Microwave calculation imaging method based on programmable metasurface and amplitude measurement

Abstract

The invention provides a microwave calculation imaging method based on a programmable metasurface and amplitude measurement, and the method comprises the following steps: configuring parameters of microwave imaging, and constructing a measurement matrix on the programmable metasurface; using a phase-free linear measurement model to linearly associate the contrast parameter of the measurement target with the scattered field; an RAF algorithm is adopted to optimize contrast parameters, wherein the RAF algorithm comprises an initialization process and a gradient iteration optimization process; and inverting the contrast parameter optimized by the RAF algorithm to obtain an actual relative parameter for microwave imaging. According to the method, a multi-dimensional measurement matrix is constructed by dynamically regulating and controlling a metasurface radiation field mode, and high-precision inversion of the dielectric characteristics of the target under the condition of no phase measurement is realized by combining an RAF algorithm two-stage optimization strategy-initialization based on energy screening and self-adaptive gradient iteration.

Description

Technical Field

[0001] The present invention relates to the field of microwave imaging, and in particular to a microwave computational imaging method based on programmable metasurface and amplitude measurement. Background Art

[0002] Microwave imaging technology analyzes the scattering field distribution of the target under the action of the incident electromagnetic field and inverts the dielectric parameter distribution of the target. It has the advantages of non-contact, non-invasive, and all-weather operation, and is widely used in security inspection, non-destructive testing, biomedicine, etc. Traditional microwave imaging mainly relies on synthetic aperture radar (SAR) and phased array radar (RAR) systems: SAR relies on the relative motion between the radar and the target, has an imaging blind spot, and high resolution requires a large synthetic aperture, resulting in low efficiency; RAR requires a phase controller and amplifier to be configured in each antenna unit, resulting in a bulky system and high cost.

[0003] With the development of metamaterial technology, programmable metasurface-assisted microwave computational imaging (PMS-MCI) has become an emerging solution. This technology produces spatially diverse illumination by encoding and regulating the metasurface radiation pattern, and combines computational imaging algorithms to achieve efficient imaging, overcoming the traditional system's reliance on mechanical scanning and complex hardware. However, existing PMS-MCI methods generally use coherent detection schemes, which require simultaneous acquisition of amplitude and phase information of the measurement data. In high-frequency band (millimeter wave / terahertz) applications, factors such as probe positioning errors and receiving circuit drift cause a sharp drop in phase measurement accuracy, which seriously restricts imaging performance.

[0004] The existing technology has the following problems in using algorithms to achieve phase-free imaging: First, the classic Gerchberg-Saxton and Fienup algorithms have defects such as sensitivity to initial values ​​and slow convergence speed; Second, although Wirtinger Flow (WF) and its improved algorithms improve convergence, the number of measurements required far exceeds the number of voxels, resulting in low data collection efficiency; Third, although the sparse WF (SWF) algorithm reduces the measurement requirements, it requires the target to have extremely high sparsity and is difficult to handle complex extended targets.

[0005] In addition, the above methods face special challenges in microwave frequency band applications: there is strong nonlinear coupling between the target scattering field and the metasurface coding pattern, which makes it difficult to accurately establish the traditional phase retrieval model; the actual measurement noise will significantly deteriorate the convergence stability of the iterative algorithm. Therefore, it is urgent to develop a phase-free computational imaging method suitable for microwave frequency bands that has both low measurement requirements and strong robustness. Summary of the invention

[0006] In view of the problems of complex hardware, poor phase measurement accuracy, and low acquisition efficiency in traditional methods, the present invention proposes a microwave computational imaging method based on programmable metasurface and amplitude measurement to achieve high-precision inversion of target dielectric properties without phase measurement conditions, so as to solve the problems raised in the above background technology. The technical solutions provided by the present invention are as follows: A microwave computational imaging method based on a programmable metasurface and amplitude measurement comprises the following steps: Step 1: Configure the parameters of microwave imaging, receive microwave scattering through a programmable metasurface and a horn antenna, and build a measurement matrix on the programmable metasurface A ; Step 2: Use the phase-free linear measurement model to measure the contrast parameters of the target linearly associated with the received amplitude data; Step 3: Use RAF algorithm to optimize contrast parameters , the optimization result is judged by the least square loss function, and the RAF algorithm includes an initialization process and a gradient iterative optimization process; Step 4, contrast parameter It is related to the dielectric properties by the following equation:

[0007] in is the relative dielectric constant, is the conductivity, is the dielectric constant of vacuum, f is the operating frequency, j is the imaginary unit; The contrast parameters optimized by the RAF algorithm Substituting into the formula, the actual relative dielectric constant to which the contrast parameter is directly mapped is obtained by inversion: and conductivity The spatial distribution of the target structure is formed.

[0008] Preferably, the measurement matrix A No. (m,n) The elements are defined as:

[0009] in Indicates m Programmable metasurface at position r n The radiation field; represents the radiation pattern model of the horn antenna, where r 0 is the horn antenna position; is the free space Green's function.

[0010] Preferably, the programmable metasurface is a 1-bit programmable metasurface, P×Q programmable metasurface units to generate M A random binary code sequence , each sequence contains P×Q The phase state of each unit , No. m Programmable metasurface at position under coding sequence r n The radiation field at is:

[0011] in is the amplitude response of each metasurface unit, D is the unit spacing, k 0 is the free space wave number, and The location The elevation and azimuth angles.

[0012] Preferably, the phase-free linear measurement model is:

[0013] in y is the phase-free amplitude information of the scattered field, n is additive white Gaussian noise, and the noise power is related to the signal-to-noise ratio.

[0014] Preferably, the RAF algorithm initialization process comprises the following steps: Step 3.1.1, from the measured vector y Select a subset of indices S , which contains measurements; Step 3.1.2, measurement matrix A Index subset S The corresponding row vector Assign weight ; Step 3.1.3, solve the initial value by power iteration method: The termination condition of the iteration is residual < 10 -6 Or iterate 500 times; Step 3.1.4, get the initial estimate by normalization and scaling: .

[0015] Preferably, the RAF algorithm gradient iterative optimization process comprises the following steps: Step 3.2.1, from the initial estimate x0 Start gradient iterative optimization, the formula is:

[0016] in is the step size parameter, For the t The weight coefficient of the iteration; Step 3.2.2: When the loss function change rate for 5 consecutive iterations is less than 0.1% or the iteration is 2000 times, it is judged to be converged and the iteration is completed.

[0017] Preferably, Use dynamic step size, initial step size , with a decay factor of 0.95 every 10 iterations.

[0018] Preferably, the weight coefficient Dynamically adjust according to the residual of the current estimate and the measurement vector, , β m is the weight coefficient.

[0019] A microwave computational imaging system based on a programmable metasurface and amplitude measurement includes a programmable metasurface transmitter, a horn antenna receiver and a signal processing unit. The system implements the phase-free microwave computational imaging method described above.

[0020] Preferably, a programmable metasurface transmitter is used for phase and amplitude modulation; a horn antenna receiver is fixed at position r 0 ; Signal processing unit, used to perform measurement matrix construction, RAF algorithm initialization and gradient iterative optimization operations.

