CN115931123A - Spectrum reconstruction calculation method and spectrum system based on self-adaptive optimization sparse dictionary - Google Patents
Spectrum reconstruction calculation method and spectrum system based on self-adaptive optimization sparse dictionary Download PDFInfo
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Abstract
The invention relates to a spectral reconstruction calculation method and a spectral system based on a self-adaptive optimization sparse dictionary, wherein the method adopts a conventional basis function sparse dictionary to carry out spectral reconstruction calculation to obtain an approximate optimal solution of a spectral signal; in the optimization process, firstly, a sparse basis function is positioned, all the rest invalid sparse basis functions are deleted, an incomplete sparse basis function is searched, and a subdivided sparse basis function is added to the incomplete sparse basis function to obtain an optimized sparse dictionary; performing spectrum reconstruction calculation again by adopting an optimized sparse dictionary to obtain an optimized reconstruction spectrum solution; and updating the spectral signal approximate optimal solution by the optimal reconstruction spectral solution, repeating iteration until the termination condition is met, and outputting a spectral reconstruction result. The method can reduce the constraint of the basis function sparse dictionary on the spectrum reconstruction calculation process, further improve the fidelity of the reconstructed spectrum, and simultaneously improve the reconstruction spectrum calculation speed.
Description
Technical Field
The invention relates to the technical field of spectrum reconstruction, in particular to a spectrum reconstruction calculation method and a spectrum system based on a self-adaptive optimization sparse dictionary.
Background
The spectral measurement method based on the broadband filtering coding and the calculation reconstruction principle is a novel spectral measurement technology, has the advantages of high luminous flux and compact structure, and is easy to be combined with various micro-nano spectral filters to realize a microminiaturized spectral measurement or spectral imaging instrument; meanwhile, the spectrum remote sensing device can be combined with various spectrum coding modulation devices (such as a Fabry-Perot interference cavity, a photoelectric modulation crystal and the like) to realize high-flux spectrum imaging remote sensing, so that the spectrum remote sensing device is a novel spectrum measurement technology with application potential.
For computational spectroscopy systems, encoding and decoding (i.e., spectral reconstruction) of the system is one of the core problems. At present, according to the design theory basis of broadband spectral coding, spectral measurement or spectral imaging systems (hereinafter referred to as broadband coding reconstruction spectral measurement systems) based on spectral dimension broadband filtering coding and calculation reconstruction can be mainly classified into three categories: 1. the broadband spectrum code is not specially designed, and such systems mostly adopt l 2 Carrying out spectrum reconstruction by using a norm optimization algorithm; 2. the broadband spectrum coding is designed based on the compressive sensing theory, and the system mostly adopts a sparse representation method combined with l 1 Carrying out spectrum reconstruction by using a norm optimization algorithm; 3. the broadband spectrum code is designed based on a machine learning method, and the system can directly complete spectrum reconstruction by adopting a machine learning model.
Since the spectrum reconstruction process is a typical inverse problem solving process, and the measurement error of the detector has a great influence on the accuracy of the reconstructed spectrum, the accuracy and resolution of the reconstructed spectrum are one of the main problems that limit the application of the technology. In order to solve the problem, related researches propose to design spectral filtering codes based on a compressive sensing theory and combine a sparse representation technology and l 1 The norm optimization algorithm for spectrum reconstruction calculation is currentlyOne of the mainstream schemes of (1). The scheme not only can effectively inhibit the ill-conditioned problem of inverse problem solution, but also can reconstruct and recover the number of spectral bands more than the number of spectral measurements by utilizing the advantages of a compressed sensing theory, thereby having great advantages and being one of the mainstream technical routes of the broadband filtering coding reconstruction spectrum technology at present.
The sparse representation method adopted by the broadband coding reconstruction spectral measurement and spectral imaging system based on the compressed sensing theory can be mainly divided into two types: one is that after a certain base function is subjected to telescopic translation transformation, the base function is discretized and arranged in a matrix form to form a base function sparse dictionary (a base function dictionary for short), and the common base functions comprise Gaussian base functions, various wavelet base functions and the like; the other type is a learning dictionary (simply referred to as learning dictionary) which is constructed by adopting a supervised learning method aiming at a certain spectrum data set. The base function type and the construction method of the base function sparse dictionary do not depend on the spectrum to be measured, so that the base function sparse dictionary has better completeness in different application scenes, but the fidelity of the reconstructed spectrum is relatively poor; the learning dictionary construction process has a large relationship with the training data set, so that completeness is difficult to guarantee in a wide application scene, but the training spectral data set generally has a better spectral reconstruction effect.
