the sparse dictionary constructed by a large number of subdivided sparse basis functions is called the subdivided sparse dictionary, abbreviated as SSD.

[0055] However, simply increasing the subdivided sparse basis functions will bring great redundancy to the sparse dictionary, affect the reconstruction calculation speed and consume a large amount of storage space for the sparse dictionary. Therefore, other methods should be considered to achieve the goal of improving the sparse representation ability.

[0056] (2) Adaptive optimization of the sparse dictionary of basis functions

[0057] Simply increasing the subdivided sparse basis functions will cause an exponential increase in the scale of the sparse dictionary, consume storage space and affect the reconstruction calculation speed. Therefore, this invention draws on the idea of optimization algorithms and designs the following spectral reconstruction calculation process:

[0058] 1. Perform spectral reconstruction using the conventional sparse dictionary of basis functions to obtain an estimated value of the spectral signal;

[0059] 2. Then, using the estimated spectral signal as prior information, specifically optimize the construction of the sparse dictionary of basis functions, and perform spectral reconstruction calculation again to obtain an optimized estimated value of the spectral signal;

[0060] 3. Iterate this process until the termination condition for spectral reconstruction calculation is reached.

[0061] The key to this process lies in how to optimize and construct a sparse dictionary according to the estimated spectral signal obtained in the first step. Here, we can achieve this goal based on a simple understanding: without considering the influence of measurement errors, if there are high-frequency spectral signals in the target spectral signal that cannot be fully represented by the conventional basis function sparse dictionary, it is very likely that they should be represented by a narrower (i.e., with a smaller FWHM) sparse basis located near the position of the high-frequency signal; therefore, simply adding a subdivided Gaussian sparse basis near the narrowest (or adding the second-narrowest sparse basis to increase the success probability) sparse basis function in the reconstructed spectral signal can complete the liberal construction of the sparse dictionary. Then, using the optimized sparse dictionary for spectral reconstruction can obtain the optimized reconstructed spectral signal value, achieving a similar effect to directly using the subdivided sparse dictionary while reducing the consumption of computing resources.

[0062] The present invention also provides a spectral system, which is a broadband filtering coding reconstruction spectral measurement system or a broadband filtering coding reconstruction spectral imaging system that adopts the compressed sensing theory. Through the high-precision spectral reconstruction algorithm, namely the spectral reconstruction calculation method based on the adaptive optimized sparse dictionary described in the foregoing embodiments, this spectral system can improve the reconstructed spectral resolution and fidelity on the basis of ensuring the completeness of the conventional sparse dictionary.

[0063] As Figure 3 shown, it is the basic principle and implementation method of the broadband filtering coding reconstruction spectral measurement / spectral imaging system. Figure 3 (a) is a passive broadband filtering coding reconstruction spectral measurement system, which mainly includes a spectral filtering device, an optical signal acquisition system, and a backend signal processing system; this system modulates and encodes the incident spectrum through the spectral filtering device, and then realizes the measurement of the spectrum of the target to be measured. Figure 3 (b) is an active broadband filtering coding reconstruction spectral measurement system, which mainly includes a spectrally tunable light source, an optical signal acquisition system, and a backend signal processing system; this system realizes spectral coding by changing the spectral distribution of the light source, and then realizes the measurement of the spectral reflectivity of the target to be measured. For spectral imaging applications, only a two-dimensional photodetector array needs to be used instead of a bucket detector for photoelectric signal conversion, and the other system components and principles are the same.

[0064] Although the compositions of these two systems are different, their measurement principles are basically the same.

[0065] A. Passive broadband filtering coding reconstruction spectral measurement system

[0066] The output signal of the optoelectronic system can be expressed as:

[0067]

[0068] where S is the ideal output signal of the detector, R(λ) is the ideal spectral response function of the photodetector, λ min is the lower bound of the system spectral response, λ max is the upper bound of the spectral response, λ is the wavelength, and E(λ) is the ideal incident spectrum. Generally, if Equation (1) is discretized into n spectral bands, it can be rewritten as:

[0069]

[0070] where λ i is the nominal wavelength of the i-th spectral band (taking it as the central wavelength of the band), R’(λ i ) is the discrete sampling of R(λ), and E(λ i ) is the corresponding discrete spectral estimate value.

[0071] For Figure 3 the passive photodetection system shown in (a), if its system spectral response R(λ) is changed and it is used to make t observations on the ideal spectrum E(λ) to be measured, then we can obtain:

[0072] [S k = [R k (λ i )][E(λ i )] (3)

[0073] where [S k is a t×1 column matrix, and each element represents the output signal of the detector in the k-th measurement; [R k (λ i )] is the spectral modulation response parameter matrix, and [E(λ i )] is a column matrix, where each element represents the reconstructed discrete spectral intensity corresponding to the spectral modulation response wavelength.

