A microwave computational imaging method based on programmable metasurface and amplitude measurement

Abstract

The present invention proposes a microwave computational imaging method based on a programmable metasurface and amplitude measurement, comprising the following steps: configuring parameters for microwave imaging and constructing a measurement matrix on the programmable metasurface; linearly correlating the contrast parameter of the measurement target with the scattered field by using a non-phase linear measurement model; optimizing the contrast parameter by using the RAF algorithm, which includes an initialization process and a gradient iteration optimization process; and inverting the contrast parameter optimized by the RAF algorithm to obtain the actual relative parameter for microwave imaging. The present invention realizes high-precision inversion of the target dielectric characteristics under the condition of non-phase measurement by dynamically regulating the radiation field mode of the metasurface to construct a multi-dimensional measurement matrix and combining the two-stage optimization strategy of the RAF algorithm - initialization based on energy screening and adaptive gradient iteration.

Description

Technical Field

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

[0002] Microwave imaging technology analyzes the scattering field distribution of a target under the action of an incident electromagnetic field and inversely calculates the dielectric parameter distribution of the target. It has advantages such as non-contact, non-invasive, and all-weather operation, and has been widely used in fields such as security inspection, non-destructive testing, and biomedicine. 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 imaging blind spots, and requires a large synthetic aperture for high resolution, resulting in low efficiency; RAR requires a phase controller and an amplifier to be configured for each antenna unit, resulting in a large system volume 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 generates spatially diverse illuminations by encoding and regulating the radiation pattern of the metasurface, and combines computational imaging algorithms to achieve efficient imaging, overcoming the dependence of traditional systems on mechanical scanning and complex hardware. However, existing PMS-MCI methods generally adopt coherent detection schemes, which require simultaneous acquisition of the amplitude and phase information of measurement data. In high-frequency band (millimeter wave / terahertz) applications, factors such as probe positioning errors and receiver circuit drift lead to a sharp decline in phase measurement accuracy, severely restricting imaging performance.

[0004] The existing technologies that use algorithms to achieve phase-free imaging have the following problems:

[0005] First, classical Gerchberg-Saxton and Fienup algorithms have defects such as sensitivity to initial values and slow convergence speed;

[0006] Second, although Wirtinger Flow (WF) and its improved algorithms improve convergence, they require the number of measurements to far exceed the number of voxels, resulting in low data acquisition efficiency;

[0007] Third, although the sparse WF (SWF) algorithm reduces the measurement requirements, it requires the target to have an extremely high sparsity and is difficult to process complex extended targets.

[0008] In addition, the above methods also face special challenges in microwave band applications: there is a strong non-linear coupling between the target scattering field and the metasurface coding pattern, making it difficult to accurately establish a traditional phase retrieval model; actual measurement noise will significantly deteriorate the convergence stability of iterative algorithms. Therefore, there is an urgent need to develop a phase-free computational imaging method suitable for the microwave band with low measurement requirements and strong robustness. Summary of the Invention

[0009] In view of the problems in the traditional methods, such as complex hardware, poor phase measurement accuracy, and low acquisition efficiency, the present invention proposes a microwave computational imaging method based on a programmable metasurface and amplitude measurement to achieve high-precision inversion of the dielectric properties of the target under the condition of no phase measurement, so as to solve the problems raised in the above background technology. The technical solution provided by the present invention is as follows:

[0010] A microwave computational imaging method based on a programmable metasurface and amplitude measurement includes the following steps:

[0011] Step 1: Configure the parameters of microwave imaging, receive microwave scattering through a programmable metasurface and a horn antenna, and construct a measurement matrix on the programmable metasurface A ;

[0012] Step 2: Use a non-phase linear measurement model to linearly correlate the contrast parameter of the measurement target with the received amplitude data;

[0013] Step 3: Use the RAF algorithm to optimize the contrast parameter , and judge the optimization result through the least squares loss function. The RAF algorithm includes an initialization process and a gradient iterative optimization process;

[0014] Step 4: The contrast parameter is correlated with the dielectric properties by the following formula:

[0015]

[0016] where is the relative dielectric constant, is the conductivity, is the vacuum dielectric constant, f is the operating frequency, and j is the imaginary unit;

[0017] Substitute the contrast parameter optimized by the RAF algorithm into the formula, and inversely obtain the spatial distribution of the actual relative dielectric constant and conductivity directly mapped by the contrast parameter, and form an image reflecting the target structure.

