CN120726169A - A near-field electromagnetic wave image reconstruction method based on information-preserving hybrid regularized sparse kernel learning - Google Patents
A near-field electromagnetic wave image reconstruction method based on information-preserving hybrid regularized sparse kernel learningInfo
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Abstract
本发明提供一种基于信息保留型混合正则化稀疏核学习的近场电磁波图像重建方法，近场电磁波图像重建的技术领域；S1：进行数据采集与预处理，归一化处理，剔除低频漂移；S2：利用高斯核或多项式核将输入数据映射到特征空间，设计动态字典更新策略；S3：进行在线递归权重更新；S4：进行混合正则化重建优化，通过拟合约束条件求解待优化向量；S5：采用FISTA加速近邻投影与对偶分解框架迭代求解优化问题，通过谱范数估计步长及动量项；S6：进行稀疏化与字典维护，更新协方差矩阵与权重系数；通过混合正则化与在线核学习的结合，解决了传统CS方法和KRLS变体的不足，集实时在线更新、稀疏先验与边缘保留于一体，解决了传统的近场电磁波图像重建技术的不足。
The present invention provides a near-field electromagnetic wave image reconstruction method based on information-preserving hybrid regularized sparse kernel learning, which belongs to the technical field of near-field electromagnetic wave image reconstruction. S1: performing data acquisition and preprocessing, normalization processing, and eliminating low-frequency drift; S2: using a Gaussian kernel or a polynomial kernel to map input data to a feature space, and designing a dynamic dictionary update strategy; S3: performing online recursive weight update; S4: performing hybrid regularized reconstruction optimization, and solving a vector to be optimized by fitting constraints; S5: using FISTA to accelerate the nearest neighbor projection and dual decomposition framework to iteratively solve the optimization problem, and estimating the step size and momentum term by using the spectral norm; S6: performing sparsification and dictionary maintenance, and updating the covariance matrix and weight coefficients; by combining hybrid regularization with online kernel learning, the shortcomings of traditional CS methods and KRLS variants are solved, and real-time online update, sparse prior and edge preservation are integrated, thus solving the shortcomings of traditional near-field electromagnetic wave image reconstruction technology.
Description
Technical Field
The invention relates to the technical field of near-field electromagnetic wave image reconstruction, in particular to a near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning.
Background
The near-field electromagnetic wave image reconstruction is a technology for reconstructing an image of a target object by collecting electromagnetic wave signals in a near-field region of an electromagnetic field near the target object and processing and analyzing the electromagnetic wave signals, and is characterized in that the characteristics of the electromagnetic waves in the near-field region are utilized to extract information such as spatial distribution, shape, materials and the like of the target object from the collected signals to finally form a visualized image.
The conventional near-field electromagnetic wave image reconstruction technology is mainly divided into two major categories, namely a conventional Compressed Sensing (CS) method and a nuclear recursive least square (KRLS) variant, wherein the conventional Compressed Sensing (CS) method (such as BP, LASSO, DS, OMP, KF-CS and CS-AMP) is used for reconstructing signals from undersampled data through sparse transformation (such as wavelet transformation and TV regularization) and depends on static sparse bases (such as a synthesis dictionary ψ or an analysis operator phi), and the typical flow is used for solving the following optimization equation: The method comprises the steps of BP, LASSO, DS, OMP, KF-CS and CS-AMP, wherein the method has the defects that 1, in an off-line batch processing mode, model parameters cannot be updated on line, when new measured data arrives, the new measured data need to be recalculated, and the new measured data are difficult to adapt to a real-time scene;
The Kernel Recursive Least Squares (KRLS) variant maps the input to the Regenerated Kernel Hilbert Space (RKHS) by a kernel function (e.g., gaussian kernel, random fourier features), recursively updating the weights: The method has the defects that 1, unstructured sparsity, dictionary is unconstrained along with data growth, overfitting and computation complexity increase exponentially (such as memory and matrix operand increase along with sample number), 2, edge information is lost, explicit regularization on image edges is lacking, reconstructed images are easy to blur, detail retaining capability is poor, robustness under non-Gaussian noise is poor (although ROB-KRLS introduces M estimation, complex noise interference cannot be effectively inhibited);
The traditional CS method depends on a static model, cannot update online, and the nuclear recursion least square (KRLS) variant supports online learning, but lacks a sparse constraint and edge protection mechanism, so that the near-field electromagnetic wave image reconstruction precision is insufficient, and therefore, the near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse nuclear learning is necessary to solve the technical problems.