[0074] For the actual measurement system, the measurement signal matrix [S k will contain noise [N k , that is:

[0075] [S k = [R k (λ i )][E(λ i )] + [N k (4)

[0076] According to the Gauss-Markov theorem, if the noise matrix is white noise, then the least-squares solution of Equation (4) will be the discrete spectrum to be measured [E(λ i) Optimal unbiased estimation. The process of spectral reconstruction is the process of solving the system of equations (4). This is the basic principle of passive broadband filtering coded computational spectral measurement technology.

[0077] B. Active broadband filtering coded spectral reconstruction measurement system

[0078] For Figure 3 the active optoelectronic detection system shown in (b), if the ideal illumination spectral distribution E’(λ) of the target to be measured is changed and the target is observed t times using a sensor, then we can obtain:

[0079]

[0080] In the formula, R(λ i ) is the discrete value of the ideal spectral response R(λ) of the sensor, E’(λ i ) is the discrete value of the ideal illumination spectral distribution E’(λ), and r(λ i ) is the discrete value of the ideal spectral reflectivity r(λ) of the target.

[0081] Discretizing equation (5) gives:

[0082] [S k = [R(λ i )E k '(λ i )][r(λ i )] + [N k (6)

[0083] Similar to the passive system, solving equation (6) can obtain the spectral reflectivity of the target to be measured. This is the basic principle of active broadband filtering coded computational spectral measurement technology.

[0084] The spectral system in the present invention includes the following three parts:

[0085] (1) Spectral modulation coding device: used to modulate and code the spectrum of the target to be measured.

[0086] For an active spectral measurement system or a spectral imaging system, the spectral modulation coding device is a spectrally tunable light source. The spectrally tunable light source is mainly used to output light with a programmable spectral distribution to irradiate the object to be measured, so as to achieve the purpose of modulating and coding the reflectivity spectrum of the target to be measured. The specific wavelength range, spectral resolution and other parameters of this spectrally tunable light source should be determined according to specific measurement requirements;

[0087] For a passive spectral measurement system or a spectral imaging system, the spectral modulation and encoding device is various spectral filtering devices. The spectral filtering device mainly completes the passive spectral filtering and encoding function of the incident spectrum. Its specific types include but are not limited to various colored optical glasses, interference filters, photonic crystals, quantum dot materials, nanowires, surface plasmon polaritons, optical metasurfaces, Fabry - Perot interferometric cavities, and other devices that can achieve similar functions.

[0088] (2) Optical signal acquisition system: used to receive the encoded spectrum of the target to be measured and complete the optoelectronic signal conversion.

[0089] The optical signal acquisition system mainly completes the function of collecting the energy of the spectrum to be measured and completing the optoelectronic signal conversion. The core of this system is the photodetector, which can consist only of a photodetector or can be attached with an energy collection system such as an imaging lens. The types of photodetectors include but are not limited to various photomultiplier tubes, photodiodes, CCD sensors, CMOS sensors, and other various optoelectronic sensor devices.

[0090] (3) Back - end signal processing system: used to receive the detector signal output by the signal acquisition system and perform spectral reconstruction calculation according to the spectral reconstruction calculation method based on the adaptive optimized sparse dictionary to obtain the reconstructed spectrum.

[0091] The function of the back - end signal processing system is to complete the processing of the spectrally aliased optoelectronic signal, and convert the aliased spectral signal into an applicable discrete spectral signal through the spectral reconstruction calculation method. This system includes two parts: a signal processing and calculation hardware module and a spectral signal reconstruction processing algorithm module. Among them, the spectral signal reconstruction processing algorithm module is the core part that determines the spectral reconstruction effect. This algorithm module uses the spectral reconstruction calculation method based on the adaptive optimized sparse dictionary described in the foregoing embodiments to achieve spectral reconstruction. The data acquisition system transmits the collected detector signal to the calculation unit, and the calculation unit performs spectral reconstruction calculation according to the pre - calibrated spectral modulation and encoding to obtain the reconstructed spectrum.

[0092] The main advantage of the spectral system proposed by the present invention is that a spectral reconstruction calculation method based on an adaptive optimized sparse dictionary is used for spectral reconstruction. On the basis of ensuring the completeness of the spectral reconstruction of the conventional basis - function sparse dictionary, higher - precision spectral reconstruction can be achieved by specifically optimizing and constructing the sparse dictionary. It should be noted that the hardware system of the spectral system in the present invention includes but is not limited to the composition methods of the spectral modulation and encoding device, the optical signal acquisition system, and the back - end signal processing system, and each part can be replaced with other devices with similar functions.