Disclosure of Invention
Aiming at the problems that the existing spectrum reconstruction methods adopting two sparse representation methods are difficult to be compatible, so that the accuracy and the completeness of spectrum reconstruction cannot be considered at the same time, the invention provides a spectrum reconstruction calculation method and a spectrum system based on a self-adaptive optimization sparse dictionary, and the method and the spectrum system improve the reconstruction spectrum resolution and accuracy on the basis of ensuring the advantage of the spectrum reconstruction completeness of a basis function sparse dictionary; meanwhile, the self-adaptive optimization construction process of the sparse dictionary is defined, so that the complexity of the sparse dictionary can be reduced, and the spectrum reconstruction speed can be increased.
The invention adopts the following technical scheme:
a spectrum reconstruction calculation method based on a self-adaptive optimization sparse dictionary comprises the following steps:
step 3, judging whether the spectrum reconstruction calculation process is terminated according to the approximate optimal solution of the spectrum signal and the termination condition of a preset algorithm, and if so, outputting a reconstructed spectrum; if not, executing the step 4;
step 4, the construction process of the basis function sparse dictionary is optimized in a targeted manner by taking the approximate optimal solution of the spectrum signal as prior information to obtain an optimized sparse dictionary;
when the construction process of the basis function sparse dictionary is optimized in a pertinence mode, firstly, all quantities larger than a threshold value in a reconstructed spectrum sparse representation vector are found, sparse basis functions corresponding to the quantities are located, and all the rest invalid sparse basis functions are deleted; searching for an incomplete sparse basis function from all the remaining sparse basis functions; positioning the center wavelengths of all incomplete sparse basis functions, and adding subdivided sparse basis functions with narrower full width at half maximum and smaller center wavelength interval near the center wavelengths; the added subdivided sparse basis functions and the conventional basis function sparse dictionary from which the invalid sparse basis functions are deleted form an optimized sparse dictionary;
step 5, performing spectrum reconstruction calculation again by adopting an optimized sparse dictionary to obtain an optimized reconstruction spectrum solution;
and 6, updating the spectral signal approximate optimal solution by the optimized reconstruction spectral solution, repeating the iteration steps 3 to 5 until a preset algorithm termination condition is met, ending the spectral reconstruction calculation process, and outputting the finally obtained optimized reconstruction spectral solution as a spectral reconstruction result.
The invention also proposes a spectroscopic system comprising:
the spectrum modulation coding device is used for modulating and coding the target spectrum to be detected;
the optical signal acquisition system is used for receiving the coded target spectrum to be detected and completing photoelectric signal conversion;
and the rear-end signal processing system is used for receiving the detector signal output by the signal acquisition system and carrying out spectrum reconstruction calculation according to the spectrum reconstruction calculation method based on the self-adaptive optimization sparse dictionary to obtain a reconstructed spectrum.
Compared with the prior art, the invention has the following beneficial effects:
(1) The spectrum reconstruction method provided by the invention is constructed based on the basis of the basis function sparse dictionary, so that the completeness of a spectrum measurement system under different application scenes can be ensured; meanwhile, by adding the subdivision basis functions, the accuracy and the resolution of the reconstructed spectrum can be improved on the basis of the existing basis function sparse dictionary construction method;
(2) According to the spectrum reconstruction method, the self-adaptive iterative optimization process of the basis function sparse dictionary is added, so that the high-precision reconstruction of the subdivided basis function sparse dictionary on the high-frequency spectrum signal can be considered on the basis of ensuring the strong spectrum reconstruction robustness of the existing sparse representation method, and the problem that the existing method cannot simultaneously consider the high-frequency part and the low-frequency part of the reconstructed spectrum signal is solved;
(3) According to the spectrum reconstruction method, the self-adaptive optimization process of the basis function sparse dictionary is set, so that the advantages are ensured, the storage resource consumption of a large-scale overcomplete dictionary is reduced, and the spectrum reconstruction calculation speed is increased.
Drawings
FIG. 1 is a flow chart of a spectral reconstruction calculation method based on an adaptive optimization sparse dictionary according to the present invention;
FIG. 2 is a schematic diagram of a feasible sparse space of Gaussian function;
FIG. 3 is a schematic diagram of a passive and active broadband filtering-encoding-reconstruction spectral measurement system;
FIG. 4 is a flow chart of numerical simulation;
FIG. 5 is a comparison graph of the reconstruction performance simulation results for a given complex spectral signal using the conventional Normal SD, the subdivided sparse dictionary SSD, and the AOSDSR method.
Detailed Description
The invention aims to provide a spectral reconstruction calculation method based on a self-adaptive optimization sparse dictionary, which can reduce the constraint of the basic function sparse dictionary on the spectral reconstruction calculation process and further improve the fidelity of the reconstructed spectrum by setting the self-adaptive iterative optimization process of the basic function sparse dictionary on the basis of the conventional basic function sparse dictionary construction method; meanwhile, the self-adaptive optimization process of the sparse dictionary can improve the calculation speed of the reconstruction spectrum when a large-scale sparse dictionary is adopted. The technical solution of the present invention will be described in detail with reference to the accompanying drawings and preferred embodiments.
