A method for enhancing the resolution of near-field millimeter-wave sparse reconstruction images

Abstract

The present invention discloses a method for enhancing the resolution of a near-field millimeter-wave sparse reconstruction image, comprising the following steps: S1. Expressing the data acquisition process in a discrete form; S2. Conducting a more detailed grid division on the plane where the object to be measured is located, omitting the grid segmentation spacings ΔL and ΔH, to obtain the corresponding representation of the data acquisition process; S3. Letting (r, s) be the coordinates in the high-resolution grid, decomposing the exponential term in the data acquisition process; S4. Determining the projection of the original resolution grid sampling data at the point (r, s) on the high-resolution grid plane; S5. Obtaining the transformation relationship between the projection of the near-field millimeter-wave original resolution grid sampling data onto the high-resolution grid and the high-resolution image; S6. Obtaining the corresponding near-field millimeter-wave sparse reconstruction image resolution enhancement model, and directly reconstructing a high-resolution image by using the near-field millimeter-wave sparse imaging algorithm. The present invention can reconstruct a high-resolution image, effectively improving the detail quality of the image.

Description

Technical Field

[0001] The present invention relates to image processing, and in particular to a method for enhancing the resolution of near-field millimeter-wave sparse reconstruction images. Background Art

[0002] To enhance the resolution of near-field millimeter-wave sparse reconstruction images, one approach is to perform image interpolation on the reconstructed original-resolution image to obtain an image with enhanced resolution. Although this image interpolation method has a very fast processing speed, there are still some deficiencies in the quality of imaging details. Summary of the Invention

[0003] The object of the present invention is to overcome the deficiencies of the prior art and provide a method for enhancing the resolution of near-field millimeter-wave sparse reconstruction images, which can reconstruct high-resolution images and effectively improve the detail quality of the images.

[0004] The object of the present invention is achieved by the following technical solutions: A method for enhancing the resolution of near-field millimeter-wave sparse reconstruction images includes the following steps:

[0005] S1. Express the data acquisition process in a discrete form;

[0006] S2. Perform a more detailed grid division on the plane where the object to be measured is located, omit the grid division spacings ΔL and ΔH, and obtain the corresponding representation of the data acquisition process;

[0007] S3. Let (r, s) be the coordinates in the high-resolution grid, and decompose the exponential term in the data acquisition process;

[0008] S4. Determine the projection of the original-resolution grid sampling data at the point (r, s) on the high-resolution grid plane;

[0009] S5. Introduce a two-dimensional FFT and unify the coordinate relationship, then obtain the transformation relationship between the projection of the near-field millimeter-wave original-resolution grid sampling data onto the high-resolution grid and the high-resolution image;

[0010] S6. Obtain the corresponding near-field millimeter-wave sparse reconstruction image resolution enhancement model, and directly reconstruct a high-resolution image using the near-field millimeter-wave sparse imaging algorithm.

[0011] Among them, the step S1 includes:

[0012] Assume that the working plane of the near-field millimeter-wave antenna probe is divided by a discrete rectangular coordinate sampling grid with a sampling pitch of Δ L The antenna probe is located at the grid point each time data is collected, and it is denoted that there is a pitch of Δ LThe sampling grid resolution is P×P, and it is considered that the plane where the object to be measured is located is also divided by a grid with the same resolution. The backscattering coefficient s(x′, y′, f a ) is represented in a discrete form as:

[0013]

[0014] where f a is the operating frequency of the antenna probe, is the wave number of the millimeter wave, and c is the speed of light. The plane where the movement trajectory of the antenna probe is located and the plane where the object to be measured is located can be considered to be parallel to each other, and the vertical distance between the two planes is z h . The reflectivity distribution function at any point (x, y, z h ) on the object to be measured is g(x, y, z h ), and its amplitude can be used to represent the pixel value of the reconstructed image.

[0015] Among them, the step S2 includes:

[0016] In order to improve the resolution of the near-field millimeter wave reconstructed image, the plane where the object to be measured is located is divided into finer grids: Denote Δ H =Δ L / μ, where μ≥1 is the resolution enhancement coefficient, then the plane grid resolution with a spacing of Δ H is N×N = μP×μP;

[0017] Therefore, the data acquisition process of the antenna probe located on the original resolution grid plane for the object to be measured located on the high-resolution grid plane is expressed as:

[0018]

[0019] Omitting the grid division spacings ΔL and ΔH, rewrite Equation (2) as:

[0020]

[0021] Among them, the step S3 includes:

[0022] Considering that a spherical wave can be decomposed into the superposition of a series of plane waves, let (r, s) be the coordinates under the high-resolution grid. Then, the exponential term in Equation (3) is decomposed as:

[0023]