[0021] Compared with the prior art, the beneficial effects achieved by the present invention are: The present invention constructs a multidimensional measurement matrix by dynamically controlling the metasurface radiation field pattern, and combines the two-stage optimization strategy of the RAF algorithm - initialization based on energy screening and adaptive gradient iteration, to achieve high-precision inversion of the target dielectric properties under phase-free measurement conditions. The present invention simplifies the hardware control complexity by using a 1-bit programmable metasurface, reduces system cost through a single receiving channel design of a horn antenna, and only retains amplitude data with an intensity measurement model to avoid phase noise interference, and improves computational efficiency with the help of the algorithm's fast convergence characteristics. This technology combines high robustness, low cost and multi-scenario adaptability, and has important application value in security imaging, biomedical testing and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings: Figure 1 Provide an overall flow chart of the method of the present invention; Figure 2 The graph is a relationship curve between the reconstruction error of a complex shape target and the signal-to-noise ratio at different sampling rates according to the method of the present invention; Figure 3 This is a comparison diagram of the reconstruction effect of the method of the present invention on three complex geometric shape targets under different signal-to-noise ratio conditions; Figure 4 A comparison diagram of the true value of the complex dielectric parameter profile of the classic "Austria" target and the reconstruction result of the method of the present invention; Figure 5 The inversion effect error curve diagram of the method of the present invention and other algorithms at different sampling ratios; Figure 6 The figure is a comparison of the reconstruction effect of the method of the present invention and other algorithms on point targets under different sparsity and sampling rate conditions; Figure 7 This is a comparison chart of the reconstruction effect of the method of the present invention and other algorithms on the classic "Austria" test target under the conditions of signal-to-noise ratio SNR=60dB and sampling rate M / N=2.5; Figure 8 This is a comparison diagram of the reconstruction effect of the method of the present invention and other algorithms on the character test target under the conditions of signal-to-noise ratio SNR=60dB and sampling rate M / N=2.5; Fig. 9 This is a comparison chart of the reconstruction effects of the method of the present invention and other algorithms on the "aircraft" test target under the conditions of signal-to-noise ratio SNR=60dB and sampling rate M / N=2.5. DETAILED DESCRIPTION

[0023] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0024] See also Figure 1-Figure 9 , the present invention provides a technical solution:

[0025] Embodiment 1: A microwave computational imaging method based on programmable metasurfaces and amplitude measurement, such as Figure 1 The process shown includes the following steps: Step 1: Configure the parameters of microwave imaging, receive microwave scattering through a programmable metasurface and a horn antenna, and build a measurement matrix on the programmable metasurface A ,matrix A No. (m,n) The elements are defined as:

[0026] in Indicates m Programmable metasurface at position r n The radiation field; represents the radiation pattern model of the horn antenna, where r 0 is the horn antenna position; is the free space Green's function.

[0027] This embodiment provides a specific parameter configuration, which is as follows: Operating frequency , corresponding to the free space wavelength The imaging area is divided into Discrete points , grid spacing ; Number of coding sequences , sampling rate .

[0028] The programmable metasurface used in this embodiment is a 1-bit programmable metasurface. P×Q programmable metasurface units to generate M A random binary code sequence , each sequence contains P×Q The phase state of each unit , No. m Programmable metasurface at position under coding sequence r n The radiation field at is:

[0029] in is the amplitude response of each metasurface unit, , cell spacing , free space wave number , and The location The elevation and azimuth angles.

[0030] Matrix Elements The final storage is a 5184×1296 complex matrix.

[0031] Step 2: Use the phase-free linear measurement model to measure the contrast parameters of the target Linearly related to the received amplitude data:

[0032] in y is the phase-free amplitude information of the scattered field, n is additive white Gaussian noise, and the noise power is related to the signal-to-noise ratio.

[0033] Verify the relationship between reconstruction error and signal-to-noise ratio for complex shape targets, such as Figure 2 As shown in the figure, it can be found that when the signal-to-noise ratio is greater than 20dB, as the signal-to-noise ratio increases, the reconstruction error at each sampling rate decreases. Figure 3 The reconstruction effect comparison chart also proves that under high signal-to-noise ratio conditions, the signal quality is good and the imaging quality is high.

[0034] This embodiment is implemented by the Born approximation model. Based on the weak scattering assumption, the contrast parameter With scattered field E scat Related:

[0035] The incident field E inc is the metasurface radiation field , G is the free space Green's function, and its discrete form is:

[0036] By neglecting the multiple scattering effect, the nonlinear integral equation is simplified to a phase-free linear measurement model The model modulos the received data and retains only the amplitude data, completely eliminating the phase measurement link and avoiding the phase noise source.

[0037] Step 3: Use RAF algorithm to optimize contrast parameters , the optimization result is judged by the least square loss function, and the RAF algorithm includes an initialization process and a gradient iterative optimization process.

