Polarization diffraction tomography method, apparatus and device based on coherence factor

Abstract

The application relates to a polarization diffraction tomography method, device and equipment based on a coherence factor. The method comprises the following steps: sampling a target based on a sparse MIMO array full polarization radar in a three-dimensional electromagnetic inversion scene, acquiring a scattering field spectrum of the target, and acquiring a contrast function spectrum through linear mapping; sequentially performing polarization fusion transformation, coordinate transformation and decoupling on the contrast function spectrum, correcting dielectric constant spectrum and conductivity spectrum mixed with multiple frequencies by adopting a multi-frequency mixed spectrum correction algorithm, performing distance normalization two-dimensional coherence factor weighting on the corrected dielectric constant spectrum and conductivity spectrum according to the scattering field of the target, obtaining a reconstructed dielectric constant profile and a reconstructed conductivity profile of the target, and completing polarization diffraction tomography of the target. By adopting the method, the precision and accuracy of target quantitative inversion can be improved by suppressing grating lobe artifacts and noise under the condition of spatial undersampling.

Description

Technical Field

[0001] This application relates to the field of electromagnetic inversion technology, and in particular to a polarization diffraction tomography method, apparatus and equipment based on coherence factor. Background Technology

[0002] Electromagnetic inverse scattering (EISP) is a nonlinear problem based on the scattering of incident waves by a measured object. By measuring the scattering field outside the object or its far-field mode, the physical and geometric properties of the object, including its location, size, quantity, boundaries, and electromagnetic parameter distribution, can be inverted or reconstructed. It has wide applications in medicine, geophysics, and civilian fields.

[0003] Over the past few decades, electromagnetic backscattering imaging technology has become increasingly sophisticated, and many different inversion methods have been developed to more effectively and reliably detect unknown scatterers within a region. Diffraction tomography (DT) is a linear method for solving the electromagnetic backscattering problem. It considers diffraction effects and uses the Born or Rytov approximation to make the scattered field linearly related to the contrast function. It achieves target imaging by calculating the spectral relationship between the target's inherent properties and the multi-angle scattered echo signals. However, traditional DT algorithms require ideal radar detection conditions, such as sufficient spatial sampling, rich frequency diversity, a large viewing angle, or simultaneous acquisition of transmission and reflection data. In practical radar systems, achieving complete target object detection at an acceptable cost remains challenging. In practical applications, sparse arrays with a limited number of elements and large aperture spacing are often used to reduce system complexity and save costs. However, due to the spatial undersampling problem of sparse arrays, the electromagnetic inversion results are affected by artifacts caused by strong grating lobes, which severely degrades the image quality of the electromagnetic inversion. Summary of the Invention

[0004] Therefore, it is necessary to provide a polarization diffraction tomography method, apparatus, and device based on coherence factor that can improve target inversion accuracy and imaging quality when solving electromagnetic backscattering problems.

[0005] A polarization diffraction tomography method based on coherence factor, the method comprising:

[0006] In a three-dimensional electromagnetic inversion scenario, a fully polarimetric radar based on a sparse MIMO array samples the target, obtains the target's scattered field, performs a Fourier transform, and obtains the target's scattered field spectrum.

[0007] The contrast function spectrum of the target is calculated based on the linear relationship between the target's scattered field spectrum and the target's contrast function spectrum. Then, a polarization fusion transformation is performed on the contrast function spectrum to obtain the polarization fusion transformed contrast function spectrum.

[0008] The contrast function spectrum after polarization fusion transformation is subjected to coordinate transformation to obtain the contrast function spectrum after coordinate transformation;

[0009] By sequentially performing inverse fast Fourier transform and three-dimensional fast Fourier transform on the contrast function spectrum after coordinate transformation, the dielectric constant spectrum and conductivity spectrum of the target multi-frequency aliasing are decoupled and obtained. Then, a multi-frequency aliasing spectrum correction algorithm is used to correct the dielectric constant spectrum and conductivity spectrum of the multi-frequency aliasing, and the corrected dielectric constant spectrum and conductivity spectrum are obtained.