[0024] where (k x′ , k y′ ) ∈ [-2k a , -2k a +4k a / P,... 2ka -4k a / P] × [-2k a ,-2k a +4k a / P,... ,2k a -4k a / P] is the variable of the spatial discrete Fourier transform with respect to the original resolution grid, (k r , k s ) ∈ [-2μk a , -2μk a +4μk a / N,... ,2μk a -4μk a / N] × [-2μk a , -2μk a +4μk a / N,... ,2μk a -4μk a / N] is the variable of the spatial discrete Fourier transform with respect to the high-resolution grid. ε(k r , k s ) is the exponential term defined according to the electromagnetic plane wave dispersion relation, and its specific form is:

[0025]

[0026] Among them, the step S4 includes:

[0027] Regarding the original resolution grid as a uniform downsampling of the high-resolution grid, then the data sampled in the plane divided by the original resolution grid is also regarded as a uniform downsampling of the data sampled in the plane divided by the high-resolution grid. Let represent the projection of the original resolution grid sampling data at the point (r, s) in the high-resolution grid plane, then there is:

[0028]

[0029] Substituting Equation (4) and Equation (6) into Equation (3), we get

[0030]

[0031] Among them, the step S5 includes:

[0032] Introducing a two-dimensional FFT and unifying the coordinate relationship, the transformation relationship between the projection of the near-field millimeter-wave original resolution grid sampling data onto the high-resolution grid and the high-resolution image is obtained; it is:

[0033]

[0034]

[0035] Among them

[0036]

[0037] Among them, the said step S6 includes:

[0038] Let be the data obtained after the near-field millimeter-wave imaging system sparsely and undersamples the object to be measured, be the uniform downsampling operator, where μ = N / P is the resolution enhancement coefficient. be the random undersampling operator. Denote the image of the object to be measured under the high-resolution grid division as According to Equation (8), there is the following relationship between the sparse observation data s and the high-resolution image g H :

[0039] s = Φ μ g H + n, (11)

[0040] can be considered as the process of randomly undersampling after downsampling the data collected by the high-resolution grid, which is also called the near-field millimeter-wave sparse resolution enhancement observation operator. Among them, is the phase compensation matrix. According to Equation (9) and Φ μ , define the inverse process of Φ μ as Among them is the zero-padding expansion operator, is the uniform upsampling operator,

[0041] Obviously, the process of directly reconstructing a high-resolution image from sparse observation data also boils down to a compressive sensing image reconstruction problem. According to Equation (11), the corresponding near-field millimeter-wave sparse reconstruction image resolution enhancement model is

[0042]

[0043] Then the unconstrained near-field millimeter-wave imaging compressive sensing optimization problem relaxed from Equation (12) can be denoted as

[0044]

[0045] Among them, is the indicator function on the set ,

[0046] For the problem of Equation (13), use the near-field millimeter-wave sparse imaging algorithm to directly reconstruct the high-resolution image The specific method is as follows.

[0047] The optimization problem of compressive sensing is transformed into a form suitable for solution by the proximal algorithm using the optimized minimization method. Let {g (i)} be the generated solution sequence of the algorithm, then an optimized minimization approximation function Q(g; g (i) ) can be set, which satisfies

[0048]

[0049] where τ ≥ λ max (Φ # Φ) is the Lipschitz constant, and λ max (Φ # Φ) is the maximum eigenvalue of Φ # Φ. The optimized minimization approximation function Q(g; g (i) ) and the objective function G(g) satisfy the relationships Q(g; g (i) ) ≥ G(g) and Q(g (i) ; g (i) ) = G(g (i) ). Therefore, the solution of the objective function G(g) can be completed by iteratively solving the optimized minimization approximation function Q(g; g (i) ).

[0050] Due to the existence of a sparse function with a mixed function structure, the optimized minimization approximation function Q(g; g (i) ) cannot be directly solved. To solve this problem, according to the characteristics of the mixed sparse function, a primal-dual framework is designed to decompose the optimized minimization approximation function Q(g; g (i) ) into a form suitable for solution by the proximal algorithm.

[0051] The original problem can be reduced to the minimization problem of the original objective sub-functions and , where

[0052]

[0053]

[0054] where is an l ∞ -l2 norm unit ball, and

[0055] is an l ∞ norm unit ball.

[0056] The dual problem can then be reduced to the minimization problem of the dual objective sub-functions and Maximization problem, where

[0057]

[0058]

[0059] where

[0060]

[0061]

[0062] is the projection operator for projecting the signal amplitude onto the set Let and be the sequences of dual solutions generated by two dual maximization sub - problems respectively. Then we can obtain

[0063]

[0064]

[0065] where L1 is the constant satisfying with L1 - Lipschitz continuity; similarly, L2 is the constant satisfying with L2 - Lipschitz continuity. Following and are the projection operators for projecting the elements in the variables and and respectively. Subsequently, we can obtain

[0066]

[0067] At this time, we can directly solve the analytical solution that minimizes Equation (23):

[0068]

[0069] Considering the time - consumption cost of the actual near - field millimeter - wave sparse imaging algorithm, an interruption condition needs to be set for the algorithm. Set the interruption tolerance When the solution sequence {g (i)} satisfies

[0070]

[0071] it can be considered that the reconstructed near - field millimeter - wave image has met the actual requirements, and the algorithm ends. For intuitive representation, all steps of the proposed near - field millimeter - wave sparse imaging method are summarized in Algorithm 1.