As shown in fig. 1, the present invention provides a spectral reconstruction calculation method (AOSDSR) based on an adaptive optimized sparse dictionary, which specifically includes the following steps:
the implementation method of the invention is explained based on a common Gaussian sparse dictionary as an example.
determining input parameters including basic parameters such as a target spectrum range, the number of reconstructed spectrum bands, a spectrum response matrix, a measurement signal vector, a regularization parameter tau, a subdivision basis function judgment threshold s and the like.
And 2, performing spectrum reconstruction calculation by adopting a conventional basis function sparse dictionary to obtain an approximate optimal solution of a spectrum signal.
In this step, when the conventional basis function sparse dictionary is used for spectrum reconstruction calculation, the spectrum measurement technique can be calculated by using a passive broadband filtering coding calculation spectrum measurement technique or an active broadband filtering coding calculation spectrum measurement technique, and the used reconstruction algorithm can be realized by using various types l 1 An optimization-like algorithm or other compressed-sensing reconstruction algorithm. The conventional basis function sparse dictionary in the embodiment may use a gaussian function as a basis function, and may also use other various wavelet basis functions or discrete cosine transform bases to perform sparse representation on a spectral signal to be detected, and the basic principle and the effect are similar.
Step 3, judging whether the spectrum reconstruction calculation process is terminated according to the approximate optimal solution of the spectrum signal and a preset algorithm termination condition, and if so, outputting a reconstructed spectrum; if not, executing the step 4.
And judging whether the spectrum reconstruction is finished or not according to a preset algorithm termination condition. The preset algorithm termination condition is that the approximate optimal solution of the spectral signal meets any one of the following conditions (1), (2) and (3):
according to the user requirement or the limitation of computing resources, terminating when the reconstructed spectrum reaches a certain preset resolution level (that is, the width of the narrowest sparse basis function in the sparse dictionary reaches a certain preset level), so that the condition (1) is that the resolution of the approximate optimal solution of the spectrum signal reaches the preset resolution level: (ii) a
According to the limitation of the compressive sensing theory, the highest resolution of the reconstructed spectrum should be theoretically lower than the numerical discrete scale of the spectral response matrix, so the condition (2) is: the highest resolution of the approximate optimal solution of the spectral signals is higher than the numerical discrete scale of the spectral response matrix;
according to the noise level limitation, if the measurement noise is large, an excessively high resolution level (an excessively narrow sparse basis function) will reduce the robustness of the reconstructed spectrum, which brings an over-fitting problem, and therefore for a high measurement noise level, the narrowest sparse basis frequency level of the adaptive optimization sparse dictionary should be correspondingly reduced, and the robustness is ensured, so the condition (3) is as follows: the resolution level of the spectral signal near the optimal solution is higher than a set noise threshold.
Step 4, self-adaptive optimization of basis function sparse dictionary
In the step, the approximate optimal solution of the spectrum signal is used as prior information, the construction process of the basis function sparse dictionary is optimized in a pertinence mode, and the optimized sparse dictionary is obtained, so that the spectrum reconstruction precision is improved.
If the reconstructed spectrum signal does not reach the calculation termination condition, starting to execute a self-adaptive optimization construction step of the basis function sparse dictionary, specifically comprising the following steps of: firstly, all the quantities which are larger than a threshold value in a reconstructed spectrum sparse representation vector x are found, sparse basis functions corresponding to the quantities are positioned, and all the rest invalid sparse basis functions are deleted (the component in the corresponding reconstructed spectrum sparse representation vector x is equal to 0 or smaller than the threshold value, and the sparse basis which is smaller than the threshold value is considered to have little influence on sparse representation of a target spectrum signal); searching incomplete sparse basis functions in all the residual sparse basis functions, namely 'incomplete sparse basis functions', the incomplete representation of high-frequency spectrum signals can be contained in the sparse basis functions, when the incomplete sparse basis functions are searched, a hard threshold judgment method can be used for searching sparse basis functions corresponding to the narrowest and the next narrowest, namely the half-maximum width (FWHM) minimum and the second minimum (other judgment conditions can be increased according to actual conditions) of a reconstructed sparse signal absolute value larger than a subdivided basis function judgment threshold s set during algorithm initialization, or a soft threshold method or a frequency amplitude screening method based on wavelet analysis is used for searching incomplete sparse basis functions in all the residual sparse basis functions, and the sparse basis functions are named as 'incomplete sparse basis'; the central wavelengths of all incomplete sparse basis functions are positioned by combining a construction method of a basis function sparse dictionary, and subdivided sparse basis functions with narrower FWHM and smaller central wavelength interval are added near the central wavelengths; and finally, the added subdivided sparse basis functions and the conventional basis function sparse dictionary from which the invalid sparse basis functions are deleted are combined to form a new optimized sparse dictionary which takes the approximate optimal solution of the spectral signals obtained by the conventional basis function sparse dictionary as prior information.
