A near-field millimeter-wave super-resolution imaging method based on kernel adaptive filtering

Abstract

This invention discloses a near-field millimeter-wave super-resolution imaging method based on kernel adaptive filtering, belonging to the field of super-resolution imaging. This method, based on a kernel adaptive filtering operator, uses a lightweight learning method to ensure maximum accuracy in predicting and reconstructing high-resolution images by accurately matching the estimated features of the original data. This invention addresses the subsequent image processing of two-dimensional near-field millimeter-wave imaging systems, reconstructing high-resolution images from low-resolution sampled data while shortening data sampling time, without requiring additional hardware, large image datasets, or dictionary learning processes. The proposed method exhibits optimal visual effects across datasets with varying shape features, providing the clearest detail in magnified views. It outperforms typical super-resolution algorithms. The proposed method demonstrates the highest numerical similarity and high structural similarity compared to typical super-resolution algorithms.

Description

Technical Field

[0001] This invention relates to the field of super-resolution imaging, and in particular to a near-field millimeter-wave super-resolution imaging method based on kernel adaptive filtering. Background Technology

[0002] With the development of materials technology, composite materials have begun to be widely used. However, due to factors such as processing and environment, composite materials often have defects and damage, which threaten structural safety and performance. To discover and eliminate these hidden dangers, non-destructive testing (NDT) is needed. NDT is a non-contact, non-destructive testing method to ensure the integrity and reliability of the object being tested. This not only reduces economic losses caused by defects in the object itself, but can also be used to improve industrial production technology. Therefore, NDT is an indispensable tool in industrial development.

[0003] However, existing mainstream detection methods, such as ultrasound and eddy current, have limited penetration capabilities into composite materials. Near-field millimeter waves, due to their strong penetration effect, have become an important detection method. Combined with algorithms, they can provide more detailed detection images and have important applications in fields such as medical imaging, contraband detection, through-wall imaging, aerospace imaging, and non-destructive testing.

[0004] For a two-dimensional near-field millimeter-wave imaging system, the working process consists of two stages: the first stage is data acquisition, which involves using an antenna probe to perform a grating scan on the object under test to obtain its backscattering data. The second stage is image processing, which uses the measured backscattering data to synthesize and reconstruct a 2D image, and then performs image processing and subsequent analysis based on this. However, due to limitations in equipment size and sampling time, it is impossible to achieve a large-scale, high-precision scanning process for objects with large scanning areas. Combined with the analysis of imaging principles, this limits the resolution of the target image and further affects subsequent scientific measurements and analysis. Improving the hardware would significantly increase both monetary and time costs. Therefore, accelerating the imaging speed and improving the resolution through algorithms in the subsequent data processing is a very cost-effective solution, making super-resolution image processing technology a good choice. Typical super-resolution algorithms include bicubic interpolation based on nonlinear fitting, soft decision interpolation based on decision filtering (SAI), new edge interpolation based on edge information (NEDI), multi-scale directional filtering and data fusion algorithm (DFDF), and sparse estimation algorithm based on image sparsity (SME).

[0005] On the other hand, emerging learning methods are not only time-consuming to train, but their performance is also highly dependent on appropriate training datasets. For example, sparse coding super-resolution algorithms and anchored neighborhood regression (ANR) require setting and training dictionary pairs and training evaluation models. Deep learning methods such as single-image autoencoder super-resolution (ZSSR) and single-image convolutional neural networks (SICNN) also require building so-called "internal datasets" and training with complex networks of a certain scale. These all require a large amount of data support and are not suitable for near-field millimeter-wave imaging systems with long sampling times.

[0006] Image reconstruction algorithms based on kernel regression (KR) were among the first to use kernel methods to improve the imaging quality of digital images. Essentially, they utilize regression functions to recover high-frequency information lost due to imaging system limitations and degradation processes; that is, they use implicit models of estimated parameters to generate point estimates of the underlying signals. From an image perspective, this method leverages sample location, density, and radiometric characteristics to allow the size and shape of the regression kernel to be locally adjusted according to image features, improving adaptability to features such as edges. However, a drawback is that classic kernel regression methods have inherent limitations in local linear data processing; essentially, it's a local weighted average of the data (linear filtering), where the order determines the type and complexity of the weighting scheme. Further extensions are needed to achieve more effective processing of nonlinear data.

[0007] Meanwhile, for previous near-field millimeter-wave imaging systems operating on a single frequency, their imaging quality is often affected by factors such as noise, reconstruction artifacts, and system hardware limitations, making it difficult to guarantee image reconstruction quality.