[0018] Preferably, the A th element of the measurement matrix (m,n) is defined as:

[0019]

[0020] where represents the programmable metasurface at the m th coding sequence at the position r nradiation field; represents the radiation pattern model of the horn antenna, where r 0 is the position of the horn antenna; is the free space Green's function.

[0021] Preferably, the programmable metasurface is a 1-bit programmable metasurface, which is composed of P×Q programmable metasurface units, generating M groups of random binary coding sequences , each sequence contains P×Q phase states of the units , the m th coding sequence, the radiation field of the programmable metasurface at the position r n is:

[0022]

[0023] where is the amplitude response of each metasurface unit, D is the unit spacing, k 0 is the free space wave number, and are the elevation angle and azimuth angle of the position respectively.

[0024] Preferably, the non-phase linear measurement model is:

[0025]

[0026] where y is the non-phase amplitude information of the scattered field, n is the additive Gaussian white noise, and the noise power is related to the signal-to-noise ratio.

[0027] Preferably, the initialization process of the RAF algorithm includes the following steps:

[0028] Step 3.1.1, select an index subset y from the measurement vector S , which contains measurement values;

[0029] Step 3.1.2, assign a weight A to the row vector S corresponding to the index subset in the measurement matrix ;

[0030] Step 3.1.3, solve the initial value by the power iteration method: , the termination condition of the iteration is that the residual < 10 -6 or iterate 500 times;

[0031] Step 3.1.4, obtain the initial estimate through normalized scaling: .

[0032] Preferably, the gradient iteration optimization process of the RAF algorithm includes the following steps:

[0033] Step 3.2.1, start gradient iteration optimization from the initial estimate x 0 , and the formula is:

[0034]

[0035] where is the step size parameter, is the weight coefficient of the t th iteration;

[0036] Step 3.2.2, when the change rate of the loss function for 5 consecutive iterations < 0.1% or iterate 2000 times, it is determined to converge and the iteration is completed.

[0037] Preferably, adopt a dynamic step size, the initial step size , and the attenuation coefficient is 0.95 every 10 iterations.

[0038] Preferably, the weight coefficient is dynamically adjusted according to the residual between the current estimate and the measurement vector, , β m is the weight coefficient.

[0039] A microwave computational imaging system based on a programmable metasurface and amplitude measurement, including a programmable metasurface transmitter, a horn antenna receiver, and a signal processing unit, and this system implements the non-phase microwave computational imaging method described above.

[0040] Preferably, the programmable metasurface transmitter is used for phase and amplitude modulation; the horn antenna receiver is fixed at the position r 0 ; the signal processing unit is used to perform measurement matrix construction, RAF algorithm initialization, and gradient iteration optimization operations.

[0041] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0042] The present invention constructs a multi-dimensional measurement matrix by dynamically regulating the radiation field mode of the metasurface, and combines the two-stage optimization strategy of the RAF algorithm - initialization based on energy screening and adaptive gradient iteration, realizing high-precision inversion of the target dielectric properties under the condition of no phase measurement. The present invention simplifies the hardware control complexity by using a 1-bit programmable metasurface, reduces the system cost through the single-receiving-channel design of a horn antenna, and only retains the amplitude data with the intensity measurement model to avoid phase noise interference, and improves the calculation efficiency by virtue of the fast convergence characteristic of the algorithm. This technology has high robustness, low cost and multi-scenario adaptability, and has important application value in the fields of security inspection imaging, biomedical detection, etc. Description of the Drawings

[0043] The drawings are used to provide further understanding of the present invention, and constitute a part of the specification, and are used to explain the present invention together with the embodiments of the present invention, and do not constitute a limitation to the present invention. In the drawings:

[0044] Figure 1 It is the overall flowchart of the method provided by the present invention;

[0045] Figure 2 It is a relationship curve graph of the reconstruction error of the method of the present invention for complex-shaped targets varying with the signal-to-noise ratio at different sampling rates;