Disclosure of Invention
In order to solve the technical problems, the invention provides a near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning.
The invention provides a near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning, which comprises the following method steps:
s1, data acquisition and preprocessing are carried out, normalization processing is carried out on near-field electromagnetic wave scanning data or chaos sequence observation values, and low-frequency drift is removed by adopting a moving average or polynomial trending technology;
s2, mapping input data to a feature space by utilizing Gaussian kernels or polynomial kernels, designing a dynamic dictionary updating strategy, adding a dictionary when the kernel similarity of a new sample and any atom in the existing dictionary is smaller than a preset threshold, and eliminating the most redundant atoms according to the contribution degree and a sparse reconstruction result if the dictionary size exceeds a preset maximum;
s3, carrying out online recursion weight updating, and carrying out recursion updating of a weight coefficient and a covariance matrix after mapping of each input data in a feature space based on a kernel recursion least square criterion to obtain a preliminary weight estimation;
S4, performing mixed regularized reconstruction optimization, taking the weight coefficient as a compressed sensing reconstruction target, and constructing a structure comprising Solving a vector to be optimized by fitting constraint conditions with a regular target function of the TV;
S5, adopting FISTA to accelerate neighbor projection and a dual decomposition frame to iteratively solve an optimization problem, estimating a step length and a momentum item through a spectrum norm, and setting a shutdown tolerance to avoid redundant iteration;
and S6, performing sparsification and dictionary maintenance, performing soft threshold clipping on the reconstruction result, deleting corresponding redundant dictionary atoms, updating covariance matrixes and weight coefficients, and realizing real-time updating of dictionary sparsity and edge information retention.
Preferably, in the step S1, electromagnetic wave near-field scanning or chaotic sequence observation values are obtainedNormalization processing is carried out, and the calculation formula is as follows:
;
;
Wherein, the Is the firstThe raw input data of the sub-acquisition,Is the firstThe target of the sub-acquisition outputs data,As a mean value of the input data,For the mean value of the output data,In order to input the standard deviation of the data,For the input data to be normalized,For the output data after normalization,Index for samples or number of iterations;
and a sliding average or polynomial trending technology is adopted, low-frequency drift is removed, and the numerical stability of nuclear mapping is improved.
Preferably, in S2, a feature map is constructed using a gaussian kernel or a polynomial kernel, and the calculation formula is as follows:
;
;
Wherein, the As a function of the gaussian kernel,For a sample point in the input space,Is the first in the dictionaryThe number of atoms in the radical is one,For the atomic index of a dictionary,Is the firstThe individual samples are mapped to feature vectors after feature space,For the size of the dictionary to be a matter of scale,As a function of the gaussian kernel,Bandwidth parameters for kernel functions;
Design of dynamic dictionary addition/removal strategy when the new sample is similar to any atom in the existing dictionary In the time-course of which the first and second contact surfaces,To add new atom threshold, dictionary is added, if the size of dictionary exceeds that of dictionary,And if the maximum dictionary size is the maximum dictionary size, removing the most redundant atoms according to the contribution degree and the sparse reconstruction result.
Preferably, in S3, for the firstSecondary input data pairBy kernel functions in feature spaceAfter the mapping is performed, the image is processed,For the kernel similarity function, the preliminary weight update is obtained by using recursive least square, and the calculation formula is as follows:
;
Wherein, the Is the firstThe weight vector of the next iteration,Is the firstThe feature matrix of the next iteration,In order for the parameters to be regularized,Is a matrix of units which is a matrix of units,Is the firstA secondary target output value;
Updating covariance matrix based on kernel recursive least squares criterion Coefficient of andThe calculation formula is as follows:
;
;
Wherein, the Is the firstThe covariance matrix of the next iteration,Is the firstThe covariance matrix of the next iteration,Is the firstThe feature vector of the individual samples is used,Is the firstThe coefficient vector of the next iteration, as a preliminary weight estimate,Is the firstThe coefficient vector of the number of iterations,Is normalized output data;
Will be As an initial estimate of the subsequent CS reconstruction.