[0008] In summary, given the technological limitations mentioned above, further improvements are needed for near-field millimeter-wave super-resolution imaging methods. Summary of the Invention

[0009] The technical problem this invention aims to solve: Inspired by the aforementioned research background, this invention proposes a multi-frequency near-field millimeter-wave super-resolution imaging method. This method is based on a kernel adaptive filtering operator and uses a lightweight learning method to ensure that the estimated features of the original data are matched to the greatest extent possible, thus efficiently predicting and reconstructing high-resolution images. This invention addresses the subsequent image processing of two-dimensional near-field millimeter-wave imaging systems, reconstructing high-resolution images from low-resolution sampled data while shortening data sampling time, without requiring additional hardware, large image datasets, or dictionary learning processes.

[0010] The technical solution of this invention is: a near-field millimeter-wave super-resolution imaging method based on kernel adaptive filtering, the method comprising:

[0011] Step 1: The system scans the object under test in a two-dimensional plane using a millimeter-wave antenna probe along a fixed trajectory to obtain the backscattering data of the object under test. ,in Represents two-dimensional plane coordinates. This refers to the operating frequency of the antenna probe. It is a complex number, containing both a real part of the magnitude and an imaginary part of the phase.

[0012] Step 2: After completing data sampling, use the backscatter data obtained in Step 1. Constructing a training dataset for kernel adaptive filtering operators and prediction dataset , Represents the input sequence. Indicates the corresponding output value;

[0013] Step 3: Obtain the training dataset Then, for the determined kernel adaptive filtering operator Training is performed by using kernel methods to enable the operator to learn the mapping function. And use the test set throughout the training process. Performance evaluation; among which For the real number field, The length of the input sequence;

[0014] Step 4: Obtain the trained kernel adaptive filtering operator Then, a super-resolution algorithm was used to process the backscattered data. Preprocessing and iterative optimization are performed to obtain the desired super-resolution backscattering data. ;

[0015] Step 5: Process the super-resolution backscatter data obtained in Step 4 Perform inversion imaging; recover target reflection data from backscatter data through phase compensation. Then, the data amplitude is calculated to obtain the target reflection image. The inversion calculation relationship is as follows:

[0016] ;

[0017] in, Indicates the perpendicular distance between the antenna and the plane being measured; FFT 2D and IFFT 2D Represents the two-dimensional Fast Fourier Transform and its inverse transform; For millimeter waves, For wavenumber in and directional component; The speed of light;

[0018] Step 6: For different antenna operating frequencies Repeat steps 1 to 5 to obtain the final super-resolution image by weighted averaging of the desired target images at different frequencies. .

[0019] Furthermore, step 2 is specifically implemented as follows: first, based on the threshold... Backscattering data Cumulative distribution function Perform effective target point screening, and screen those that meet the criteria target point To set a threshold, the obtained target point pixels are used as kernel adaptive filtering operators. The output prediction and input sequence are used to form target point training pairs, which are then proportionally divided to obtain training and prediction datasets.

[0020] Furthermore, the kernel adaptive filtering operator in step 3 The training process is specifically implemented as follows: taking the kernel least mean square operator as an example, through the mapping operator... Input sequences from the training set Nonlinear mapping to kernel regenerative Hilbert space abbreviated as The updated data Substitute the values ​​into the least mean square algorithm for training.

[0021] Furthermore, the super-resolution algorithm in step 4 employs both direct prediction and interpolation prediction methods, and the final result is a weighted average of the two methods.

[0022] Furthermore, the training method in step 3 is specifically as follows:

[0023] Training using gradient descent:

[0024] ;

[0025] in This represents the estimate of the weight vector during iteration. Indicates the first Error value in the next iteration Indicates the first The corresponding output of the input training sequence in each iteration. The compensation coefficient is represented by the iterative weight update equation:

[0026] ;

[0027] After After the training step, the weight estimate is updated to a linear combination of all past and current input data, and adjusted by the prediction error and compensation coefficient. Scaling will be applied; the system will then process the new input. response Calculate the inner product of the input signals:

[0028] ;

[0029] Using nuclear techniques The efficient computational output obtained is:

[0030] ;

[0031] Thus far, the kernel adaptive filtering operator Complete training and predict the dataset during the training process. Used as new input for prediction calculation, compared Conduct a performance evaluation.

