Multi-frequency near-field millimeter wave super-resolution imaging method based on compressed sensing model

Abstract

The invention discloses a multi-frequency near-field millimeter wave super-resolution imaging method based on a compressed sensing model, and relates to the field of super-resolution imaging. Aiming at the problems in the prior art, the invention provides a multi-frequency near-field millimeter wave super-resolution imaging method, the method is based on a compressed sensing model, the selection of multi-frequency near-field millimeter waves is used for improving the stability of imaging quality, and the compressed sensing model is used for constructing a mixed sparse function. And a wavelet transform domain norm and a TV (Total variation) operator are taken as optimization targets, so that the reconstruction of the high-resolution image is realized. Aiming at a subsequent image processing process of a two-dimensional near-field millimeter wave imaging system, under the condition of shortening data sampling time, a high-resolution image is reconstructed from low-resolution sampling data, and redundant hardware, a large number of image data sets and a dictionary learning process are not needed.

Description

Technical Field

[0001] The present invention relates to the field of super-resolution imaging and is used for performance upgrading of near-field millimeter wave imaging systems. Background Art

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

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

[0004] For the two-dimensional near-field millimeter wave imaging system, its working process is divided into two stages: the first stage is data acquisition, that is, using the antenna probe to perform raster scanning on the object to be measured to obtain the backscattering data of the object to be measured. The second stage is image processing, which uses the measured backscattering data to perform 2D image synthesis and reconstruction, and then performs image processing and subsequent analysis on this basis. However, due to the limitations of equipment size and sampling time, it is impossible to achieve a large-scale and high-precision scanning process for objects with a large scanning area. Combined with the analysis of imaging principles, this limits the resolution of the target image and further affects subsequent scientific measurements and analysis. For this problem, improvements in hardware will significantly increase monetary and time costs. Therefore, it is a very cost-effective solution to speed up the imaging speed and improve the resolution through algorithms in the subsequent data processing after sampling, so super-resolution image processing technology is a good choice. Typical super-resolution algorithms include bicubic interpolation based on nonlinear fitting, soft decision interpolation based on decision screening, new edge interpolation based on edge information, directional filtering and data fusion algorithm based on multi-scale (DFDF), and kernel method based on kernel regression theory (KR). Among them, the sparse estimation algorithm (SME) was the first to introduce image sparsity into super-resolution research. It can supplement the structural information that may be missing in high-resolution images, but its essence is to calculate the interpolation problem by adaptively mixing linear estimators with different priors. The sparse function is used to calculate the image block weight, and the overall correlation between the target imaging and the original data in terms of sparsity is not considered. These algorithms have achieved good performance in natural image processing, but have not achieved ideal results in the field of near-field millimeter wave imaging.

[0005] On the other hand, the emerging learning methods are not only time-consuming to train, but their performance is also highly dependent on appropriate training data sets. For example, sparse coding super-resolution algorithms and anchored domain regression methods (ANR) require setting and training dictionary pairs and training evaluation models, which require a large amount of data support and are not suitable for near-field millimeter-wave imaging systems with long sampling times. At the same time, for near-field millimeter-wave imaging systems that used to work at a single frequency, their imaging quality is often affected by multiple factors such as noise, reconstruction artifacts, and system hardware limitations, making it difficult to guarantee image reconstruction quality. In general, under the above technical constraints, the near-field millimeter-wave super-resolution imaging method still needs to be improved. Summary of the invention

[0006] In view of the problems of the prior art, the present invention proposes a multi-frequency near-field millimeter wave super-resolution imaging method, which is based on a compressed sensing model, wherein the selection of multi-frequency near-field millimeter waves is used to improve the stability of imaging quality, and the compressed sensing model is used to construct a mixed sparse function, with the wavelet transform domain norm and TV (Total variation) operator as optimization targets to achieve high-resolution image reconstruction. The invention aims at the subsequent image processing process of a two-dimensional near-field millimeter wave imaging system, and reconstructs a high-resolution image from low-resolution sampled data under the condition of shortening the data sampling time, without the need for redundant hardware, a large number of image data sets, and a dictionary learning process.