Preferably, in the step S4, the weight is updated to the coefficient matrix in each updateViewed as a compressed perceived reconstruction target, construct withThe calculation formula of the regular objective function with TV is as follows:
;
Wherein, the For the hybrid regularization objective function,As a matrix of features,For the updated coefficient vector KRLS,In order for the parameters to be regularized,Is thatThe norm of the sample is calculated,Is thatThe norm of the sample is calculated,In order to transform the matrix in a sparse manner,For the TV regularization parameters,For the total variation regularization term,Indicating a function for the constraint;
Defining vectors to be optimized To fit toThe calculation formula is as follows:
;
Wherein, the In order to be a matrix of dictionary features,In order to constrain the range of the device,In order to constrain the indication function,Is thatIs the first of (2)A component.
Preferably, in the step S5, a FISTA acceleration neighbor projection and dual decomposition frame is adopted, the interrupt tolerance is iteratively updated and set, and the iteration is performed according to the following formula:
;
;
Wherein, the For the iterative indexing of the values,As an auxiliary variable, a control signal is provided,Is the firstThe sparse representation of the vectors for the next iteration,Is the firstThe momentum term of the next iteration,For the near-end operator,In order to be a step size,A gradient that is an objective function;
Step size Momentum through spectral norm estimation, wherein,Setting a stopping criterion for the motion term,Redundant iterations are avoided for downtime tolerance.
Preferably, in the step S6, the result is reconstructedSoft threshold clipping is performed, and the calculation formula is as follows:
;
Wherein, the Is thatIs the first of (2)The number of components of the composition,A threshold value tailored for the soft threshold value,Is a dictionary atomic index;
deleting corresponding dictionary atoms and updating And (3) withAnd finally, replacing the reconstruction matrix back to the recursive formula to finish the real-time updating of dictionary sparsity and edge preservation.
Preferably, the method is applied to a near-field millimeter wave imaging system, the near-field millimeter wave imaging system comprises a control terminal, a mechanical arm, a millimeter wave probe antenna and a vector network analyzer, the mechanical arm is controlled by the control terminal, the mechanical arm controls the antenna to scan a target in a grid mode, and the vector network analyzer performs real-time image reconstruction after collecting echo signals.
Compared with the related art, the near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning has the following beneficial effects:
1. in the invention, the real-time and robust reconstruction of electromagnetic wave signals is realized by mixing and regularizing Compressed Sensing (CS) and seamlessly embedding a Kernel Recursion Least Square (KRLS) online updating process, the real-time response to new data is realized by dynamic dictionary management and recursion weight updating, and the method is introduced The method comprises the steps of carrying out mixed optimization on regularization and TV (total variation) regularization, forcing sparse representation in reconstruction and protecting image edges by combining a dynamic dictionary regularization strategy, suppressing noise interference by mixed regularization, combining a dynamic dictionary updating mechanism, recovering missing information by using sparse prior in undersampled scenes, accelerating neighbor projection and dual decomposition frames by FISTA, avoiding redundant iteration, removing redundant atoms by the dynamic dictionary, and reducing calculation complexity.
2. The invention solves the defects of the traditional CS method and KRLS variants by combining mixed regularization and online kernel learning, realizes real-time, high-precision and anti-interference reconstruction of the near-field electromagnetic wave image, integrates real-time online updating, sparse prior and edge reservation, and solves the defects of the traditional near-field electromagnetic wave image reconstruction technology.
Drawings
Fig. 1 is a schematic diagram of steps of a near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning;
Fig. 2 is a schematic diagram of a frame of a near field millimeter wave imaging system of the present invention;
FIG. 3 is a schematic flow chart of an algorithm in the present invention;
FIG. 4 is a schematic representation of a two-dimensional dataset used in the present invention.
Detailed Description
The invention is further described below with reference to the drawings and examples.