[0032] Furthermore, the direct prediction method is as follows:

[0033] First, the data matrix Upsampled to desired magnification The magnified matrix is ​​obtained. The coordinates of each point are as follows: Then, the coordinates of that point are scaled down to match the original matrix. The dimension is approximated to the nearest edge point. The other three edge points were determined to have corresponding values ​​in the original matrix using the same method; the center points of the remaining four edges were calculated by applying a proportional weighting from the edge points using distance factors; this yielded the input sequence. The target dataset is formed after traversing all points. Input it into the kernel adaptive filter operator In the process, the target output value that conforms to the training data structure is obtained, and then the super-resolution backscatter data is reconstructed based on the target point position. .

[0034] Furthermore, the interpolation prediction method is as follows:

[0035] First, zero-interpolation sampling is used on the backscattered data matrix. Upscaling, transforming images from low resolution Expand to high resolution Then, filtering operators are used for image preprocessing to obtain the initial target image. Based on this, the dataset construction method from step 2 is used to traverse the initial target images. All points, combined with the values ​​of their neighboring pixels, constitute the target dataset. Input it into the kernel adaptive filter operator In the process, the target output value that conforms to the training data structure is obtained, and then the super-resolution backscatter data is reconstructed based on the target point position. ;

[0036] The final super-resolution data is obtained by adaptively adjusting the local contrast of the image:

[0037] ;

[0038] Finally, phase compensation was used to extract the backscattered data. Recovery of target reflection data Then, the target reflection image is obtained using the data amplitude. Then, the desired target images at different frequencies are averaged and weighted to obtain the final super-resolution image. .

[0039] The method proposed in this invention achieves optimal visual effects across datasets with varying shape features, providing the clearest detail in magnified views. It outperforms typical super-resolution algorithms. Furthermore, the method presented in this invention exhibits the highest numerical similarity and high structural similarity compared to typical super-resolution algorithms. Attached Figure Description

[0040] Figure 1 This is a flowchart of a multi-frequency near-field millimeter-wave super-resolution imaging method.

[0041] Figure 2 This is a schematic diagram of a super-resolution algorithm based on kernel adaptive filtering.

[0042] Figure 3 The image shows a comparison of detection results between the present invention and a new edge interpolation method based on edge information. The left side represents the present invention, and the right side represents the new edge interpolation method based on edge information. Detailed Implementation

[0043] This scheme, based on a two-dimensional near-field millimeter-wave imaging system, consists of four stages: data acquisition, data processing, model training, and algorithm prediction. The flowchart of the multi-frequency near-field millimeter-wave super-resolution imaging method proposed in this invention is as follows: Figure 1 As shown.

[0044] During the data acquisition phase, the system uses a millimeter-wave antenna probe to scan the object under test in a two-dimensional plane along a fixed trajectory to obtain the backscattering data of the object. .

[0045] Data processing stage: backscattering data Constructing kernel adaptive filtering operators training dataset and prediction dataset The kernel adaptive filtering process is as follows: Figure 2 As shown; the kernel adaptive filtering operator Defined as a nonlinear mapping function based on kernel-reproducible Hilbert space, its core is the Gaussian kernel function.

[0046] ;

[0047] in This refers to the kernel width parameter. The specific implementation for training set construction is as follows:

[0048] First, based on the threshold Backscattering data Cumulative distribution function Targeting effective points The screening process requires that the following conditions be met:

[0049] ;

[0050] The obtained target point pixels are used as kernel adaptive filtering operators. Output prediction Then, the neighboring pixels of the target point are selected as the input sequence of the kernel adaptive filtering operator. This constitutes the target point training pair After traversing the valid points, then according to the ratio By dividing the dataset, we obtain the training dataset. and prediction dataset .

[0051] Model training: Obtaining the training dataset Then, for the determined kernel adaptive filtering operator Training is performed by using kernel methods to enable the operator to learn the mapping function. And use the test set throughout the training process. Performance evaluation. (Among them) For the real number field, The length of the input sequence. The specific implementation is as follows:

[0052] Taking the kernel least mean square operator as an example, through the mapping operator Input sequences from the training set Nonlinear mapping to kernel regenerative Hilbert space abbreviated as The updated data Substituting into the least mean square algorithm, we use gradient descent for training:

[0053] ;

[0054] in This represents the estimate of the weight vector during iteration. Applying the weight update equation iteratively yields:

[0055] ;

[0056] After After the training step, the weight estimate is updated to a linear combination of all past and current input data, and adjusted by the prediction error and compensation coefficient. Scaling is applied. The system scales new input. response The inner product of the input signals is calculated as follows:

[0057] ;

[0058] Using nuclear techniques The efficient computational output obtained is:

[0059] ;

[0060] Thus far, the kernel adaptive filtering operator Complete training and predict the dataset during the training process. Used as new input for prediction calculation, compared Conduct a performance evaluation.