[0007] The technical solution of the present invention is: a multi-frequency near-field millimeter wave super-resolution imaging method based on a compressed sensing model, the method comprising:

[0008] Step 1: The system uses the millimeter wave antenna probe to scan the object under test in a two-dimensional plane with a fixed trajectory to obtain the backscattered data s (x, y, f a ), where (x, y) represents the two-dimensional plane coordinates, f a is the working frequency of the antenna probe; s(x,y,f a ) is a complex data, including the real amplitude and the imaginary phase part;

[0009] Step 2: After data sampling is completed, use the backscattered data s(x, y, f) obtained in step 1 a ) for basic imaging, and recover the target reflection data g(x,y,z) from the backscattered data through phase compensation h ), and then calculate the data amplitude to obtain the target reflection image g. The data recovery calculation relationship is as follows:

[0010]

[0011] where z h Indicates the vertical distance between the antenna and the measured plane, FFT 2D and IFFT 2D represents the two-dimensional fast Fourier transform and its inverse transform, is the wave number of millimeter wave, k x ,k y is the component of wave number in x and y direction; c is the speed of light;

[0012] Step 3: After obtaining the target reflection image, use the super-resolution algorithm to preprocess and iteratively optimize the target reflection image g to obtain the desired target image g; for the convenience of explanation, s is used in the subsequent text to represent backscattering data;

[0013] Step 4: For different antenna operating frequencies f a, repeat steps 1 to 3, weighted average the desired target images at different frequencies to obtain the final super-resolution imaging;

[0014] Furthermore, the super-resolution algorithm in step 3 first uses zero interpolation sampling to increase the dimension of the target reflection image g, expands the image from low resolution N×N to high resolution M×M, and then uses a filtering operator to preprocess the image to obtain the initial target image; on this basis, the generation of the high-resolution image is regarded as a compressed sensing reconstruction problem of the original image, and the corresponding model is:

[0015]

[0016] C=[g min ,g max ] represents the constraint range of the amplitude of each point in the reconstructed image, g min ,g max Corresponding to the minimum and maximum values; the function p(.) is used to characterize the sparse function of the image; the st condition represents minimizing the difference between the high-resolution image and , the operator Φ represents the dimensionality reduction operation on the high-resolution image g, and ε represents the control accuracy threshold, represents the L2 norm square operation; and the model is an underdetermined system, so the mixed sparse function is designed as the optimization problem constraint, so the objective function of the super-resolution imaging model is recorded as:

[0017]

[0018] where ζ c (g) is the indicative function, defined as:

[0019]

[0020] Therefore, the process of reconstructing the image is to find the optimal solution that satisfies the compressed sensing problem, and finally obtain the desired target image g;

[0021]

[0022] Furthermore, the wavelet transform domain is used to 1 The norm and TV operator construct the corresponding mixed sparse function p(.).

[0023] Furthermore, the non-local means algorithm is used as the filtering operator in step 3.

[0024] Furthermore, an arithmetic average method is used as the weighted average method in step 4.

[0025] Furthermore, in step 3 The calculation method is:

[0026] Step 3.1: Determine the iteration condition, when the number of iterations When , calculate, Indicates the maximum number of iterations;

[0027] Step 3.2: Calculate the error b between the target image and the backscattered data s (i) :

[0028]

[0029] Among them, τ ≥ 1 is the step size factor, which controls the convergence speed and accuracy of the algorithm, g (i) represents the target image solution sequence in iteration;

[0030] Step 3.3: Calculate the sparse function of the target image separately: TV operator and wavelet operator Where Grad represents the gradient calculation function, and W represents the wavelet transform;

[0031] Step 3.4: Solve for variables using nearest neighbors To compute the dual solution variable:

[0032]

[0033] To update the target image in, represents the neighbor solution variable in the iterative process, τ represents the regularization parameter used to balance the loss, and λ 1 ,λ 2 ,ρ 1 ,ρ 2 is an empirical auxiliary variable greater than 0, Div represents the divergence calculation function, Π c (x) is the projection operator, represents the dual solution variable of the iterative process, represents the smoothness constrained projection operator, represents the sparsity constrained projection operator, L 1 , L 2 represents the step size parameter;

[0034] Step 3.5: To speed up the iteration: When , the algorithm is interrupted. Represents the iterative convergence threshold and outputs the current g (i+1) is g. If not satisfied, the next round of iteration is performed until the end;

[0035] Finally, the desired target images at different frequencies are arithmetic averaged to obtain the final super-resolution imaging.