Example 1
Referring to fig. 1 in combination, a near-field electromagnetic wave image reconstruction method based on information retention type hybrid regularization sparse kernel learning includes the following method steps:
s1, data acquisition and preprocessing are carried out, normalization processing is carried out on near-field electromagnetic wave scanning data or chaos sequence observation values, and low-frequency drift is removed by adopting a moving average or polynomial trending technology;
s2, mapping input data to a feature space by utilizing Gaussian kernels or polynomial kernels, designing a dynamic dictionary updating strategy, adding a dictionary when the kernel similarity of a new sample and any atom in the existing dictionary is smaller than a preset threshold, and eliminating the most redundant atoms according to the contribution degree and a sparse reconstruction result if the dictionary size exceeds a preset maximum;
s3, performing online recursion weight updating, and performing recursion updating of a weight coefficient and a covariance matrix to obtain preliminary weight estimation after mapping each input data in a feature space based on a Kernel Recursion Least Square (KRLS) criterion;
S4, performing mixed regularized reconstruction optimization, taking the weight coefficient as a compressed sensing reconstruction target, and constructing a structure comprising Solving a vector to be optimized by fitting constraint conditions with a regular target function of the TV;
S5, adopting FISTA to accelerate neighbor projection and a dual decomposition frame to iteratively solve an optimization problem, estimating a step length and a momentum item through a spectrum norm, and setting a shutdown tolerance to avoid redundant iteration;
and S6, performing sparsification and dictionary maintenance, performing soft threshold clipping on the reconstruction result, deleting corresponding redundant dictionary atoms, updating covariance matrixes and weight coefficients, and realizing real-time updating of dictionary sparsity and edge information retention.
Further, in S1, electromagnetic wave near field scanning or chaotic sequence observation values are obtainedNormalization processing is carried out, and the calculation formula is as follows:
;
;
Wherein, the Is the firstThe raw input data of the sub-acquisition,Is the firstThe target of the sub-acquisition outputs data,As a mean value of the input data,For the mean value of the output data,In order to input the standard deviation of the data,For the input data to be normalized,For the output data after normalization,Index for samples or number of iterations;
and a sliding average or polynomial trending technology is adopted, low-frequency drift is removed, and the numerical stability of nuclear mapping is improved.
In the above, the normalization processing of the data can eliminate the influence of different dimension data, ensure the stability of the numerical value in the nuclear mapping process, avoid the calculation deviation caused by the data scale difference, eliminate the low-frequency drift by adopting the moving average or polynomial trend removal technology, effectively filter the interference caused by the environmental noise or the equipment drift, and provide purer input data for the subsequent feature extraction.
Further, in S2, a feature map is constructed using a gaussian kernel or a polynomial kernel, and the calculation formula is as follows:
;
;
Wherein, the As a function of the gaussian kernel,For a sample point in the input space,Is the first in the dictionaryThe number of atoms in the radical is one,For the atomic index of a dictionary,Is the firstThe individual samples are mapped to feature vectors after feature space,For the size of the dictionary to be a matter of scale,As a function of the gaussian kernel,Bandwidth parameters for kernel functions;
Design of dynamic dictionary addition/removal strategy when the new sample is similar to any atom in the existing dictionary In the time-course of which the first and second contact surfaces,To add new atom threshold, dictionary is added, if the size of dictionary exceeds that of dictionary,And if the maximum dictionary size is the maximum dictionary size, removing the most redundant atoms according to the contribution degree and the sparse reconstruction result.
In the method, the Gaussian kernel or the polynomial kernel is used for mapping the input data to the high-dimensional feature space, the nonlinear representation capability of the data can be enhanced, the complex distribution characteristic of near-field electromagnetic wave signals is adapted, the newly added atoms are controlled by the dynamic dictionary updating strategy through the kernel similarity threshold, redundant dictionary expansion is avoided, meanwhile, redundant atoms are removed based on contribution degree, the fact that the dictionary always keeps the most critical features for reconstruction is ensured, the calculation complexity is effectively reduced, and the sparse representation efficiency is improved.