Step 5, performing spectrum reconstruction calculation again by using the optimized sparse dictionary obtained in the step 4 to obtain an optimized reconstruction spectrum solution;
and 6, updating the replaced spectrum signal approximate optimal solution by adopting the optimal reconstruction spectrum solution obtained in the step 5, then repeating the steps 3 to 5 until a preset algorithm termination condition is met, ending the spectrum reconstruction calculation process, and outputting the finally obtained optimal reconstruction spectrum solution as a spectrum reconstruction result.
Further, when performing spectral reconstruction calculation in step 2 and step 5, in the framework of the compressed sensing principle, the dissociated astigmatism spectral distributions of equations (4) and (6) obtained by the active broadband filtering coding calculation spectral measurement system or the passive broadband filtering coding calculation spectral measurement system can be regarded as the following optimization problem:
wherein D is a spectrum coding matrix, and D = [ R ] for a passive spectrum measurement system k (λ i )]，R k (λ i ) For discrete values of the ideal spectral response function R (λ) at the kth measurement, D = [ R (λ) = for an active spectral measurement system i )E' k (λ i )]，R(λ i ) Is a discrete value, E ', of the ideal spectral response R (λ) of the sensor' k (λ i ) The discrete value of the ideal illumination spectral distribution E (lambda) to be measured in the kth measurement; psi is a sparse dictionary, and D psi can be generally called a spectral observation matrix; x is a sparse representation vector, ψ x = E s ；S n To measure the signal vector, τ is a regularization parameter that controls the sparseness (and also the smoothness) of the solution.
The basic principle of the spectrum reconstruction method based on the adaptive optimization sparse dictionary can be understood in two parts, and the following description is provided respectively.
(1) Sparse representation capability of spectral signals of basis function sparse dictionary
Relevant researches show that natural spectrum signals have a piecewise continuous smooth characteristic and can be generally sparsely represented in certain transform domains. According to the basic characteristic, a large number of basic functions such as Gaussian basic functions or various wavelet basic functions are adopted in related researches to carry out sparse representation on spectral signals. The invention is explained by taking a construction method of a conventional Gaussian basis function sparse dictionary as an example.
For measuring range λ min To lambda max The spectral imaging system with the number of spectral channels being N is uniformly distributed in a target spectral interval by using the central wavelength and has the full width at half maximum FWHM of (lambda) max -λ min ) A Gaussian function of/N is used as a basic function for constructing the sparse dictionary; after the central wavelength and FWHM are translated and stretched by integral multiple, the central wavelength is taken to be lambda min To lambda max In the range of (lambda) max -λ min )/N≤FWHM≤(λ max -λ min ) Transformed Gaussian basis functions with values discretized into columnsThe vectors are combined and arranged into a matrix, which is a common fixed parameter gaussian basis function sparse dictionary, and hereinafter referred to as a Normal sparse dictionary, or NormalSD for short.
Fig. 2 is a schematic diagram of a feasible sparse solution space of the gaussian function, where the two abscissa coordinates are the full width at half maximum FWHM and the center wavelength (central wavelength) of the gaussian basis function, and the ordinate coordinate is the optimization function value (optimization function value). It can be seen that the conventional basis function sparse dictionary construction method can be regarded as artificially dividing discrete grids in a Gaussian basis function feasible domain of a spectrum reconstruction solution, and the reconstruction spectrum optimization solution can be selected only on divided grid nodes. However, the division of the grid is artificially specified in practice, and for natural spectrum signals, if gaussian base functions are adopted to perform best fit representation on the natural spectrum signals, the gaussian base functions are not always exactly located on the divided grid; in other words, this common gaussian basis function sparse dictionary construction method actually limits the sparse representation capability of the gaussian basis function on the target spectrum. From the angle, the sparse representation capability of the basis function sparse dictionary can be effectively improved by improving the construction mode of the basis function sparse dictionary.
It can also be seen from fig. 2 that the purpose of improving the sparse representation capability can be achieved only by improving the "grid" density, that is, adding more narrow-band gaussian basis functions with small center wavelength intervals in the sparse dictionary. Such a sparse dictionary constructed by largely adopting the subdivided sparse basis functions is hereinafter referred to as a subdivided sparse dictionary, SSD for short.
However, the simple addition of the subdivided sparse basis functions brings about great redundancy of the sparse dictionary, affects the reconstruction calculation speed and consumes a large amount of sparse dictionary storage space, so that the aim of improving the sparse representation capability by combining with other methods is considered.