[0072]

[0073]

[0074] Since Algorithm 1 is based on the proximal gradient method, its convergence rate satisfies During the actual image reconstruction process, it consumes a large amount of time. Therefore, by introducing the Nesterov update method, the algorithm can achieve the convergence rate. The specific steps of the algorithm with the Nesterov update are summarized in Algorithm 2.

[0075]

[0076]

[0077] The beneficial effects of the present invention are as follows: By using the relationship between the original resolution sampling grid of the near-field millimeter-wave imaging system and the high-resolution image, the present invention constructs a near-field millimeter-wave sparse resolution enhancement observation operator, and constructs a near-field millimeter-wave sparse resolution enhancement observation model based on this observation operator. According to the near-field millimeter-wave sparse resolution enhancement observation model, a near-field millimeter-wave sparse resolution enhancement imaging model is further constructed to reconstruct a high-resolution image, effectively improving the detail quality of the image. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 is the flowchart of the method of the present invention;

[0079] Figure 2 is the imaging schematic diagram of the near-field millimeter-wave system under two different resolution grid divisions in the embodiment;

[0080] Figure 3 is the schematic diagram of the full sampling data and reconstructed image of the near-field millimeter-wave of the object to be measured by the near-field millimeter-wave imaging system under the high-resolution sampling grid at a working frequency of 74 GHz;

[0081] Figure 4 is the schematic diagram of the comparison of the effects of the high-resolution images reconstructed by the direct enhancement method constructed in this application and the high-resolution images generated by the interpolation method at different undersampling rates in the simulation experiment;

[0082] Figure 5 is the schematic diagram of the comparison of the effects of the high-resolution images reconstructed by the direct enhancement method constructed in this application and the high-resolution images generated by the interpolation method at different undersampling rates in the actual measurement experiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0083] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the following description.

[0084] As Figure 1 shown, a method for enhancing the resolution of a near-field millimeter-wave sparse reconstruction image includes the following steps:

[0085] S1. Express the data acquisition process in a discrete form;

[0086] S2. Divide the plane where the object to be measured is located into finer grids, omit the grid segmentation spacings ΔL and ΔH, and obtain the corresponding representation of the data acquisition process;

[0087] S3. Let (r, s) be the coordinates in the high-resolution grid, and decompose the exponential term in the data acquisition process;

[0088] S4. Determine the projection of the original resolution grid sampling data at the point (r, s) on the high-resolution grid plane;

[0089] S5. Introduce a two-dimensional FFT and unify the coordinate relationship, then obtain the transformation relationship between the projection of the near-field millimeter-wave original resolution grid sampling data onto the high-resolution grid and the high-resolution image;

[0090] S6. Obtain the corresponding near-field millimeter-wave sparse reconstruction image resolution enhancement model, and directly reconstruct the high-resolution image using the near-field millimeter-wave sparse imaging algorithm.

[0091] Among them, the step S1 includes:

[0092] Assume that the working plane of the near-field millimeter-wave antenna probe is divided by a discrete rectangular coordinate sampling grid with a sampling spacing of Δ L . Each time the antenna probe performs data acquisition, it is located at a grid point. Denote the sampling grid resolution with a spacing of Δ L as P×P, and assume that the plane where the object to be measured is located is also divided by a grid with the same resolution. The collected backscattering coefficient s(x′, y′, f a ) is expressed in a discrete form as:

[0093]

[0094] where f a is the working frequency of the antenna probe, is the wave number of the millimeter wave, and c is the speed of light. It can be considered that the plane where the movement trajectory of the antenna probe is located and the plane where the object to be measured is located are parallel to each other, and the perpendicular distance between the two planes is z h . The reflectivity distribution function at any point (x, y, z h ) on the object to be measured is g(x, y, z h ), and its amplitude can be used to represent the pixel value of the reconstructed image.

[0095] Among them, the step S2 includes:

[0096] To improve the resolution of the near-field millimeter-wave reconstructed image, the plane where the object to be measured is located is divided into finer grids: Denote Δ H =Δ L / μ, where μ≥1 is the resolution enhancement factor. Then, the plane grid with a spacing of Δ H has a resolution of N×N = μP×μP; As Figure 2 shown, in the embodiments of the present application, schematic diagrams of the near-field millimeter-wave system imaging under two different resolution grid divisions are given.