Further, in S3, for the firstSecondary input data pairBy kernel functions in feature spaceAfter the mapping is performed, the image is processed,For the kernel similarity function, the preliminary weight update is obtained by using recursive least square, and the calculation formula is as follows:
;
Wherein, the Is the firstThe weight vector of the next iteration,Is the firstThe feature matrix of the next iteration,In order for the parameters to be regularized,Is a matrix of units which is a matrix of units,Is the firstA secondary target output value;
Updating covariance matrix based on kernel recursive least squares criterion Coefficient of andThe calculation formula is as follows:
;
;
Wherein, the Is the firstThe covariance matrix of the next iteration,Is the firstThe covariance matrix of the next iteration,Is the firstThe feature vector of the individual samples is used,Is the firstThe coefficient vector of the next iteration, as a preliminary weight estimate,Is the firstThe coefficient vector of the number of iterations,Is normalized output data;
Will be As an initial estimate of the subsequent CS reconstruction.
In the above, on-line weight updating is performed based on a Kernel Recursion Least Square (KRLS) criterion, dynamic changes of input data are adapted in real time, a retraining model is not needed, the requirement of near-field electromagnetic wave real-time reconstruction is met, a mechanism for recursively updating covariance matrix and coefficients can be quickly integrated into new samples while effective information of historic is maintained, more accurate initial estimation is provided for subsequent compressed sensing reconstruction, and reconstruction dynamic response capability is improved.
Example 2
Further, referring to fig. 1 to 2, in S4, in each update, the weight is updated to the coefficient matrixViewed as a compressed perceived reconstruction target, construct withThe calculation formula of the regular objective function with TV is as follows:
;
Wherein, the For the hybrid regularization objective function,As a matrix of features,For the updated coefficient vector KRLS,In order for the parameters to be regularized,Is thatThe norm of the sample is calculated,Is thatThe norm of the sample is calculated,In order to transform the matrix in a sparse manner,For the TV regularization parameters,For the total variation regularization term,Indicating a function for the constraint;
Defining vectors to be optimized To fit toThe calculation formula is as follows:
;
Wherein, the In order to be a matrix of dictionary features,In order to constrain the range of the device,In order to constrain the indication function,Is thatIs the first of (2)A component.
In the above, the structure comprisesAn objective function regularized with TV, whereinRegularization promotes weight coefficient sparsification, realizes sparse representation of signals, reduces redundant information interference, TV regularization (total variation regularization) protects image edge details by constraining gradient norms, avoids edge blurring in the reconstruction process, combines sparsity and structural fidelity in a compressed sensing frame, and improves reconstruction quality of electromagnetic wave images in complex scenes.
Further, in S5, using FISTA an accelerated neighbor projection and dual decomposition framework, iteratively updating and setting an interruption tolerance, and iterating according to the following formula:
;
;
Wherein, the For the iterative indexing of the values,As an auxiliary variable, a control signal is provided,Is the firstThe sparse representation of the vectors for the next iteration,Is the firstThe momentum term of the next iteration,For the near-end operator,In order to be a step size,A gradient that is an objective function;
Step size Momentum through spectral norm estimation, wherein,Setting a stopping criterion for the motion term,Redundant iterations are avoided for downtime tolerance.
In the above, the FISTA acceleration neighbor projection frame is adopted, the iteration step can be adaptively adjusted through the spectrum norm estimation step length, convergence oscillation or slowness caused by fixed step length is avoided, the convergence process can be accelerated by introducing the motion item through utilizing the historical iteration information, the setting of the shutdown tolerance can terminate the redundant iteration on the premise of ensuring the reconstruction precision, the calculation time consumption is greatly reduced, and the efficiency requirement of real-time reconstruction is met.
Further, in S6, the result is reconstructedSoft threshold clipping is performed, and the calculation formula is as follows:
;
Wherein, the Is thatIs the first of (2)The number of components of the composition,A threshold value tailored for the soft threshold value,Is a dictionary atomic index;
deleting corresponding dictionary atoms and updating And (3) withAnd finally, replacing the reconstruction matrix back to the recursive formula to finish the real-time updating of dictionary sparsity and edge preservation.
In the above, soft threshold clipping is performed on the reconstruction result, so that redundant dictionary atoms with low reconstruction contribution degree can be deleted, dynamic sparsification of the dictionary is realized, covariance matrix and weight coefficient are synchronously updated, key information such as edges can be reserved while sparsification is realized, feature loss caused by dictionary simplification is avoided, and detail integrity and real-time updating capability of the reconstructed image are ensured.