[0036] Compared with the traditional typical super-resolution method, this method considers the overall correlation between the target imaging and the original data in terms of sparsity, applies the idea of ​​compressed sensing, reconstructs a high-resolution image from the low-resolution original data, and combines multi-frequency scanning data to ensure the imaging quality. The generated high-resolution image has a high objective quality evaluation value and a significant improvement in visual quality. This invention introduces for the first time the hybrid sparse function constructed by the compressed sensing model for the reconstruction of high-resolution images, and combines multi-frequency near-field millimeter wave data for imaging. Experiments show that this algorithm can be effectively applied to near-field millimeter wave imaging systems, and can achieve better imaging effects than typical super-resolution algorithms on a variety of data sets. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a flow chart of the multi-frequency near-field millimeter-wave super-resolution imaging method.

[0038] Figure 2 This is the principle diagram of the super-resolution algorithm based on the compressed sensing model.

[0039] Figure 3 The experimental results of different algorithms on the Scissors dataset.

[0040] Figure 4 The following is a graph showing the experimental results of different algorithms on the letter iron piece dataset.

[0041] Figure 5 The figure shows the experimental results of different algorithms on the letter iron piece combination dataset.

[0042] Figure 6 Figure 2 shows the experimental results of different algorithms on the tool combination dataset.

[0043] Figure 7 Graphs showing the experimental results of the method of the present invention on test plates of different materials. DETAILED DESCRIPTION

[0044] This scheme is based on a two-dimensional near-field millimeter wave imaging system and is divided into two stages: data acquisition and image processing. The multi-frequency near-field millimeter wave super-resolution imaging method proposed in the present invention is as follows: Figure 1 shown.

[0045] In the data acquisition stage, the system uses the millimeter wave antenna probe to scan the object under test in a two-dimensional plane with a fixed trajectory to obtain the backscattered data s of the object under test, and then recovers the target reflection data from the backscattered data through phase compensation, and then uses the data amplitude to obtain the target reflection image g. In the image processing stage, the target reflection image g is upgraded using zero interpolation sampling, and then the image is filtered and preprocessed using the non-local mean algorithm to obtain the initial target image g. (0)The objective function G(g) of the super-resolution imaging model is constructed, and then the super-resolution algorithm based on the compressed sensing model is used to solve it, and then the desired target image g is obtained.

[0046] To solve the objective function G(g), we need to use the optimization minimization method to first convert the problem into a minimization approximate function form Q(g; g (i) )≥G(g), and then use the nearest neighbor algorithm to solve it, where i≥1 is the number of iterations, g ( i ) Represents the target image solution sequence in iteration.

[0047] The principle of super-resolution algorithm based on compressed sensing model is as follows Figure 2 As shown. First, determine the iteration condition. When the number of iterations is First, the error b between the target image and the backscattered data s is calculated. (i) calculate,

[0048]

[0049] Among them, τ≥1 is the step size factor, which controls the convergence speed and accuracy of the algorithm. Then the sparse functions of the target image are calculated separately: TV operator and wavelet operator Where Grad represents the gradient calculation function and W represents the wavelet transform. However, since the TV operator and the wavelet operator are used as mixed sparse constraints at the same time, the minimization approximation function Q cannot be solved directly. According to convex optimization theory, the original problem and the dual problem have the same saddle point, and the nearest neighbor can be used to solve the variables To compute the dual solution variable:

[0050]

[0051] To update the target image where λ 1 ,λ 2 ,ρ 1 ,ρ 2 is an empirical auxiliary variable greater than 0, Div represents the divergence calculation function. c (x) is the projection operator. To speed up the iteration, the algorithm adds an interrupt tolerance judgment. When the algorithm is interrupted, the current g is output (i+1) is g. If it is not satisfied, the next round of iteration is performed until the end. Finally, the desired target images at different frequencies are arithmetic averaged to obtain the final super-resolution imaging.