[0097] Therefore, the data acquisition process of the antenna probe located on the original resolution grid plane for the object to be measured located on the high-resolution grid plane is expressed as:

[0098]

[0099] Omitting the grid division spacings ΔL and ΔH, rewrite Equation (2) as:

[0100]

[0101] Among them, the step S3 includes:

[0102] Considering that a spherical wave can be decomposed into a superposition of a series of plane waves, let (r, s) be the coordinates under the high-resolution grid. Then, the exponential term in Equation (3) is decomposed as:

[0103]

[0104] where (k x′ , k y′ ) ∈ [-2k a , -2k a +4k a / P,..., 2k a -4k a / P] × [-2k a , -2k a +4k a / P,..., 2k a -4k a / P] is the variable of the spatial discrete Fourier transform with respect to the original resolution grid, and (k r , k s ) ∈ [-2μk a , -2μk a +4μk a / N,..., 2μk a -4μk a / N] × [-2μk a , -2μka +4μk a / N, ..., 2μk a -4μk a / N] are the variables of the spatial discrete Fourier transform with respect to the high-resolution grid. ε(k r , k s ) is the exponential term defined according to the electromagnetic plane wave dispersion relation, and its specific form is:

[0105]

[0106] Among them, the step S4 includes:

[0107] Regarding the original resolution grid as a uniform downsampling of the high-resolution grid, then the data sampled in the plane divided by the original resolution grid is also regarded as a uniform downsampling of the data sampled in the plane divided by the high-resolution grid. Let represent the projection of the original resolution grid sampling data at the point (r, s) in the high-resolution grid plane, then there is:

[0108]

[0109] Substituting Equation (4) and Equation (6) into Equation (3), we get

[0110]

[0111] Among them, the step S5 includes:

[0112] Introducing a two-dimensional FFT and unifying the coordinate relationship, the transformation relationship between the projection of the original resolution grid sampling data of the near-field millimeter wave to the high-resolution grid and the high-resolution image is obtained; it is:

[0113]

[0114]

[0115] Among them

[0116]

[0117] Among them, the step S6 includes:

[0118] Let be the data obtained after the near-field millimeter wave imaging system sparsely under-samples the object to be measured, be the uniform downsampling operator, where μ = N / P is the resolution enhancement coefficient. be the random under-sampling operator. Denote the image of the object to be measured under the high-resolution grid division as According to Equation (8), the relationship between the sparse observation data s and the high-resolution image gH is as follows:

[0119] s = Φ μ g H + n, (11)

[0120] It can be regarded as the process of downsampling and then randomly under-sampling the data collected from the high-resolution grid, which is also called the near-field millimeter-wave sparse resolution enhancement observation operator. Among them, is the phase compensation matrix. According to Equation (9) and Φ μ , the inverse process of Φ μ can be defined as where is the zero-padding extension operator, is the uniform upsampling operator,

[0121] Obviously, the process of directly reconstructing a high-resolution image from sparse observation data also boils down to a compressed sensing image reconstruction problem. According to Equation (11), the corresponding near-field millimeter-wave sparse reconstruction image resolution enhancement model is

[0122]

[0123] Then, the unconstrained near-field millimeter-wave imaging compressed sensing optimization problem relaxed from Equation (12) can be denoted as

[0124]

[0125] Among them, is the indicator function on the set ,

[0126] For the problem of Equation (13), use the near-field millimeter-wave sparse imaging algorithm to directly reconstruct a high-resolution image The specific method is as follows.

[0127] Adopt the optimization minimization method to transform the compressed sensing optimization problem into a form suitable for solving by the proximal algorithm. Let {g (i)} be the generated solution sequence of the algorithm, then an optimization minimization approximation function Q(g; g (i) ) can be set, which satisfies

[0128]

[0129] Among them, τ ≥ λ max (Φ # Φ) is the Lipschitz constant, λ max (Φ# Let Φ be Φ # The maximum eigenvalue of Φ. Optimize the minimization approximation function Q(g; g (i) ) and the objective function G(g) satisfy the relationship Q(g; g (i) ) ≥ G(g) and Q(g (i) ; g (i) ) = G(g (i) ). Thus, the solution of the objective function G(g) can be completed by iteratively solving the optimization minimization approximation function Q(g; g (i) ).

[0130] Due to the existence of sparse functions with a mixed function structure, it is impossible to directly solve the optimization minimization approximation function Q(g; g (i) ). To solve this problem, according to the characteristics of the mixed sparse function, a primal-dual framework is designed to decompose the optimization minimization approximation function Q(g; g (i) ) into a form suitable for solving by the proximal algorithm.

[0131] The original problem can be reduced to the minimization problem of the original objective sub-function and , where

[0132]

[0133]

[0134] Among them, is an l ∞ -l2 norm unit ball, is an l ∞ norm unit ball.