(2) Adaptive optimization of basis function sparse dictionaries
The simple addition of the subdivided sparse basis functions causes exponential increase of the scale of the sparse dictionary, consumes storage space and influences the reconstruction calculation speed. Therefore, the invention designs the following spectrum reconstruction calculation flow by using the idea of an optimization algorithm:
1. performing spectrum reconstruction by using a conventional basis function sparse dictionary to obtain a spectrum signal estimation value;
2. then, the spectral signal estimation value is used as prior information, the construction of the basis function sparse dictionary is optimized in a pertinence manner, and spectral reconstruction calculation is carried out again to obtain an optimized spectral signal estimation value;
3. this process is iterated until a spectral reconstruction calculation termination condition is reached.
The key of the process lies in how to construct the sparse dictionary through targeted optimization according to the spectral signal estimation value obtained in the step 1. Here we can achieve this object according to a simple recognition: regardless of the measurement error influence, if the high-frequency spectrum signal existing in the target spectrum signal cannot be completely represented by the conventional basis function sparse dictionary, the high-frequency spectrum signal has a very high probability to be represented by a narrower (i.e. smaller FWHM) sparse basis located near the position of the high-frequency signal; therefore, the free construction of the sparse dictionary can be completed only by adding the subdivided Gaussian sparse basis near the narrowest (or adding the secondary narrow sparse basis to improve the success probability) sparse basis function in the reconstructed spectrum signal. And the optimized sparse dictionary is adopted to perform spectrum reconstruction, so that the optimized reconstructed spectrum signal value can be obtained, the similar effect of directly using the subdivided sparse dictionary is achieved, and meanwhile, the consumption of computing resources is reduced.
The invention also provides a spectrum system which is a broadband filtering coding reconstruction spectrum measurement system or a broadband filtering coding reconstruction spectrum imaging system adopting the compressed sensing theory. According to the spectrum system, the spectrum reconstruction algorithm with high precision, namely the spectrum reconstruction calculation method based on the adaptive optimization sparse dictionary, can improve the reconstruction spectrum resolution and fidelity on the basis of ensuring the completeness of the conventional sparse dictionary.
As shown in fig. 3, it is the basic principle and implementation of the broadband filtering coding reconstruction spectral measurement/spectral imaging system. Fig. 3 (a) is a passive broadband filtering coding reconstruction spectrum measurement system, which mainly includes a spectrum filtering device, an optical signal acquisition system and a back-end signal processing system; the system modulates and codes the incident spectrum through the spectrum filter device, and further realizes the measurement of the target spectrum to be measured. Fig. 3 (b) shows an active broadband filtering coding reconstruction spectrum measurement system, which mainly includes a spectrum tunable light source, an optical signal acquisition system and a back-end signal processing system; the system realizes spectrum coding by changing the spectral distribution of the light source, and further realizes the measurement of the spectral reflectivity of the target to be measured. For spectral imaging application, only a two-dimensional photoelectric detector array is used for replacing a barrel detector to perform photoelectric signal conversion, and other system components are consistent with the principle.
Although the two systems have different compositions, the measurement principles are basically the same.
A. Passive broadband filtering coding reconstruction spectrum measuring system
The optoelectronic system output signal can be expressed as:
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 spectral response of the system, λ max Is the upper bound of the spectral response, λ is the wavelength, and E (λ) is the ideal incident spectrum. In general, when formula (1) is discretized into n spectral bands, it can be rewritten as:
wherein λ is i Is the nominal wavelength of the ith spectral band (taking it as the center wavelength of that band), R' (λ i ) Is a discrete sample of R (λ), E (λ) i ) Are corresponding discrete spectral estimates.
For the passive photoelectric detection system shown in fig. 3 (a), if the system spectral response R (λ) is changed and t times of observations are performed on the ideal spectrum E (λ) to be detected, then:
[S k ]＝[R k (λ i )][E(λ i )] (3)
wherein [ S ] k ]Is a column matrix of t x 1, each element representing the k-th measurement of the detector output signal, [ R k (λ i )]For the spectral modulation response parameter matrix, [ E (λ) i )]Is a column matrix in which each element represents the reconstructed discrete spectral intensity corresponding to the spectral modulation response wavelength.
For a real measurement system, the signal matrix [ S ] is measured k ]Will contain noise N k ]Namely:
[S k ]＝[R k (λ i )][E(λ i )]+[N k ] (4)
according to the Gauss-Markov theorem, if the noise matrix is white noise, the least squares solution of equation (4) will be the discrete spectrum [ E (λ) i )]Optimal unbiased estimation of (1). The process of spectrum reconstruction is the process of solving the equation set (4). This is the basic principle of the passive broadband filtering coding calculation spectrum measurement technology.