[0061] Algorithm prediction phase: Obtain the trained kernel adaptive filtering operator. Then, a super-resolution algorithm was used to process the backscattered data. Preprocessing and iterative optimization are performed to obtain the desired super-resolution backscattering data. Specifically, the super-resolution algorithm is divided into direct prediction and interpolation prediction methods:

[0062] In the direct prediction method, the data matrix is ​​first... Upsampled to desired magnification The magnified matrix is ​​obtained. The coordinates of each point are as follows: Then, the coordinates of that point are scaled down to match the original matrix. The dimension is approximated to the nearest edge point. For simplicity, details have been omitted. Parameters. The other three edge points are determined using the same method (they have corresponding values ​​in the original matrix). The center points of the remaining four edges are calculated by applying a proportional weighting from the edge points using distance factors. This yields the input sequence. The target dataset is formed after traversing all points. Input it into the kernel adaptive filter operator In the process, the target output value that conforms to the training data structure is obtained, and then the super-resolution backscatter data is reconstructed based on the target point position. .

[0063] In the interpolation prediction method, zero-interpolation sampling is first used on the backscattered data matrix. Upscaling, transforming images from low resolution Expand to high resolution Then, filtering operators are used for image preprocessing to obtain the initial target image. Based on this, the dataset construction method from step 2 is used to traverse the initial target images. All points, combined with the values ​​of their neighboring pixels, constitute the target dataset. Input it into the kernel adaptive filter operator In the process, the target output value that conforms to the training data structure is obtained, and then the super-resolution backscatter data is reconstructed based on the target point position. .

[0064] The final super-resolution data is obtained by adaptively adjusting the local contrast of the image.

[0065] ;

[0066] Finally, phase compensation was used to extract the backscattered data. Recovery of target reflection data Then, the target reflection image is obtained using the data amplitude. Then, the desired target images at different frequencies are averaged and weighted to obtain the final super-resolution image. .

[0067] This invention verifies the effectiveness of the aforementioned multi-frequency near-field millimeter-wave super-resolution imaging method based on kernel adaptive filtering through experiments on multiple real-world datasets. The real-world datasets include scanned data of scissors and tools with metal parts, and sheet metal with letter markings. To demonstrate the penetrability of near-field millimeter waves, the objects were scanned while covered by a paper material plate.

[0068] In the experiment, four representative kernel adaptive filtering algorithms (KLMS, KRLS, KRMC, and NstRKMPL) were selected for operator improvement. They were compared with some existing typical super-resolution algorithms (Bicubic, NEDI, SME, and KR) in terms of image quality parameters peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) to reflect the numerical and structural similarity between the generated high-resolution image and the target image, so as to evaluate the algorithm performance.

[0069] The imaging comparison results of the super-resolution imaging method proposed in this invention with other super-resolution algorithms are as follows: Figure 3 As shown in the figure. The results indicate that the method proposed in this invention achieves the best visual effect in datasets with different shape features, and the details in the magnified view are the clearest. It performs better than typical super-resolution algorithms.

[0070] The peak signal-to-noise ratio and structural similarity index of the proposed method and the comparison algorithm are shown in Tables 1 and 2. The results show that the proposed method achieves the highest numerical similarity and higher structural similarity compared to typical super-resolution algorithms.

[0071] In summary, compared with typical super-resolution algorithms, the multi-frequency near-field millimeter-wave super-resolution imaging method based on kernel adaptive filtering, as invented, generates images with higher objective quality evaluation value and significant improvement in visual quality.

[0072] Table 1 Peak Signal-to-Noise Ratio of Each Algorithm on Different Datasets

[0073]

[0074] Table 2. Structural similarity index of algorithms on different datasets.