[0135] The dual problem can then be reduced to the maximization problem of the dual objective sub-function and , where

[0136]

[0137]

[0138] Among them

[0139]

[0140]

[0141] is the projection operator that projects the signal amplitude onto the set . Let and The dual solution sequences generated for two dual maximization subproblems respectively, thus we can obtain

[0142]

[0143]

[0144] where L1 is the constant satisfying with L1-Lipschitz continuity; similarly, L2 is the constant satisfying with L2-Lipschitz continuity. Followed by For the projection operators that project the elements in the variables and onto and respectively. Subsequently, we can obtain

[0145]

[0146] At this time, the analytical solution that minimizes Equation (23) can be directly solved:

[0147]

[0148] Considering the time consumption cost of the actual near-field millimeter-wave sparse imaging algorithm, an interruption condition needs to be set for the algorithm. Set the interruption tolerance When the solution sequence {g (i)} satisfies

[0149]

[0150] it can be considered that the reconstructed near-field millimeter-wave image has met the actual requirements, and the algorithm ends. For intuitive representation, all steps of the proposed near-field millimeter-wave sparse imaging algorithm are summarized in Algorithm 1.

[0151]

[0152]

[0153] Since Algorithm 1 is based on the proximal gradient method, its convergence rate satisfies A large amount of time will be consumed in the actual image reconstruction process. Thus, by introducing the Nesterov update method, the algorithm can achieve the convergence rate. The specific steps of the algorithm with Nesterov update are summarized in Algorithm 2.

[0154]

[0155]

[0156] In the embodiments of the present application, the evaluation of the imaging effect belongs to the situation of making an evaluation without a reference image. The existing evaluation criteria based on reference images will no longer apply. Since the subjective estimates of different personnel participating in the evaluation will vary greatly due to personal experience and differences in the understanding of objective things, the evaluation results cannot be uniformly quantified and compared. In order to evaluate the image quality relatively objectively, no-reference image quality evaluation criteria have been proposed and widely adopted by scholars at home and abroad. The no-reference image quality evaluation method will be adopted in the embodiments of the present application. Four commonly used no-reference image quality evaluation methods are introduced below.

[0157] Gray Mean Gradients (GMG) method: The GMG method is a method for judging the image quality by measuring the mean value of the amplitude gradient change of the image itself. Let the image to be evaluated be Then the definition of GMG is:

[0158]

[0159] where Dx and Dy are difference operators. In the GMG method, the higher the score, the better the image quality; conversely, the lower the score, the worse the image quality.

[0160] BLIINDS-II (blind image integrity notator using DCT statistics II) method: This method first divides the picture into blocks and extracts the generalized Gaussian distribution parameter features, frequency change parameter features, energy sub-band ratio measurement features, and model direction features of each block under the discrete cosine transform (DCT), then trains the obtained features and gets the corresponding probability model, and then evaluates the image through the probability model. In the BLIINDS-II method, the lower the score, the better the image quality; conversely, the higher the score, the worse the image quality.

[0161] NIQE (natural image quality evaluator) method: This method divides the picture into blocks, screens out the blocks with significant local contrast means, and then uses a multivariate Gaussian model to fit and obtain the corresponding feature model. During the evaluation process, the distance between the feature model parameters of the image to be evaluated and the pre-established model parameters is used to determine the image quality. In the NIQE method, the lower the score, the better the image quality; conversely, the higher the score, the worse the image quality.

[0162] NQRM (no-reference quality metric) method: This method first extracts the frequency change parameter features under DCT transformation, the frequency change parameter features under wavelet transformation, and the discontinuous parameter features of points in the spatial domain. After training, the corresponding parameter models are fitted, and the obtained models are used to evaluate the image quality. Under the NQRM method, the higher the score, the better the image quality; conversely, the lower the score, the worse the image quality.

[0163] In the embodiment of the present application, in the near-field millimeter-wave sparse reconstruction image resolution enhancement simulation experiment, the imaging system scans the object to be measured at a position 28 mm below the 128 mm×128 mm sampling plane through an antenna probe operating in the 74 GHz frequency band. Let the original resolution grid step be 1 mm, and its resolution be 128×128; the high-resolution grid step be 0.5 mm, and its resolution be 256×256. Thus, the resolution enhancement coefficient μ = 2 can be obtained. Figure 3 For the near-field millimeter-wave imaging system to perform full sampling data and reconstructed images of the object to be measured at a high-resolution sampling grid with a working frequency of 74 GHz, where the full sampling data of the near-field millimeter-wave imaging system for the object to be measured at the high-resolution grid is as Figure 3 (a) shown, and the full sampling reconstructed image reconstructed from the high-resolution full sampling data is as Figure 3 (b) shown. Among them, Figure 3 (b)'s full sampling image can be used as a reference image for image quality evaluation criteria SSIM and PSNR. The selection of each parameter of the algorithm is as follows: The wavelet transform selected for the l1 norm is the Symlet wavelet with 8 vanishing moments; the sparse trade-off parameters λ1 = 0.005, λ2 = 0.005; the Moreau envelope approximation performance balance parameters ρ1 = 1, ρ2 = 1; the optimization minimization Lipschitz constant τ = 1; the Lipschitz constant of the dual objective subfunction gradient; Interruption tolerance