[0038] The initialization process adopted in this embodiment includes the following steps: Step 3.1.1, from the measured vector y Select the top 13% of the energy index to construct a subset S , which contains measurements, ; Step 3.1.2, measurement matrix AIndex subset S The corresponding row vector Assign weight ; Furthermore, random weight assignment can be used , I N is the identity matrix with a covariance matrix of NxN, indicating that each dimension is independent and has a variance of 1.

[0039] Step 3.1.3, solve the initial value by power iteration method: The termination condition of the iteration is residual < 10 -6 Or iterate 500 times; Step 3.1.4, get the initial estimate by normalization and scaling: .

[0040] The gradient iterative optimization process adopted in this embodiment includes the following steps: Step 3.2.1, from the initial estimate x 0 Start gradient iterative optimization, the formula is:

[0041] in is the step size parameter, the initial step size =0.5, attenuation factor 0.95 every 10 iterations; is the weight coefficient of the tth iteration, , β m is the weight coefficient.

[0042] Step 3.2.2: When the loss function change rate for 5 consecutive iterations is less than 0.1% or the iteration is 2000 times, it is considered to be converged and the iteration is completed; The loss function is: .

[0043] Step 4, contrast parameter It is related to the dielectric properties by the following equation:

[0044] in is the relative dielectric constant, is the conductivity, is the dielectric constant of vacuum, f is the operating frequency, j is the imaginary unit; The final solution after RAF algorithm optimization Mapped to equivalent contrast:

[0045] The actual relative permittivity to which the contrast parameter is directly mapped is obtained by inversion. and conductivity The spatial distribution of the target structure is formed.

[0046] The result of reconstructing the classic "Austria" using this embodiment is as follows: Figure 4 As shown in the figure, the comparison between the true value of the target complex dielectric parameter profile and the reconstruction result of the method of this embodiment is shown, where the setting x= 0.4-0.3 j , where a, b, c, and d are: Figure a: Real distribution of true values: shows the true dielectric constant of the target model; b: Imaginary distribution of real values: characterizes the loss characteristics of the material (conductivity or equivalent loss factor); Figure c: real part distribution of reconstruction result: spatial distribution of dielectric constant restored by RAF algorithm of the present invention; Figure d: distribution of the imaginary part of the reconstruction result: the spatial distribution of conductivity restored by the RAF algorithm of the present invention.

[0047] Embodiment 2: The method of the present invention (RAF) and other known methods (SWF, WF, TWF) were used for microwave imaging to compare and verify the effects.

[0048] Experiment 1: Comparison of the reconstruction effects of the four algorithms under different sampling ratios. The error curves are shown in Figure 1. Figure 5 shown.

[0049] Experiment 2: Under the conditions of dilution 20, sampling rate 1 and sparseness 80, sampling rate 2, four algorithms, SWF, RAF, WF and TWF, are used to reconstruct point targets. The reconstruction results are as follows: Figure 6 shown.

[0050] Test 3: Under the conditions of SNR=60dB and sampling rate M / N=2.5, four algorithms were used to reconstruct the classic "Austria" test target, character test target, and "aircraft" test target. The reconstruction results are as follows: Figure 7-Figure 9 As shown, a, b, c, and d represent RAF, SWF, WF, and TWF methods respectively.

[0051] Embodiment 3: A microwave computational imaging system based on programmable metasurface and amplitude measurement includes a programmable metasurface transmitter, a horn antenna receiver and a signal processing unit, wherein the programmable metasurface transmitter is used for phase and amplitude modulation; the horn antenna receiver is fixed at position r0; and the signal processing unit is used to perform measurement matrix construction, RAF algorithm initialization and gradient iterative optimization operations. The system is used to implement the phase-free microwave computational imaging method in Example 1.