Further, the method is applied to a near-field millimeter wave imaging system, the near-field millimeter wave imaging system comprises a control terminal, a mechanical arm, a millimeter wave probe antenna and a vector network analyzer, the mechanical arm is controlled by the control terminal, the mechanical arm controls an antenna grid scanning target, and the vector network analyzer acquires echo signals and then carries out real-time image reconstruction.
In the above, when the method is applied to a near-field millimeter wave imaging system, the cooperation of the control terminal and the mechanical arm can realize the accurate scanning of the antenna grid, the electromagnetic wave signal acquisition of the coverage target area, the Vector Network Analyzer (VNA) acquires echo signals in real time and transmits the echo signals to the reconstruction algorithm, undersampled electromagnetic wave data can be quickly reconstructed into a high-resolution image, and the problems of low offline processing efficiency and blurred edges in the traditional imaging system are solved.
Example 3
Further, referring to fig. 1 to 4, on the basis of the second embodiment, the method is applied to a near-field millimeter wave imaging system, and the real-time reconstruction of the two-dimensional scan data is realized by mutually matching a control terminal, a mechanical arm, a millimeter wave probe antenna and a Vector Network Analyzer (VNA).
To further verify the effectiveness of the present invention, a one-dimensional data time series (M-G, lorenz) was independently performed, with the reconstruction result being an average of 20 times, wherein the M-G series was generated from a nonlinear time-lag differential equation, and the calculation formula was as follows:
;
Parameters (parameters) The lorentz sequence derives the lorentz system from a differential equation,
;
The parameters areThe experimental results are shown in table 1:
TABLE 1 one-dimensional data time series reconstruction Algorithm Performance (hybrid regularized ablation contrast)
The results in table 1 show that compressed perceived reconstruction enhances the model building ability of KRLS algorithm on experimental datasets, the mixed sparse function improves CKRLS algorithm more effectively than single sparse optimization, analysis of the training curve shows that the WT-induced reconstruction effect is more pronounced than the TV operator for sequence reconstruction, training duration data shows that internal reconstruction iterations increase the running cost, however, these costs remain within acceptable limits compared to the kernel operation of RLS algorithm in KRLS algorithm.
The invention further extends the algorithm to a plurality of near-field millimeter wave two-dimensional imaging data sets for performing a sequence reconstruction experiment, wherein the reconstruction result is 20 times of average value, the two-dimensional data from the scissor, tool and iron sheet data sets comprise direct reflection data, the real data are collected under the operation of 41GHz scanning frequency, and the reconstruction experiment result is shown in Table 2:
TABLE 2 two-dimensional image data sequence reconstruction Algorithm Performance (hybrid regularized ablation contrast)
The experimental results in table 2 show that the KAF operator effectively fits the two-dimensional image data, however, compared with the one-dimensional data, the more complex structure of the KAF operator introduces instability in the model construction process, as shown by fluctuation of the training curve, the compressed sensing reconstruction improves the structural efficiency of KRLS, the higher convergence precision is realized on the training curve, and the superiority of the mixed sparse function is remarkably reflected in the comparison of the training curve.
The present invention also compares the algorithm to several representative KRLS variants, including ALD-KRLS, RFFKRLS, ROB-KRLS and NysKRLS, which solve the sparseness, robustness, and computational efficiency problems in online kernel learning, the results of which are shown in Table 3:
TABLE 3 comparison of reconstruction results for different KRLS algorithm variants
The results in table 3 show that CSKRLS has a better reconstruction effect.
The invention also compares the algorithm with other compressed sensing regression algorithms, including basic tracking (BP), LASSO, dantzig Selector (DS), orthogonal matching tracking (OMP), kalman filtering compressed sensing (KF-CS) and dynamic approximate message passing (CS-AMP), and the results are shown in Table 4:
TABLE 4 comparison of reconstruction results for different compressed sensing regression algorithms
As can be seen from the results of Table 4, CSKRLS has a good reconstruction effect.