[0164] Figure 4 Shows the comparison of the imaging effects of the high-resolution images reconstructed by the method constructed in the present application and the high-resolution images generated by the image interpolation method using cubic spline interpolation when different undersampling rates (14%, 21%, 28%) are selected in the case of no noise. Figure 4 (a), Figure 4 (d) and Figure 4 (g) are the original resolution images reconstructed by the near-field millimeter-wave sparse imaging algorithm at each undersampling rate respectively. Figure 4 (b), Figure 4 (e) and Figure 4(h) are high-resolution images generated by the image interpolation method at each undersampling rate, where: Figure 4 (b) SSIM = 5515, PSNR = 23.7204; Figure 4 (e) SSIM=5637, PSNR=23.8175; Figure 4 (h) has SSIM=5706 and PSNR=23.9661. Figure 4 (c) Figure 4 (f) and Figure 4 (i) are respectively high-resolution images directly reconstructed by the construction method of the present application at various undersampling rates, wherein: Figure 4 (c)’s SSIM=5752, PSNR=23.7795; Figure 4 (f)’s SSIM=5813, PSNR=23.8497; Figure 4 (i) has SSIM=5895 and PSNR=24.0054. From the enlarged detail of the edge of the circular pattern in the figure, it can be observed that the image edge generated by the image interpolation method has a jagged effect, while the edge transition in the image reconstructed by the method constructed in the present application is smoother. As for the overall reconstructed image effect, the image reconstructed by the direct enhancement method constructed in the present application has a clearer and more discernible background than the image background generated by the image interpolation method.

[0165] Table 1 shows the conditions for the interruption tolerance when the undersampling rate is 14%. After repeating the experiment 50 times independently, the average effect of each index of the high-resolution image directly reconstructed by the algorithm constructed in this application and the high-resolution image generated by interpolation of the original resolution image under different Gaussian white noise SNRs is compared. It can be found from Table 1 that under different noise levels, the method of directly reconstructing high-resolution images from sparse observation data proposed in this application has better performance than the high-resolution image generated by interpolation of the original resolution image under the image quality evaluation standards SSIM and PSNR.

[0166] Table 1

[0167]

[0168] In the actual measurement experiment, the antenna probe of the near-field millimeter-wave imaging system operates at a frequency of 150 GHz, and data is collected from the object to be measured 40 mm below the sampling plane of 64 mm × 64 mm with a grid step of 0.5 mm. Thus, the original resolution grid size obtained is 128 × 128. The object to be measured is composed of a metal ball, a metal washer, and a metal nut. In the actual measurement experiment, the resolution enhancement coefficient μ = 2 is set, and the corresponding high-resolution grid is 256 × 256. For the direct enhancement method constructed in this application, the sparse trade-off parameters are set as λ1 = 0.001 and λ2 = 0.0015; for the near-field millimeter-wave sparse imaging algorithm using the image interpolation method, the sparse trade-off parameters are set as λ1 = 0.003 and λ2 = 0.007, and the cubic spline interpolation method is selected for interpolation. At the same time, for all algorithms in this experiment, the Symlet wavelet with 8 vanishing moments is selected for the l1 norm; the Moreau envelope approximation performance balance parameters ρ1 = 1 and ρ2 = 1; the optimized minimization Lipschitz constant τ = 1; the Lipschitz constant of the dual objective subfunction gradient Algorithm interruption tolerance

[0169] Figure 5 The comparison of the images reconstructed by the direct enhancement method constructed in this application and the images generated by the image interpolation method is shown under different undersampling rates (14%, 21%, 28%). Figure 5 (a), Figure 5 (d) and Figure 5 (g) are the original resolution images reconstructed by the existing near-field millimeter-wave sparse imaging algorithm under each undersampling rate respectively. Figure 5 (b), Figure 5 (e) and Figure 5 (h) are the high-resolution images generated by the image interpolation method under each undersampling rate respectively. Figure 5 (c), Figure 5 (f) and Figure 5 (i) are the high-resolution images directly reconstructed by the method constructed in this application under each undersampling rate respectively. From the enlarged detail view of the metal nut in the figure, it can be observed that when the undersampling rate is 14%, the orifice of the metal nut is hardly distinguishable in the high-resolution image generated by the interpolation method, while the orifice of the metal nut can be easily distinguished in the high-resolution image directly reconstructed by the method proposed in this application; and as the undersampling rate increases, the reconstruction effect of the orifice of the metal nut in the high-resolution image directly reconstructed by the method proposed in this application is also better than that in the high-resolution image generated by the interpolation method.