[0075]

Claims

1. A method for near-field millimeter-wave super-resolution imaging based on kernel adaptive filtering, characterized in that, The method comprises the steps of: Step 1: The system scans the object under test in a two-dimensional plane with a fixed trajectory by a millimeter wave antenna probe to obtain backscattering data of the object under test wherein represents a two-dimensional plane coordinate, is the working frequency of the antenna probe; is a complex data containing a real part amplitude and an imaginary part phase. Step 2: After the data sampling is completed, use the backscatter data obtained in Step 1 Training data set for constructing the kernel adaptive filter operator and prediction data set , denotes the input sequence, denotes the corresponding output value; Step 3: Obtain training dataset Afterwards, the kernel adaptive filter operator is determined trained, i.e. the operator learns the mapping function using kernel methods and the test set is used throughout the training process to evaluate the performance; wherein is the real number field, is the input sequence length; Step 4: Obtain trained kernel adaptive filter operator Afterwards, the backscatter data is processed using a super-resolution algorithm Pre-processing and iterative optimization are performed to obtain the desired super- resolved backscatter data ; Step 5: Super-resolution backscattered data obtained in step 4 is processed to perform inversion imaging; target reflection data is recovered from the backscattered data by phase compensation , and then the data amplitude is calculated to obtain the target reflection image , and the inversion calculation relationship is as follows: ； wherein represents the distance of the antenna from the plane under test; FFT 2D and IFFT 2D denotes the two-dimensional fast Fourier transform and its inverse; is the wave number of the millimeter wave, is the wave number in the and component in the direction; is the speed of light; Step 6: Repeat steps 1 to 5 for different antenna operating frequencies , and weight average the desired target images at different frequencies to obtain the final super-resolution imaging .

2. The kernel adaptive filter based near-field millimeter wave super-resolution imaging method of claim 1, wherein, The specific implementation of step 2 is as follows: First, based on the threshold... Backscattering data Cumulative distribution function Perform effective target point screening, and screen those that meet the criteria target point To set a threshold, the obtained target point pixels are used as kernel adaptive filtering operators. The output prediction and input sequence are used to form target point training pairs, which are then proportionally divided to obtain training and prediction datasets.

3. The kernel adaptive filter based near-field millimeter-wave super-resolution imaging method of claim 1, wherein, The step 3 kernel adaptive filter operator The training process is implemented by using kernel least mean square algorithm through mapping operator The input sequence in the training set Nonlinearly mapped into kernel reproducing hilbert space , abbreviated as The updated data Is substituted into the least mean square algorithm for training.

4. The kernel adaptive filter based near-field millimeter wave super-resolution imaging method of claim 1, wherein, The super-resolution algorithm in the step 4 simultaneously adopts a direct prediction method and an interpolation prediction method, and the final result uses a weighted average value of the two methods.

5. The kernel adaptive filter based near-field millimeter-wave super-resolution imaging method of claim 1, wherein, The training method in the step 3 is specifically: The gradient descent method is used for training: ； wherein denotes the estimate of the weight vector at iteration denotes the error value in the th iteration, denotes the corresponding output of the input training sequence in the th iteration, denotes the compensation factor, the weight update equation is applied iteratively as ； After After the training step, the weight estimate is updated to a linear combination of all past and current input data, and adjusted by the prediction error and compensation coefficient. Scaling will be applied; the system will then process the new input. response Calculate the inner product of the input signals: ； Using the kernel trick The high efficiency computation output is achieved: ； To this end, a kernel adaptive filter operator The training is completed, in the training process the prediction dataset The prediction computation is performed as a new input, comparison Performance evaluation is performed.

6. The kernel adaptive filter based near-field millimeter-wave super-resolution imaging method of claim 4, wherein, The direct prediction method is: Firstly, the data matrix is up-sampled to the desired magnification , resulting in an enlarged matrix , where each point coordinate corresponds to , then the point coordinate is scaled down to match the dimension of the original matrix and approximated to the nearest edge point ; the other three edge points are determined in the same way, and have corresponding values in the original matrix; the remaining four edge center points are calculated by applying a scaling weight from the edge points through a distance factor; thus, the input sequence is obtained, and after traversing all points, the target data set is formed, which is input into the kernel adaptive filter operator to obtain the target output value that conforms to the training data structure, and then the super-resolution backscatter data is reconstructed according to the target point position .

7. The kernel adaptive filter based near-field millimeter-wave super-resolution imaging method of claim 4, wherein, The interpolation prediction method is: First, the zero interpolation sampling is used to the backscattering data matrix to increase the dimension, the image is expanded from low resolution to high resolution , then the image is preprocessed using the filter operator to obtain the initial target image ; on this basis, all points of the initial target image are traversed, and the adjacent pixel values of each point are combined to form a target data set , which is input into the kernel adaptive filter operator to obtain the target output value conforming to the training data structure, and then the super-resolution backscattering data is reconstructed according to the target point position ; The final super-resolution data is adaptively adjusted according to local contrast of an image. ； Finally, the target reflection data is recovered from the backscattered data by phase compensation , and then the target reflection image is obtained using the data amplitude The final super-resolution image is obtained by averaging the desired target images at different frequencies .​

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