[0052] The present invention verifies the effectiveness of the multi-frequency near-field millimeter wave super-resolution imaging method based on the compressed sensing model by conducting experiments on multiple measured data sets. The measured data sets include measured scanning data of scissors and tools with metal parts, letter iron sheets, and test boards with hole defects (including polytetrafluoroethylene (PTFE), ordinary cardboard, glass fiber, silicon nitride, quartz and zirconium oxide materials, etc.). In order to reflect the penetrability of near-field millimeter waves, the non-test board test objects are scanned under the cover of paper material boards.

[0053] In the experiment, the image quality parameters peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) were compared with some existing typical super-resolution algorithms (Bicubic, SAI, NEDI, DFDF, SME, KR), reflecting the numerical similarity and structural similarity between the generated high-resolution image and the target image, in order to evaluate the algorithm effect.

[0054] The imaging comparison results of the super-resolution imaging method proposed in this invention and other super-resolution algorithms are as follows: Figure 3-7 shown. Figure 3 Comparison of the Scissor dataset. (a) is the input, (b) is the present invention, (c) is Bicubic, (d) is SAI, (e) is NEDI, (f) is DFDF, (g) is SME, and (h) is KR; Figure 3 Two magnified views are shown in Figure 1. The green frame shows the restoration of the dots at the shaft, and the red frame shows the pixel connection at the handle and the pixel loss at the junction of different materials.

[0055] Figure 4 Comparison of alphabetical datasets; (a) is input, (b) is the present invention, (c) is Bicubic, (d) is SAI, (e) is NEDI, (f) is DFDF, (g) is SME, and (h) is KR; Figure 4 There is an enlarged part in the picture, and the red frame shows the details of the edge of the iron sheet and the ghosting phenomenon in the narrow gap.

[0056] Figure 5 Comparison of alphabetic combination datasets. (a) is input, (b) is the present invention, (c) is Bicubic, (d) is SAI, (e) is NEDI, (f) is DFDF, (g) is SME, and (h) is KR; Figure 5 There are four enlarged views in the figure. The red frame shows the artifact phenomenon at the lower arc of the letter U, the yellow frame shows the smoothness of the circular cut at the upper arc of the letter C, the green frame shows the pixel blur at the lower part of the letter E, and the blue frame shows the details of the middle part of the letter S.

[0057] Figure 6Comparison of tool combination datasets, where (a) is input, (b) is the present invention, (c) is Bicubic, (d) is SAI, (e) is NEDI, (f) is DFDF, (g) is SME, and (h) is KR; Figure 6 There are two magnified views in the figure. The red frame shows the pixel details and artifacts of the non-metallic handle, and the green frame shows the smoothness of the polygonal edges on the inside of the wrench.

[0058] Figure 7 Dataset of polytetrafluoroethylene (PTFE) test panels and paperboard. (a) is polytetrafluoroethylene, the test panel contains circular defects of different sizes; (b) is polytetrafluoroethylene, the test panel contains triangular and square defects of different sizes; (c) is polytetrafluoroethylene, the test panel contains many circular defects of different sizes; (d) is paperboard, the test panel has irregular defects; (e) is glass fiber, (f) is silicon nitride; (g) is quartz, and (h) is zirconia; these test panels (e)-(h) contain circular defects of different sizes. The sub-figure shows the scanned surface of the test panel, a schematic diagram illustrating the defects, a low-resolution image, and a high-resolution image from left to right.

[0059] The results show that the method proposed by the present invention has the best visual effect in data sets with different shape features, and the details in the enlarged view are the clearest. It has better effect than the typical super-resolution algorithm.

[0060] The imaging results of the super-resolution imaging method proposed in the present invention on a test plate with hole defects are shown in the figure. The results show that the method proposed in the present invention has a good effect in defect detection of different composite materials.