[0170] Since there is no high-resolution full-sampling reconstructed image as the reference image for the image quality evaluation criteria SSIM and PSNR in the actual measurement experiment, four no-reference image quality evaluation criteria given above are considered here, that is, the GMG method, the BLIINDS-II method, the NIQE method, and the NQRM method are used to evaluate the quality of the high-resolution images reconstructed in the actual measurement experiment. At different undersampling rates (14%, 21%, 28%), the results obtained by the direct enhancement method constructed in this application for reconstructing high-resolution images and the image interpolation method for generating high-resolution images under each no-reference image quality evaluation criteria method are summarized in Table 2.

[0171] Table 2

[0172]

[0173] As can be seen from Table 2, the scores obtained for the high-resolution images reconstructed by the direct enhancement method constructed in this application under each no-reference image quality evaluation criteria method are better than those of the high-resolution images generated by the image interpolation method. Combining Figure 5 the analysis of the intuitive image effect and the comparison of the no-reference image quality evaluation criteria method in Table 2, it can be considered that the near-field millimeter-wave sparse reconstruction image resolution enhancement processing method constructed in this application has a better effect on the imaging quality compared to the images generated by the image interpolation method.

[0174] The above description shows and describes a preferred embodiment of the present invention. However, as mentioned above, it should be understood that the present invention is not limited to the form disclosed herein, should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications, and environments, and can be changed within the scope of the inventive concept described herein through the above teachings or the techniques or knowledge in related fields. And any changes and variations made by those skilled in the art without departing from the spirit and scope of the present invention shall fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for enhancing the resolution of near-field millimeter-wave sparse reconstruction images, characterized in that: It includes the following steps: S1. Express the data acquisition process in a discrete form; S2. Conduct a more detailed grid division on the plane where the object to be measured is located, omit the grid division spacings ΔL and ΔH, and obtain the corresponding representation of the data acquisition process; S3. Let (r, s) be the coordinates in the high-resolution grid, and decompose the exponential term in the data acquisition process; S4. Determine the projection of the original resolution grid sampling data on the high-resolution grid plane at the point (r, s); S5. Introduce a two-dimensional FFT and unify the coordinate relationship, then obtain the transformation relationship between the projection of the original resolution grid sampling data of the near-field millimeter wave onto the high-resolution grid and the high-resolution image; The step S5 includes: Introduce a two-dimensional FFT and unify the coordinate relationship, then obtain the transformation relationship between the projection of the original resolution grid sampling data of the near-field millimeter wave onto the high-resolution grid and the high-resolution image; as follows: Where S6. Obtain the corresponding near-field millimeter wave sparse reconstruction image resolution enhancement model, and directly reconstruct the high-resolution image using the near-field millimeter wave sparse imaging algorithm; The step S6 includes: Let be the data obtained after the near-field millimeter-wave imaging system sparsely under-samples the object to be measured, be the uniform down-sampling operator, where μ = N / P is the resolution enhancement factor; be the random under-sampling operator; Denote the image of the object to be measured under the high-resolution grid division as According to Equation (8), there is the following relationship between the sparse observation data s and the high-resolution image g H as follows: s = Φ μ g H +n, (11) It can be regarded as the process of downsampling the data collected by the high-resolution grid and then randomly undersampling, which is also called the near-field millimeter-wave sparse resolution enhancement observation operator; among them, is the phase compensation matrix. According to Equation (9) and Φ μ , Φ μ The inverse process of is Among them is the zero-padding extension operator, is the uniform upsampling operator, Obviously, the process of directly reconstructing a high-resolution image from sparse observation data also boils down to a compressive sensing image reconstruction problem. According to Equation (11), the corresponding near-field millimeter wave sparse reconstruction image resolution enhancement model is Then the unconstrained near-field millimeter wave imaging compressive sensing optimization problem relaxed from Equation (12) can be denoted as Among them, is the indicator function on the set , For the problem of formula (13), a high-resolution image is directly reconstructed using the near-field millimeter-wave sparse imaging algorithm The specific method is as follows: The optimization minimization method is used to transform the compressed sensing optimization problem into a form suitable for solution by the proximal algorithm. Let {g (i)} be the generated solution sequence of the algorithm, then an optimization minimization approximation function Q(g; g (i) ) can be set, which satisfies Among them, τ ≥ λ max (Φ # Φ) is the Lipschitz constant, λ max (Φ # Φ) is the maximum eigenvalue of Φ # Φ; The optimized minimization approximation function Q(g; g (i) ) and the objective function G(g) satisfy the relationships Q(g; g (i) ) ≥ G(g) and Q(g (i) ; g (i) ) = G(g (i) ); Therefore, the solution of the objective function G(g) can be completed by iteratively solving the optimized minimization approximation function Q(g; g (i) ). Due to the existence of sparse functions with hybrid function structures, it is impossible to directly solve the optimization minimization approximation function Q(g; g (i) ). To solve this problem, according to the characteristics of the hybrid sparse function, a primal-dual framework is designed to decompose the optimization minimization approximation function Q(g; g (i) ) into a form suitable for solution by the proximal algorithm; The original problem can be reduced to minimizing the original objective sub - functions and where Among them, is a norm unit ball, is a norm unit ball; The dual problem can then be reduced to maximizing the dual objective sub-function and where: Where The projection operator for projecting the signal amplitude onto the set ; Let and be the sequences of dual solutions generated by two dual maximization subproblems respectively, then we obtain where L1 is a constant satisfying with L1-Lipschitz continuity; similarly, L2 is a constant satisfying with L2-Lipschitz continuity; and is the projection operator that projects the elements in the variables and onto and respectively; subsequently, we obtain At this time, the analytical solution that minimizes Equation (23) can be directly solved: Considering the time consumption cost of the actual near-field millimeter-wave sparse imaging algorithm, it is necessary to set an interruption condition for the algorithm; set the interruption tolerance When the solution sequence {g (i)} satisfies When it is considered that the reconstructed near-field millimeter-wave image has met the actual requirements, 2. A method for enhancing the resolution of a near-field millimeter-wave sparse reconstruction image according to claim 1, characterized in that: The step S1 includes: Assume that the working plane of the near-field millimeter-wave antenna probe is divided by a discrete rectangular coordinate sampling grid with a sampling interval of Δ L . When the antenna probe performs data acquisition each time, it is located at the grid point. Denote the sampling grid resolution with an interval of Δ L as P×P, and assume that the plane where the object to be measured is located is also divided by a grid with the same resolution. The backscattering coefficient s(x′, y′, f a ) collected is expressed in a discrete form as: Among them, f a is the operating frequency of the antenna probe, is the wave number of the millimeter wave, and c is the speed of light; the plane where the movement trajectory of the antenna probe is located and the plane where the object to be measured is located can be considered to be parallel to each other, and the perpendicular distance between the two planes is z h ; the reflectivity distribution function at any point (x, y, z h ) on the object to be measured is g(x, y, z h ), and its amplitude can be used to represent the pixel value of the reconstructed image.