[0052] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention is described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A microwave computational imaging method based on programmable metasurface and amplitude measurement, characterized in that: The following steps are involved: Step 1: Configure the parameters of microwave imaging, receive microwave scattering through a programmable metasurface and a horn antenna, and build a measurement matrix on the programmable metasurface A ; Step 2: Use the phase-free linear measurement model to measure the contrast parameters of the target linearly associated with the received amplitude data; Step 3: Use RAF algorithm to optimize contrast parameters , the optimization result is judged by the least square loss function, and the RAF algorithm includes an initialization process and a gradient iterative optimization process; Step 4, contrast parameter It is related to the dielectric properties by the following equation: ； in is the relative dielectric constant, is the conductivity, is the dielectric constant of vacuum, f is the operating frequency, j is an imaginary unit; The contrast parameters optimized by the RAF algorithm Substituting into the formula, the actual relative dielectric constant to which the contrast parameter is directly mapped is obtained by inversion: and conductivity The spatial distribution of the target structure is formed.

2. The microwave computational imaging method based on programmable metasurface and amplitude measurement according to claim 1, characterized in that: The measurement matrix A The first ( m,n ) elements are defined as: ； in Indicates m Programmable metasurface at position r n The radiation field; represents the radiation pattern model of the horn antenna, where r 0 is the horn antenna position; is the free space Green's function.

3. The microwave computational imaging method based on programmable metasurface and amplitude measurement according to claim 2, characterized in that: The programmable metasurface is a 1-bit programmable metasurface. P×Q programmable metasurface units to generate M A random binary code sequence , each sequence contains P×Q The phase state of each unit , No. m Programmable metasurface at position under coding sequence r n The radiation field at is: ； in is the amplitude response of each metasurface unit, D is the unit spacing, k 0 is the free space wave number, and The location The elevation and azimuth angles.

4. The microwave computational imaging method based on programmable metasurface and amplitude measurement according to claim 3, characterized in that: The phase-free linear measurement model is: ； in y is the phase-free amplitude information of the scattered field, n is additive white Gaussian noise, and the noise power is related to the signal-to-noise ratio.

5. The microwave computational imaging method based on programmable metasurface and amplitude measurement according to claim 4, characterized in that: The RAF algorithm initialization process includes the following steps: Step 3.1.1, from the measured vector y Select a subset of indices S , which contains measurements; Step 3.1.2, measurement matrix A In and index subset S The corresponding row vector Assign weight ; Step 3.1.3, solve the initial value by power iteration method: The termination condition of the iteration is residual < 10 -6 Or iterate 500 times; Step 3.1.4, get the initial estimate by normalization and scaling: .

6. The microwave computational imaging method based on programmable metasurface and amplitude measurement according to claim 5, characterized in that: The RAF algorithm gradient iterative optimization process includes the following steps: Step 3.2.1, from the initial estimate x 0 Start gradient iterative optimization, the formula is: ； in is the step size parameter, For the t The weight coefficient of the iteration; Step 3.2.2: When the loss function change rate for 5 consecutive iterations is less than 0.1% or the iteration is 2000 times, it is judged to be converged and the iteration is completed.

7. The microwave computational imaging method based on programmable metasurface and amplitude measurement according to claim 6, characterized in that: Use dynamic step size, initial step size , with a decay factor of 0.95 every 10 iterations.

8. The microwave computational imaging method based on programmable metasurface and amplitude measurement according to claim 7, characterized in that: Weight coefficient Dynamically adjust according to the residual of the current estimate and the measurement vector, , β m is the weight coefficient.

9. A microwave computational imaging system based on programmable metasurface and amplitude measurement, comprising a programmable metasurface transmitter, a horn antenna receiver and a signal processing unit, characterized in that: The system implements a microwave computational imaging method based on a programmable metasurface and amplitude measurement as described in any one of claims 1-8.

10. The microwave computational imaging system based on programmable metasurface and amplitude measurement according to claim 9, characterized in that: Programmable metasurface transmitter for phase and amplitude modulation; horn antenna receiver, fixed in position r 0 ; Signal processing unit, used to perform measurement matrix construction, RAF algorithm initialization and gradient iterative optimization operations.

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