B. Active broadband filtering coding reconstruction spectrum measuring system
For the active photoelectric detection system shown in fig. 3 (b), if the ideal illumination spectrum distribution E' (λ) of the target to be detected is changed, and the target is observed t times by using the sensor, then:
in the formula, R (lambda) i ) Is a discrete value of the ideal spectral response R (λ) of the sensor, E' (λ) i ) Is a discrete value of the ideal illumination spectral distribution E' (λ), r (λ) i ) Is a discrete value of the target's ideal spectral reflectance r (λ).
Discretizing equation (5) yields:
[S k ]＝[R(λ i )E k '(λ i )][r(λ i )]+[N k ] (6)
similar to the passive system, the spectral reflectance of the target to be measured can be obtained by solving equation (6). This is the basic principle of the active broadband filtering coding calculation spectrum measurement technology.
The spectroscopic system of the present invention comprises the following 3 parts:
(1) Spectral modulation coding device: the method is used for modulating and coding the target spectrum to be detected.
For an active spectral measurement system or a spectral imaging system, a spectral modulation coding device is a spectral tunable light source which is mainly used for outputting light with programmable spectral distribution to irradiate on an object to be measured so as to realize the purpose of modulating and coding the reflectivity spectrum of a target to be measured. Parameters such as specific waveband range, spectral resolution and the like of the spectrum tunable light source are determined according to specific measurement requirements;
for a passive spectral measurement system or a spectral imaging system, the spectral modulation coding device is a spectral filtering device of various types, the spectral filtering device mainly completes the passive spectral filtering coding function of the incident spectrum, and the specific types of the spectral filtering device include but are not limited to devices which can realize similar functions such as various colored optical glass, interference filters, photonic crystals, quantum dot materials, nanowires, surface plasmons, optical super surfaces, fabry-Perot interference cavities and the like.
(2) The optical signal acquisition system: and the optical receiver is used for receiving the coded target spectrum to be detected and completing photoelectric signal conversion.
The optical signal acquisition system mainly finishes the functions of collecting spectral energy to be measured and converting photoelectric signals. The core of the system is a photoelectric detector, which can be composed of only the photoelectric detector, and can be attached with an energy collecting system such as an imaging lens. The types of photodetectors include, but are not limited to, various types of photomultiplier tubes, photodiodes, CCD sensors, CMOS sensors, and various other types of photo-sensing devices.
(3) Back end signal processing system: and the spectrum reconstruction computing device is used for receiving the detector signal output by the signal acquisition system and performing spectrum reconstruction computing according to a spectrum reconstruction computing method based on the self-adaptive optimization sparse dictionary to obtain a reconstructed spectrum.
The back-end signal processing system has the functions of processing the spectral dimension aliasing photoelectric signals and converting the aliasing spectral signals into applicable discrete spectral signals by a spectral reconstruction calculation method. The system comprises a signal processing and computing hardware module and a spectrum signal reconstruction processing algorithm module, wherein the spectrum signal reconstruction processing algorithm module is a core part for determining a spectrum reconstruction effect, and the algorithm module adopts the spectrum reconstruction computing method based on the self-adaptive optimization sparse dictionary to realize spectrum reconstruction. The data acquisition system transmits acquired detector signals to the calculation unit, and the calculation unit carries out spectrum reconstruction calculation according to the pre-calibrated spectrum modulation code to obtain a reconstructed spectrum.
The spectral system provided by the invention has the main advantages that the spectral reconstruction is carried out by adopting a spectral reconstruction calculation method based on the self-adaptive optimization sparse dictionary, and the spectral reconstruction with higher precision can be realized by purposefully optimizing and constructing the sparse dictionary on the basis of ensuring the completeness of the spectrum reconstructed by the conventional basis function sparse dictionary. It should be noted that the hardware system of the spectroscopy system of the present invention includes, but is not limited to, the components of the spectral modulation encoding device, the optical signal acquisition system, and the back-end signal processing system, and each part can be replaced by other devices with similar functions.
The spectral signal reconstruction performance of the spectral reconstruction calculation method is evaluated by adopting a numerical simulation method. Fig. 4 is a flowchart illustrating a method for evaluating spectral signal reconstruction performance of the AOSDSR method according to the present invention by using a numerical simulation method, which specifically includes the following steps:
(1) A simulation input data set is determined. The spectrum observation matrix (or the transmittance matrix) can be a Gaussian random matrix generated by a computer or a real optical filter transmittance matrix screened by correlation verification; the reference spectrum to be detected selects various different forms of spectrum signals such as continuous spectrum, linear spectrum and the like; therefore, the influence of different measurement matrixes and different types of spectrum signals on the variable parameter sparse dictionary and the optimized spectrum reconstruction algorithm is researched;
(2) According to the input data set, multiplying the high-resolution standard reference spectrum vector E with the generated high-resolution random spectral response matrix D, integrating, and calculating to obtain a simulated accurate signal vector S n Are combined with each otherGaussian random noise with different levels is added to simulate measurement error, and the noise is added to obtain a measurement signal S 'containing the error' n ；
(3) Respectively adopting the Normal SD, the SSD and the AOSDSR to carry out spectrum reconstruction to obtain a reconstructed spectrum signal vector E s Will reconstruct the spectral signal vector E s And comparing the spectrum vector E with a high-resolution standard reference spectrum vector E to obtain a simulation comparison result.