3. A method for enhancing the resolution of a near-field millimeter-wave sparse reconstruction image according to claim 1, characterized in that: The step S2 includes: To improve the resolution of the near-field millimeter-wave reconstructed image, a finer grid division is performed on the plane where the object under test is located. Denote Δ H = Δ L / μ, where μ ≥ 1 is the resolution enhancement factor. Then, the plane grid resolution with a spacing of Δ H is N×N = μP×μP; Thus, the data acquisition process of the antenna probe located on the original resolution grid plane for the object to be measured located on the high-resolution grid plane is expressed as: Omit the grid division spacings ΔL and ΔH, and rewrite Equation (2) as:

4. A method for enhancing the resolution of a near-field millimeter-wave sparse reconstruction image according to claim 1, characterized in that: The step S3 includes: Considering that a spherical wave can be decomposed into the superposition of a series of plane waves, let (r, s) be the coordinates in the high-resolution grid. Thus, the exponential term in Equation (3) is decomposed as: where (k x′ , k y′ ) ∈ [-2k a , -2k a + 4k a / P, …, 2k a - 4k a / P] × [-2k a , -2k a + 4k a / P, …, 2k a -4k a / P] is the variable of the spatial discrete Fourier transform with respect to the original resolution grid, (k r , k s ) ∈ [-2μk a , -2μk a + 4μk a / N, …, 2μk a - 4μk a / N] × [-2μk a , -2μk a + 4μk a / N, …, 2μk a -4μk a / N] is the variable of the spatial discrete Fourier transform relative to the high-resolution grid; ε(k r , k s ) is the exponential term defined according to the electromagnetic plane wave dispersion relation, and its specific form is:

5. A method for enhancing the resolution of a near-field millimeter-wave sparse reconstruction image according to claim 1, characterized in that: The step S4 includes: Regarding the original resolution grid as a uniform downsampling of the high-resolution grid, the data sampled within the plane divided by the original resolution grid is also regarded as a uniform downsampling of the data sampled within the plane divided by the high-resolution grid. Let represent the projection of the data sampled by the original resolution grid on the high-resolution grid plane at the point (r, s), then we have: Substitute Equation (4) and Equation (6) into Equation (3) to obtain

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