[0093] Next, a numerical simulation method is used to evaluate the spectral signal reconstruction performance of the spectral reconstruction calculation method of the present invention. Figure 4The figure shows a flowchart for evaluating the spectral signal reconstruction performance of the AOSDSR method of the present invention using numerical simulation methods, specifically including the following steps:

[0094] (1) Determine the simulation input data set. The spectral observation matrix (or transmittance matrix) can be a Gaussian random matrix generated by a computer or a true filter transmittance matrix screened through correlation verification; the reference spectrum to be measured can be various different forms of spectral signals such as continuous spectra and linear spectra; in this way, the effects of different measurement matrices and different types of spectral signals on the variable-parameter sparse dictionary and the optimized spectral reconstruction algorithm can be studied;

[0095] (2) According to the input data set, multiply the high-resolution standard reference spectral vector E by the generated high-resolution random spectral response matrix D and then integrate to calculate the simulated accurate signal vector S n , and add Gaussian random noise of different levels to it to simulate measurement errors. After adding noise, the error-containing measurement signal S' n ;

[0096] (3) Respectively use the above-mentioned Normal SD, SSD, and AOSDSR for spectral reconstruction to obtain the reconstructed spectral signal vector E s , and compare the reconstructed spectral signal vector E s with the high-resolution standard reference spectral vector E to obtain the simulation comparison result.

[0097] As Figure 5 shown is a comparison chart of the simulation results of the reconstruction performance of the given complex spectral signal using the traditional Normal SD, the refined sparse dictionary SSD, and the AOSDSR method. Among them Figure 5 (a) is the spectral reconstruction effect using SSD under 50 dB noise, Figure 5 (b) is the spectral reconstruction effect using Normal SD and AOSDSR under 50 dB noise, Figure 5 (c) is the spectral reconstruction effect using SSD under 60 dB noise, Figure 5 (d) is the spectral reconstruction effect using Normal SD and AOSDSR under 60 dB noise. The RMSE shown in the figure is the root mean square error between the reconstructed spectrum and the standard reference spectrum, τ is the regularization coefficient used in the reconstruction calculation process, T is the spectral reconstruction calculation time, threshold is the incomplete basis function determination threshold parameter, Ground truth is the standard reference spectrum, Normal SD represents the reconstruction result of the conventional Gaussian sparse dictionary, SSD represents the spectral reconstruction result of the refined sparse dictionary, and AOSDSR represents the spectral reconstruction result of the adaptive optimized sparse dictionary. It can be seen that the AOSDSR proposed by the present invention has the following advantages:

[0098] 1. Reconstruction spectral fidelity and resolution improvement: At different measurement noise levels, AOSDSR has better reconstruction spectral fidelity (lower RMSE) than Normal SD and SSD; meanwhile, both SSD and AOSDSR can achieve the resolution of high-frequency spectral signals (close to the compressive sensing theory constraint of the spectral response measurement matrix).

[0099] 2. From Figure 5 the shown simulation results, it can be seen that although both AOSDSR and SSD can achieve the restoration and resolution of high-frequency spectral signals, the SSD method can only restore high-frequency signals by adopting a smaller regularization coefficient τ. At this time, the restoration ability of the low-frequency smooth position signals is poor, and a lot of high-frequency noise is introduced; if the SSD method adopts a larger regularization coefficient τ, it is difficult to accurately restore the high-frequency spectral signals. In contrast, the reconstructed spectrum obtained by using AOSDSR can take into account both the low-frequency smooth and high-frequency sharp spectral signal characteristics. Therefore, although the RMSE values of the reconstructed spectra obtained by SSD and AOSDSR are not much different, in fact, the performance of the AOSDSR method is much better than that of the SSD method and is even better than the Normal SD method.

[0100] 3. On the premise of ensuring the performance of the reconstructed spectrum, the spectral reconstruction calculation time required by AOSDSR is shortened to less than 1 / 10 of that using the SSD method. The specific numerical value of the spectral reconstruction calculation time and the improvement degree of the reconstruction calculation speed will vary according to the complexity of the specific problem.

[0101] The simulation results can prove the effectiveness of the spectral measurement system based on the AOSDSR method proposed by the present invention for improving the accuracy and resolution of the reconstructed spectrum.

[0102] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0103] The above-described embodiments only represent several implementation manners of the present invention. The description is relatively specific and detailed, but it cannot be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention patent shall be subject to the appended claims.