Fig. 5 is a comparison graph of the simulation results of reconstruction performance for a given complex spectrum signal by using the conventional Normal SD, the SSD with the subdivided sparse dictionary and the AOSDSR method, where fig. 5 (a) shows the spectral reconstruction effect of the SSD with 50dB noise, fig. 5 (b) shows the spectral reconstruction effect of the Normal SD and the AOSDSR with 50dB noise, fig. 5 (c) shows the spectral reconstruction effect of the SSD with 60dB noise, and fig. 5 (d) shows the spectral reconstruction effect of the Normal SD and the AOSDSR with 60dB noise. Shown in the figure, RMSE is a root mean square error between a reconstructed spectrum and a standard reference spectrum, τ is a regularization coefficient adopted in a reconstruction calculation process, T is spectrum reconstruction calculation time, threshold is an incomplete basis function determination threshold parameter, ground truth is a standard reference spectrum, normal SD represents a conventional gaussian sparse dictionary reconstruction result, SSD represents a subdivided sparse dictionary spectrum reconstruction result, and AOSDSR represents an adaptive optimized sparse dictionary spectrum reconstruction result. It can be seen that the AOSDSR proposed by the present invention has the following advantages:
1. improving the fidelity and resolution of the reconstructed spectrum: AOSDSR has better reconstructed spectral fidelity (lower RMSE) than Normal SD, SSD at different measured noise levels; meanwhile, both SSD and AOSDSR can achieve resolution of high frequency spectral signals (approaching the compressive sensing theory constraint of the spectral response measurement matrix).
2. As can be seen from the simulation result shown in fig. 5, although both AOSDSR and SSD can realize restoration and resolution of high-frequency spectrum signals, the SSD method can only restore the high-frequency signals by using a smaller regularization coefficient τ, and at this time, the capability of restoring low-frequency smooth position signals is poor, and a lot of high-frequency noise is introduced; however, if the SSD method employs a large regularization coefficient τ, the high-frequency spectrum signal is difficult to recover accurately. In contrast, the reconstructed spectrum obtained by adopting the AOSDSR can simultaneously take low-frequency smooth and high-frequency sharp spectrum signal characteristics into consideration, so that although the difference between the RMSE values of the reconstructed spectrum obtained by the SSD and the reconstructed spectrum obtained by the AOSDSR is not large, the performance of the AOSDSR method is far better than that of the SSD method and is better than that of the Normal SD method.
3. On the premise of ensuring the performance of the reconstructed spectrum, the time for reconstructing the spectrum required by the AOSDSR is shortened to be less than 1/10 of that of the SSD method. The specific value of the reconstruction spectrum calculation time and the reconstruction calculation speed increase degree are different according to the complexity of the specific problem.
The simulation result can prove the effectiveness of the spectral measurement system based on the AOSDSR method in improving the accuracy and resolution of the reconstructed spectrum.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent should be subject to the appended claims.
Claims (10)
1. A spectrum reconstruction calculation method based on a self-adaptive optimization sparse dictionary is characterized by comprising the following steps:
step 1, determining input parameters, wherein the input parameters comprise a target spectrum range, the number of reconstructed spectrum bands, a spectrum response matrix, a measurement signal vector, a regularization parameter and a subdivision basis function judgment threshold;
step 2, performing spectrum reconstruction calculation by adopting a conventional basis function sparse dictionary to obtain an approximate optimal solution of a spectrum signal;
step 3, judging whether the spectrum reconstruction calculation process is terminated according to the approximate optimal solution of the spectrum signal and a preset algorithm termination condition, and if so, outputting a reconstructed spectrum; if not, executing the step 4;
step 4, the construction process of the basis function sparse dictionary is optimized in a targeted manner by taking the approximate optimal solution of the spectrum signal as prior information to obtain an optimized sparse dictionary;
when the construction process of the basis function sparse dictionary is optimized in a pertinence manner, firstly, all quantities larger than a threshold value in a reconstructed spectrum sparse representation vector are found, sparse basis functions corresponding to the quantities are located, and all the rest invalid sparse basis functions are deleted; searching for an incomplete sparse basis function from all the remaining sparse basis functions; positioning the central wavelengths of all incomplete sparse basis functions, and adding subdivided sparse basis functions with narrower full width at half maximum and smaller central wavelength interval near the central wavelengths; the added subdivision sparse basis function and the conventional basis function sparse dictionary from which the invalid sparse basis function is deleted form an optimized sparse dictionary;
step 5, performing spectrum reconstruction calculation again by adopting the optimized sparse dictionary to obtain an optimized reconstruction spectrum solution;
and 6, updating the spectral signal approximate optimal solution by the optimized reconstruction spectral solution, repeating the iteration steps 3 to 5 until a preset algorithm termination condition is met, ending the spectral reconstruction calculation process, and outputting the finally obtained optimized reconstruction spectral solution as a spectral reconstruction result.