[0061] The peak signal-to-noise ratio and structural similarity index of the method of the present invention and the comparison algorithm are shown in Table 1 and Table 2. The results show that the method proposed by the present invention has the highest numerical similarity and higher structural similarity compared with the typical super-resolution algorithm.

[0062] In summary, compared with typical super-resolution algorithms, the images generated by the invented multi-frequency near-field millimeter-wave super-resolution imaging method based on compressed sensing model have higher objective quality evaluation value and significant visual quality improvement.

[0063] Table 1 Peak signal-to-noise ratio of each algorithm under different data sets

[0064] Dataset\Algorithm Bicubic SAI NEDI SME KR DFDF The present invention Scissors Dataset 26.74 26.98 28.45 28.05 18.62 28.96 29.19 Alphabet Dataset 25.58 26.78 24.29 26.98 23.01 26.95 28.01 Letter combination dataset 23.69 23.80 25.73 25.19 25.57 27.23 27.17 Tool combination dataset 22.36 22.38 19.16 23.37 18.73 20.01 24.51 PTFE(a) test plate 25.16 25.06 23.96 25.12 23.55 24.19 25.41 PTFE (b) test plate 21.98 21.65 21.78 22.15 19.68 20.12 23.65 PTFE(c) test plate 22.13 22.08 18.61 22.45 17.98 19.57 23.18 Paper test board 24.56 24.72 23.39 24.67 22.94 24.30 25.43 Fiberglass Test Panel 24.56 24.72 23.39 24.67 22.94 24.30 25.43 Silicon Nitride Test Board 23.45 23.63 22.25 23.50 21.87 22.91 24.35 Quartz test board 24.23 24.41 23.07 24.26 22.70 23.88 25.23 Zirconia test plate 24.01 24.18 22.78 24.05 22.47 23.64 24.83

[0065] Table 2 Structural similarity index of each algorithm under different data sets

[0066] Dataset\Algorithm Bicubic SAI NEDI SME KR DFDF The present invention Scissors Dataset 0.9109 0.9379 0.9293 0.9489 0.7182 0.9216 0.9523 Alphabet Dataset 0.8606 0.8838 0.7325 0.9044 0.7969 0.8820 0.8965 Letter combination dataset 0.8156 0.8090 0.8755 0.8399 0.8407 0.8194 0.8870 Tool combination dataset 0.8513 0.8515 0.7183 0.8618 0.7098 0.8219 0.8795 PTFE(a) test plate 0.9021 0.9166 0.8976 0.9187 0.9057 0.9286 0.9367 PTFE (b) test plate 0.8101 0.8193 0.8251 0.8267 0.8117 0.8528 0.8446 PTFE(c) test plate 0.8209 0.8176 0.7411 0.8503 0.7982 0.8216 0.8497 Paper test board 0.9152 0.9401 0.9246 0.9388 0.8614 0.9275 0.9487 Fiberglass Test Panel 0.8321 0.8265 0.8023 0.8257 0.8096 0.8142 0.8479 Silicon Nitride Test Board 0.8012 0.8187 0.8134 0.8279 0.7846 0.8213 0.8245 Quartz test board 0.8703 0.8765 0.8421 0.8897 0.8051 0.8712 0.8804 Zirconia test plate 0.8254 0.8316 0.7432 0.8593 0.7897 0.8156 0.8492