[0046] Figure 3 It is a comparison graph of the reconstruction effects of the method of the present invention for three complex geometric-shaped targets under different signal-to-noise ratio conditions;

[0047] Figure 4 It is a comparison graph 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;

[0048] Figure 5 It is an error curve graph of the inversion effects of the method of the present invention and other algorithms at different sampling ratios;

[0049] Figure 6 It is a comparison graph of the point target reconstruction effects of the method of the present invention and other algorithms under different sparsity and sampling rate conditions;

[0050] Figure 7 It is a comparison graph of the reconstruction effects of the method of the present invention and other algorithms for the classic "Austria" test target under the conditions of signal-to-noise ratio SNR = 60 dB and sampling rate M / N = 2.5;

[0051] Figure 8 It is a comparison graph of the reconstruction effects of the method of the present invention and other algorithms for the character test target under the conditions of signal-to-noise ratio SNR = 60 dB and sampling rate M / N = 2.5;

[0052] Figure 9Comparison diagram of the reconstruction effects of the method of the present invention and other algorithms on the "airplane" test target under the conditions of signal-to-noise ratio SNR = 60 dB and sampling rate M / N = 2.5. Detailed implementation manners

[0053] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0054] Please refer to Figures 1 - 9 , the present invention provides a technical solution:

[0055] Embodiment 1:

[0056] A microwave computational imaging method based on a programmable metasurface and amplitude measurement, as shown in the following process, includes the following steps: Figure 1 as shown, includes the following steps:

[0057] Step 1, configure the parameters of microwave imaging, receive microwave scattering through a programmable metasurface and a horn antenna, and construct a measurement matrix on the programmable metasurface. The A matrix A The (m,n) th element is defined as:

[0058]

[0059] where represents the radiation field of the programmable metasurface at the position m under the r n th coding sequence; represents the radiation pattern model of the horn antenna, where r 0 is the position of the horn antenna; is the free space Green's function.

[0060] This embodiment gives a specific parameter configuration, which is as follows:

[0061] Operating frequency , the corresponding free space wavelength ; the imaging area is divided into discrete points , the grid spacing ; the number of coding sequences , the sampling rate .

[0062] The programmable metasurface adopted in this embodiment is a 1-bit programmable metasurface, which is composed of P×Q programmable metasurface units, generating M groups of random binary coding sequences . Each sequence contains P×Q phase states of the units . The radiation field of the programmable metasurface at position m under the r n th coding sequence is:

[0063]

[0064] where is the amplitude response of each metasurface unit, , the unit spacing , the free-space wavenumber , and are the elevation angle and azimuth angle of position respectively.

[0065] The matrix element is finally stored as a 5184×1296 complex matrix.

[0066] Step 2: Use the non-phase linear measurement model to linearly correlate the contrast parameter of the measurement target with the received amplitude data:

[0067]

[0068] where y is the non-phase amplitude information of the scattered field, n is the additive Gaussian white noise, and the noise power is correlated with the signal-to-noise ratio.

[0069] Verify the relationship between the reconstruction error of the complex-shaped target and the change of the signal-to-noise ratio. As Figure 2 shown, it can be found that when the signal-to-noise ratio is greater than 20 dB, with the increase of the signal-to-noise ratio, the reconstruction errors at each sampling rate are all reduced. Figure 3 The comparison diagram of the reconstruction effect of

[0070] also proves that under the condition of high signal-to-noise ratio, the signal quality is good and the imaging quality is good. This embodiment is implemented through the Born approximation model. Based on the weak scattering assumption, the contrast parameter E scat is correlated with the scattered field

[0071]

[0072] where the incident field Einc For the above-mentioned metasurface radiation field , G is the free space Green's function, and its discrete form is:

[0073]

[0074] By neglecting the multiple scattering effect, the non-linear integral equation is simplified to a non-phase linear measurement model . This model takes the modulus of the received data, only retains the amplitude data, completely eliminates the phase measurement link, and avoids the phase noise source.

[0075] Step 3: Optimize the contrast parameter using the RAF algorithm , and judge the optimization result through the least square loss function. The RAF algorithm includes an initialization process and a gradient iterative optimization process.