2. The spectral reconstruction computing method based on the adaptive optimization sparse dictionary according to claim 1, wherein in the spectral reconstruction computing in the steps 2 and 5, within a compressed sensing principle framework, the dissociated astigmatism spectral distribution obtained by the active broadband filtering coding computing spectral measurement system or the passive broadband filtering coding computing spectral measurement system is regarded as the following convex optimization problem:
wherein D is a spectrum coding matrix, and D = [ R ] for a passive spectrum measurement system k (λ i )]，R k (λ i ) For discrete values of the ideal spectral response function R (λ) at the kth measurement, D = [ R (λ) for an active spectral measurement system i )E' k (λ i )]，R(λ i ) Is a discrete value, E ', of the ideal spectral response R (λ) of the sensor' k (λ i ) The discrete value of the ideal illumination spectral distribution E (lambda) to be measured in the k measurement; psi is a sparse dictionary, and D psi is a spectrum observation matrix; x is a sparse representation vector, ψ x = E s ；S n For the measurement signal vector, τ is the regularization parameter;
spectral reconstruction was performed according to equation (7).
3. The spectral reconstruction computing method based on the adaptive optimization sparse dictionary according to claim 1, characterized in that, of all the remaining sparse basis functions, the narrowest and next narrowest sparse basis functions corresponding to the reconstruction of which the absolute value of the sparse signal is greater than the decision threshold of the subdivision basis function are taken as incomplete sparse basis functions.
4. The spectral reconstruction computing method based on the adaptive optimization sparse dictionary as claimed in claim 1, wherein the incomplete sparse basis functions are searched for in all the remaining sparse basis functions by adopting a soft threshold method or a frequency amplitude screening method based on wavelet analysis.
5. The spectral reconstruction computing method based on the adaptive optimization sparse dictionary according to claim 1, wherein the preset algorithm termination condition is that the approximate optimal solution of the spectral signal satisfies any one of the following conditions (1), (2) and (3):
condition (1): the resolution of the spectral signal approximate to the optimal solution reaches a preset resolution level;
condition (2): the highest resolution of the approximate optimal solution of the spectral signals is higher than the numerical discrete scale of the spectral response matrix;
condition (3): the resolution level of the spectral signal approximate optimal solution is higher than a set noise threshold.
6. The spectrum reconstruction computing method based on the adaptive optimization sparse dictionary as claimed in claim 1, wherein the conventional basis function sparse dictionary has a gaussian function, a wavelet basis function or a discrete cosine transform basis as a basis function.
7. A spectroscopic system, comprising:
the spectrum modulation coding device is used for modulating and coding the target spectrum to be detected;
the optical signal acquisition system is used for receiving the coded target spectrum to be detected and completing photoelectric signal conversion;
the back-end signal processing system is used for receiving the detector signal output by the signal acquisition system and carrying out spectrum reconstruction calculation according to the spectrum reconstruction calculation method based on the adaptive optimization sparse dictionary, which is claimed in any one of claims 1 to 6, so as to obtain a reconstructed spectrum.
8. The spectroscopy system of claim 7, wherein the spectral modulation encoding device is a spectral filter device or a spectrally tunable light source.
9. The spectroscopy system of claim 8, wherein the spectral filter device is any one of a colored optical glass, an interference filter, a photonic crystal, a quantum dot material, a nanowire, a surface plasmon, an optical super surface, and a Fabry-Perot interference cavity.
10. The spectroscopy system of claim 7, wherein the optical signal acquisition system comprises a photodetector, the photodetector being any one of a photomultiplier tube, a photodiode, a CCD sensor, and a CMOS sensor.
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| CN116858797B (en) * | 2023-09-04 | 2024-01-19 | 中山大学 | Mid-infrared spectrum analysis system and method based on super-surface calculation reconstruction |
| CN116879195A (en) * | 2023-09-07 | 2023-10-13 | 中山大学 | Phase change material-based calculation reconstruction spectrum system and spectrum imaging method |
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