To further explore the effects of external noise, the present invention performed additional noise sequence reconstruction experiments on these dataset sequences, in which noise was randomly introduced, the average0, Standard deviation0.05, And then subjected to a sequence reconstruction test, the results of which are shown in table 5:
TABLE 5 comparison of reconstruction results for different algorithms in noisy environments
In Table 5, the results of the sequence reconstruction experiments indicate CSKRLS is the most accurate at medium noise, achieving the lowest average mean square error over the four data sets
In practice reconstruction of sample data is often hampered by undersampling problems, and in order to further investigate the effect of missing or contaminated data on the performance of algorithms, additional experiments were performed on these data sets with undersampled sequences, in which experiments an algorithm was performed according to the pre-sampling rateA mask is randomly generated, a part of training sequence is set to zero, and then a reconstruction experiment is carried out, and the result is shown in table 6:
TABLE 6 comparison of reconstruction results for different algorithms in an undersampled environment
In Table 6, the reconstruction experiment results show that CSKRLS is under-sampled seriously) The average mean square error is kept to be the lowest, and the average is 40% -60% better than that of all other methods.
FIG. 4 is a schematic diagram of a two-dimensional dataset used, shown as a scissors dataset (a), a tool dataset (b), an iron sheet dataset (c), and an iron sheet combination dataset (d), respectively.
When the method is applied to a near-field millimeter wave imaging system, the control terminal and the mechanical arm cooperate to realize accurate scanning of an antenna grid and electromagnetic wave signal acquisition of a coverage target area, a Vector Network Analyzer (VNA) acquires echo signals in real time and transmits the echo signals to a reconstruction algorithm, and under-sampled electromagnetic wave data can be quickly reconstructed into a high-resolution image by combining a dynamic dictionary and a mixed regularization strategy, so that the problems of low offline processing efficiency and blurred edges in the traditional imaging system are solved.
The foregoing is only illustrative of the present invention and is not to be construed as limiting the scope of the invention, and all equivalent structures or equivalent flow modifications which may be made by the teachings of the present invention and the accompanying drawings or which may be directly or indirectly employed in other related art are within the scope of the invention.
Claims (8)
1. The near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning is characterized by comprising the following steps of:
s1, data acquisition and preprocessing are carried out, normalization processing is carried out on near-field electromagnetic wave scanning data or chaos sequence observation values, and low-frequency drift is removed by adopting a moving average or polynomial trending technology;
s2, mapping input data to a feature space by utilizing Gaussian kernels or polynomial kernels, designing a dynamic dictionary updating strategy, adding a dictionary when the kernel similarity of a new sample and any atom in the existing dictionary is smaller than a preset threshold, and eliminating the most redundant atoms according to the contribution degree and a sparse reconstruction result if the dictionary size exceeds a preset maximum;
s3, carrying out online recursion weight updating, and carrying out recursion updating of a weight coefficient and a covariance matrix after mapping of each input data in a feature space based on a kernel recursion least square criterion to obtain a preliminary weight estimation;
S4, performing mixed regularized reconstruction optimization, taking the weight coefficient as a compressed sensing reconstruction target, and constructing a structure comprising Solving a vector to be optimized by fitting constraint conditions with a regular target function of the TV;
S5, adopting FISTA to accelerate neighbor projection and a dual decomposition frame to iteratively solve an optimization problem, estimating a step length and a momentum item through a spectrum norm, and setting a shutdown tolerance to avoid redundant iteration;
and S6, performing sparsification and dictionary maintenance, performing soft threshold clipping on the reconstruction result, deleting corresponding redundant dictionary atoms, updating covariance matrixes and weight coefficients, and realizing real-time updating of dictionary sparsity and edge information retention.
2. The near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning of claim 1, wherein in S1, electromagnetic wave near-field scanning or chaotic sequence observation values are obtainedNormalization processing is carried out, and the calculation formula is as follows:
;
;
Wherein, the Is the firstThe raw input data of the sub-acquisition,Is the firstThe target of the sub-acquisition outputs data,As a mean value of the input data,For the mean value of the output data,In order to input the standard deviation of the data,For the input data to be normalized,For the output data after normalization,Index for samples or number of iterations;
and a sliding average or polynomial trending technology is adopted, low-frequency drift is removed, and the numerical stability of nuclear mapping is improved.