Claims

1. A spectral reconstruction calculation method based on an adaptive optimized sparse dictionary, characterized in that Including the following steps: Step 1: Determine the input parameters, which include the target spectral range, the number of reconstructed spectral bands, the spectral response matrix, the measured signal vector, the regularization parameter, and the subdivision basis function determination threshold; Step 2: Perform spectral reconstruction calculation using a conventional basis function sparse dictionary to obtain an approximately optimal solution of the spectral signal; Step 3: Determine whether the spectral reconstruction calculation process terminates according to the approximately optimal solution of the spectral signal and the preset algorithm termination condition. If so, output the reconstructed spectrum; if not, execute Step 4; Step 4: Use the approximately optimal solution of the spectral signal as prior information to specifically optimize the construction process of the basis function sparse dictionary to obtain an optimized sparse dictionary; When specifically optimizing the construction process of the basis function sparse dictionary, first find all the quantities greater than the threshold in the sparse representation vector of the reconstructed spectrum, and locate the sparse basis functions corresponding to these quantities, and delete all the remaining invalid sparse basis functions; find the incomplete sparse basis functions among all the remaining sparse basis functions; locate the central wavelengths of all the incomplete sparse basis functions, and add subdivision sparse basis functions with a narrower full width at half maximum and a smaller central wavelength interval near these central wavelengths; the added subdivision sparse basis functions and the conventional basis function sparse dictionary after deleting the invalid sparse basis functions together constitute the optimized sparse dictionary; Step 5: Perform spectral reconstruction calculation again using the optimized sparse dictionary to obtain an optimized reconstructed spectrum solution; Step 6: Update the approximately optimal solution of the spectral signal with the optimized reconstructed spectrum solution, and repeat Steps 3 to 5 iteratively until the preset algorithm termination condition is satisfied, then end the spectral reconstruction calculation process, and output the finally obtained optimized reconstructed spectrum solution as the spectral reconstruction result.

2. The spectral reconstruction calculation method based on an adaptive optimized sparse dictionary according to claim 1, characterized in that, When performing spectral reconstruction calculation in Step 2 and Step 5, within the framework of the compressed sensing principle, regard the discrete spectral distribution obtained by the active broadband filtering coded spectral measurement system or the passive broadband filtering coded spectral measurement system as the following convex optimization problem: where D is the spectral encoding matrix. For a passive spectral measurement system, D = [R k (λ i )], where R k (λ i ) is the discrete value of the ideal spectral response function R(λ) at the k-th measurement. For an active spectral measurement system, D = [R(λ i )E' k (λ i )], where R(λ i ) is the discrete value of the ideal spectral response R(λ) of the sensor, and E' k (λ i ) is the discrete value of the ideal illumination spectral distribution E(λ) to be measured at the k-th measurement; ψ is the sparse dictionary, Dψ is the spectral observation matrix; x is the sparse representation vector, ψx = E s ; S n is the measurement signal vector, and τ is the regularization parameter; Perform spectral reconstruction according to formula (7).

3. A spectral reconstruction calculation method based on an adaptive optimized sparse dictionary according to claim 1, characterized in that, Among all the remaining sparse basis functions, regard the narrowest and the second narrowest sparse basis functions corresponding to the absolute value of the reconstructed sparse signal greater than the subdivision basis function determination threshold as the incomplete sparse basis functions.

4. A spectral reconstruction calculation method based on an adaptive optimized sparse dictionary according to claim 1, wherein, Similarly, the soft threshold method or the frequency amplitude screening method based on wavelet analysis can be used to find the incomplete sparse basis functions among all the remaining sparse basis functions.

5. A spectral reconstruction calculation method based on an adaptive optimized sparse dictionary according to claim 1, characterized in that, The preset algorithm termination condition is that the approximately optimal solution of the spectral signal satisfies any one of the following conditions (1), (2), and (3): Condition (1): The resolution of the approximately optimal solution of the spectral signal reaches the preset resolution level; Condition (2): The highest resolution of the approximately optimal solution of the spectral signal is higher than the numerical discretization scale of the spectral response matrix; Condition (3): The resolution level of the approximately optimal solution of the spectral signal is higher than the set noise threshold.

6. A spectral reconstruction calculation method based on an adaptive optimized sparse dictionary according to claim 1, characterized in that, The conventional basis function sparse dictionary uses a Gaussian function, a wavelet basis function, or a discrete cosine transform basis as the basis function.

7. A spectral system, characterized in that, Including: A spectral modulation coding device for modulating and coding the spectral of the target to be measured; An optical signal acquisition system for receiving the coded spectral of the target to be measured and completing the optoelectronic signal conversion; A backend signal processing system is configured to receive the detector signals output by the signal acquisition system, and perform spectral reconstruction calculations according to the spectral reconstruction calculation method based on an adaptive optimized sparse dictionary described in any one of claims 1 to 6 to obtain a reconstructed spectrum.

8. A spectral system according to claim 7, wherein The spectral modulation and encoding device is a spectral filtering device or a spectrally tunable light source.

9. A spectral system according to claim 8, characterized in that, The spectral filtering device is any one of colored optical glass, interference filter, photonic crystal, quantum dot material, nanowire, surface plasmon, optical metasurface, and Fabry-Perot interferometer cavity.

10. A spectral system according to claim 7, characterized in that, The optical signal acquisition system includes a photodetector, and the photodetector is any one of a photomultiplier tube, a photodiode, a CCD sensor, and a CMOS sensor.

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