Claims

1. A multi-frequency near-field millimeter wave super-resolution imaging method based on a compressed sensing model, the method comprising: Step 1: The system uses the millimeter wave antenna probe to scan the object under test in a two-dimensional plane with a fixed trajectory to obtain the backscattered data s (x, y, f a ), where (x, y) represents the two-dimensional plane coordinates, f a is the working frequency of the antenna probe; s(x,y,f a ) is a complex data, including the real amplitude and the imaginary phase part; Step 2: After data sampling is completed, use the backscattered data s(x, y, f) obtained in step 1 a ) for basic imaging, and recover the target reflection data g(x,y,z) from the backscattered data through phase compensation h ), and then calculate the data amplitude to obtain the target reflection image g. The data recovery calculation relationship is as follows: where z h Indicates the vertical distance between the antenna and the measured plane, FFT 2D and IFFT 2D represents the two-dimensional fast Fourier transform and its inverse transform, is the wave number of millimeter wave, k x ,k y is the component of wave number in x and y direction; c is the speed of light; Step 3: After obtaining the target reflection image, use the super-resolution algorithm to preprocess and iteratively optimize the target reflection image g to obtain the desired target image g; for the convenience of explanation, s is used in the subsequent text to represent backscattering data; Step 4: For different antenna operating frequencies f a , repeat steps 1 to 3, perform weighted averaging of the desired target images at different frequencies, and obtain the final super-resolution imaging.

2. The multi-frequency near-field millimeter wave super-resolution imaging method based on a compressed sensing model as claimed in claim 1, characterized in that: The super-resolution algorithm in step 3 first uses zero interpolation sampling to increase the dimension of the target reflection image g, expands the image from low resolution N×N to high resolution M×M, and then uses a filter operator to preprocess the image to obtain the initial target image; on this basis, the generation of the high-resolution image is regarded as a compressed sensing reconstruction problem of the original image, and the corresponding model is: C=[g min ,g max ] represents the constraint range of the amplitude of each point in the reconstructed image, g min ,g max Corresponding to the minimum and maximum values; the function p(.) is used to characterize the sparse function of the image; The st condition represents minimizing the difference between the high-resolution image and , the operator Φ represents the dimensionality reduction operation on the high-resolution image g, and ε represents the control accuracy threshold. represents the L2 norm square operation; and the model is an underdetermined system, so the mixed sparse function is designed as the optimization problem constraint, so the objective function of the super-resolution imaging model is recorded as: where ζ c (g) is the indicative function, defined as: Therefore, the process of reconstructing the image is to find the optimal solution that satisfies the compressed sensing problem, and finally obtain the desired target image g; 3. The multi-frequency near-field millimeter wave super-resolution imaging method based on a compressed sensing model as claimed in claim 1, characterized in that: The l1 norm and TV operator in the wavelet transform domain are used to construct the corresponding mixed sparse function p(.).

4. The multi-frequency near-field millimeter wave super-resolution imaging method based on a compressed sensing model as claimed in claim 1, characterized in that: The non-local means algorithm is used as the filtering operator in step 3.

5. The multi-frequency near-field millimeter wave super-resolution imaging method based on a compressed sensing model as claimed in claim 1, characterized in that: The arithmetic mean method is used as the weighted average method in step 4.

6. The multi-frequency near-field millimeter wave super-resolution imaging method based on a compressed sensing model as claimed in claim 2, characterized in that: In step 3 The calculation method is: Step 3.1: Determine the iteration condition, when the number of iterations When , calculate, Indicates the maximum number of iterations; Step 3.2: Calculate the error b between the target image and the backscattered data s (i) : Among them, τ ≥ 1 is the step size factor, which controls the convergence speed and accuracy of the algorithm, g (i) represents the target image solution sequence in iteration; Step 3.3: Calculate the sparse function of the target image separately: TV operator and wavelet operator Where Grad represents the gradient calculation function, and W represents the wavelet transform; Step 3.4: Solve for variables using nearest neighbors To compute the dual solution variable: To update the target image in, represents the neighbor solution variable in the iterative process, τ represents the regularization parameter used to balance the loss, λ1,λ2,ρ1,ρ2 are empirical auxiliary variables greater than 0, Div represents the divergence calculation function, Π c (x) is the projection operator, represents the dual solution variable of the iterative process, represents the smoothness constrained projection operator, represents the sparsity constrained projection operator, L1 and L2 represent the step size parameters; Step 3.5: To speed up the iteration: When , the algorithm is interrupted. Represents the iterative convergence threshold and outputs the current g (i+1) is g. If not satisfied, the next round of iteration is performed until the end; Finally, the desired target images at different frequencies are arithmetic averaged to obtain the final super-resolution imaging.

Images