3. The near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning of claim 1, wherein in S2, a gaussian kernel or polynomial kernel construction feature map is used, and a calculation formula is as follows:
;
;
Wherein, the As a function of the gaussian kernel,For a sample point in the input space,Is the first in the dictionaryThe number of atoms in the radical is one,For the atomic index of a dictionary,Is the firstThe individual samples are mapped to feature vectors after feature space,For the size of the dictionary to be a matter of scale,As a function of the gaussian kernel,Bandwidth parameters for kernel functions;
Design of dynamic dictionary addition/removal strategy when the new sample is similar to any atom in the existing dictionary In the time-course of which the first and second contact surfaces,To add new atom threshold, dictionary is added, if the size of dictionary exceeds that of dictionary,And if the maximum dictionary size is the maximum dictionary size, removing the most redundant atoms according to the contribution degree and the sparse reconstruction result.
4. The near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning of claim 1, wherein in S3, for the firstSecondary input data pairBy kernel functions in feature spaceAfter the mapping is performed, the image is processed,For the kernel similarity function, the preliminary weight update is obtained by using recursive least square, and the calculation formula is as follows:
;
Wherein, the Is the firstThe weight vector of the next iteration,Is the firstThe feature matrix of the next iteration,In order for the parameters to be regularized,Is a matrix of units which is a matrix of units,Is the firstA secondary target output value;
Updating covariance matrix based on kernel recursive least squares criterion Coefficient of andThe calculation formula is as follows:
;
;
Wherein, the Is the firstThe covariance matrix of the next iteration,Is the firstThe covariance matrix of the next iteration,Is the firstThe feature vector of the individual samples is used,Is the firstThe coefficient vector of the next iteration, as a preliminary weight estimate,Is the firstThe coefficient vector of the number of iterations,Is normalized output data;
Will be As an initial estimate of the subsequent CS reconstruction.
5. The near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning of claim 1, wherein in S4, in each update, a weight update coefficient matrix is usedViewed as a compressed perceived reconstruction target, construct withThe calculation formula of the regular objective function with TV is as follows:
;
Wherein, the For the hybrid regularization objective function,As a matrix of features,For the updated coefficient vector KRLS,In order for the parameters to be regularized,Is thatThe norm of the sample is calculated,Is thatThe norm of the sample is calculated,In order to transform the matrix in a sparse manner,For the TV regularization parameters,For the total variation regularization term,Indicating a function for the constraint;
Defining vectors to be optimized To fit toThe calculation formula is as follows:
;
Wherein, the In order to be a matrix of dictionary features,In order to constrain the range of the device,In order to constrain the indication function,Is thatIs the first of (2)A component.
6. The near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning of claim 1, wherein in S5, a FISTA acceleration neighbor projection and dual decomposition frame is adopted, the interrupt tolerance is iteratively updated and set, and the iteration is performed according to the following formula:
;
;
Wherein, the For the iterative indexing of the values,As an auxiliary variable, a control signal is provided,Is the firstThe sparse representation of the vectors for the next iteration,Is the firstThe momentum term of the next iteration,For the near-end operator,In order to be a step size,A gradient that is an objective function;
Step size Momentum through spectral norm estimation, wherein,Setting a stopping criterion for the motion term,Redundant iterations are avoided for downtime tolerance.
7. The near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning of claim 1, wherein in S6, the reconstruction result isSoft threshold clipping is performed, and the calculation formula is as follows:
;
Wherein, the Is thatIs the first of (2)The number of components of the composition,A threshold value tailored for the soft threshold value,Is a dictionary atomic index;
deleting corresponding dictionary atoms and updating And (3) withAnd finally, replacing the reconstruction matrix back to the recursive formula to finish the real-time updating of dictionary sparsity and edge preservation.
8. The near-field electromagnetic wave image reconstruction method based on information retention type mixed regularization sparse kernel learning of any one of claims 1-7, wherein the method is applied to a near-field millimeter wave imaging system, the near-field millimeter wave imaging system comprises a control terminal, a mechanical arm, a millimeter wave probe antenna and a vector network analyzer, the mechanical arm is controlled by the control terminal, the mechanical arm controls an antenna grid scanning target, and the vector network analyzer acquires echo signals and then performs real-time image reconstruction.
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