[0076] The initialization process adopted in this embodiment includes the following steps:

[0077] Step 3.1.1: Select the indices with the top 13% energy from the measurement vector y to construct a subset S , which contains measurement values, ;

[0078] Step 3.1.2: Assign weights A to the row vectors S corresponding to the index subset in the measurement matrix ;

[0079] Furthermore, random weight assignment can be adopted , I N is the identity matrix with covariance matrix NxN, indicating that each dimension is independent and the variance is 1.

[0080] Step 3.1.3: Solve the initial value through the power iteration method: , and the termination condition of the iteration is that the residual < 10 -6 or iterate 500 times;

[0081] Step 3.1.4: Obtain the initial estimate through normalization scaling: .

[0082] The gradient iterative optimization process adopted in this embodiment includes the following steps:

[0083] Step 3.2.1: Start the gradient iterative optimization from the initial estimate x 0 , and the formula is:

[0084]

[0085] where is the step parameter, and the initial step = 0.5, and the decay coefficient is 0.95 every 10 iterations;

[0086] is the weight coefficient at the t-th iteration, , β m is the weight coefficient.

[0087] Step 3.2.2, when the change rate of the loss function for 5 consecutive iterations < 0.1% or the iteration reaches 2000 times, it is determined to converge and the iteration is completed;

[0088] where the loss function is: .

[0089] Step 4, the contrast parameter is related to the dielectric properties by the following formula:

[0090]

[0091] where is the relative dielectric constant, is the conductivity, is the vacuum permittivity, f is the operating frequency, and j is the imaginary unit;

[0092] The final solution optimized by the RAF algorithm is mapped to the equivalent contrast:

[0093]

[0094] The actual relative dielectric constant and conductivity directly mapped by the contrast parameter are obtained by inversion, and the spatial distribution is formed to create an image reflecting the target structure.

[0095] The result of reconstructing the classic "Austria" using this embodiment is as Figure 4 shown. The figure shows the comparison between the true value of the target complex dielectric parameter profile and the reconstruction result of the method of this embodiment, where x= 0.4 - 0.3 j , and the a, b, c, and d figures are respectively:

[0096] Figure a: Real part distribution of the true value: showing the true dielectric constant of the target model;

[0097] Figure b: Imaginary part distribution of the true value: characterizing the loss characteristics of the material (conductivity or equivalent loss factor);​​​​​​​​​

[0098] Figure c: Real part distribution of the reconstruction result: Spatial distribution of the dielectric constant restored by the RAF algorithm based on the present invention;

[0099] Figure d: Imaginary part distribution of the reconstruction result: Spatial distribution of the conductivity restored by the RAF algorithm based on the present invention.

[0100] Example 2:

[0101] Effect comparison and verification test of the method (RAF) of the present invention and other known methods (SWF, WF, TWF) for microwave imaging.

[0102] Test 1: Compare the reconstruction effects of the four algorithms under different sampling ratios, and the error curves are as Figure 5 shown.

[0103] Test 2: Under the conditions of dilution 20, sampling rate 1, sparsity 80, and sampling rate 2, use the four algorithms of SWF, RAF, WF, and TWF to reconstruct point targets, and the reconstruction effects are as Figure 6 shown.

[0104] Test 3: Under the conditions of signal-to-noise ratio SNR = 60 dB and sampling rate M / N = 2.5, use the four algorithms to reconstruct the classic "Austria" test target, character test target, and "airplane" test target, and the reconstruction effects are as Figures 7 - 9 shown, where Figures a, b, c, and d represent the RAF, SWF, WF, and TWF methods respectively.

[0105] Example 3:

[0106] A microwave computational imaging system based on a programmable metasurface and amplitude measurement, comprising a programmable metasurface transmitter, a horn antenna receiver, and a signal processing unit. The programmable metasurface transmitter is used for phase and amplitude modulation; the horn antenna receiver is fixed at position r0; the signal processing unit is used to perform measurement matrix construction, RAF algorithm initialization, and gradient iteration optimization operations. This system is used to implement the phase-free microwave computational imaging method in Example 1.

[0107] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, 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 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 measurement 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.

Images