[0010] Based on the target's scattering field, the corrected dielectric constant spectrum and conductivity spectrum are weighted by a range-normalized two-dimensional coherence factor to obtain the reconstructed dielectric constant profile and reconstructed conductivity profile of the target, thus completing the polarization diffraction tomography imaging of the target.

[0011] In one embodiment, in a three-dimensional electromagnetic inversion scenario, a fully polarimetric radar based on a sparse MIMO array samples the target to obtain the target's scattered field, including:

[0012] In a three-dimensional electromagnetic inversion scenario, a fully polarized radar based on a sparse MIMO array samples a target located within the detection region Ω in free space. The radar transmitting antenna radiates electromagnetic waves towards the target as the incident field, and the radar receiving antenna samples the target's scattered field, denoted as...

[0013]

[0014] Among them, E tot For the total field, k = ω(ε0μ0) 1 / 2 Let ω be the wavenumber corresponding to a certain radar frequency, ω be the angular frequency, and ε0 and μ0 be the permittivity and permeability of free space, respectively. Let r be the dyadic Green's function. R The coordinates of the radar receiving antenna, r T Let represent the coordinates of the radar transmitting antenna, r represent the coordinates of the target and r∈Ω, and χ(r,k) be the contrast function of the target.

[0015] In one embodiment, the contrast function spectrum of the target is obtained by calculating based on the linear relationship between the target's scattered field spectrum and the target's contrast function spectrum, and is expressed as follows:

[0016]

[0017] Where j represents the imaginary unit, The scattered field spectrum of the target. As the first intermediate variable, The second intermediate variable is z0, which represents the position of the antenna array, and k is the second intermediate variable.x It is the x-component of the scattered field spectrum at the receiving antenna, k' x It is the x-component of the scattered field spectrum at the transmitting antenna, k y With k' y These are the y-components of the scattered field spectrum at the receiving antenna and the y-component of the scattered field spectrum at the transmitting antenna, respectively, with x and y being the horizontal and vertical axes, respectively; I(ω) is the spectral amplitude of the incident field at a certain frequency. Indicates the polarization direction of the receiving antenna. Indicates the polarization direction of the transmitting antenna; This represents the spectral domain form of the receiving antenna's dyadic Green's function. K represents the spectral domain form of the dyadic Green's function of the transmitting antenna; X =k x -k′ x As the first component, K Y =k y -k′ y For the second component, K Z =γ res +γ′ res This is the third component.

[0018] In one embodiment, a polarization fusion transform is performed on the contrast function spectrum to obtain the polarization fusion transformed contrast function spectrum, denoted as:

[0019]

[0020] Where PFT{·} represents polarization fusion transformation.

[0021] In one embodiment, a coordinate transformation is performed on the contrast function spectrum after polarization fusion transformation to obtain the coordinate-transformed contrast function spectrum, including:

[0022] Spectrum of contrast function after polarization fusion transformation Discretization is performed to obtain the x component k′ of the scattered field spectrum at the transmitting antenna. xx Discretized into k′ x0 ,k' x1 ,k' x2 ,…,k' xl ,…,k' xL-1 And the y component k′ of the scattered field spectrum at the transmitting antenna. y Discretized into k′ y0 ,k' y1 ,k' y2 ,…,k' yi ,…,k' yI-1 Among them, k' xl and k' yi They represent k′ respectively xThe l-th discrete component and k′ y The i-th discrete component, l = 0, 1, ..., L-1 and L is k′ x The number of discrete numbers, i = 0, 1, ..., I-1 and I is k′ y The number of discrete numbers;

[0023] According to k' xl and k' yi The discretized first, second, and third components are calculated and represented as follows:

[0024] K Xl =k x -k' xl ,K Yi =k y -k' yi ;

[0025]

[0026] Among them, K Xl For the first component K X Discrete components, K Yi For the second component K Y The discrete components, and K Xl and K Yi Uniform arrangement; K Zli For the third component K Z Discrete components, K Zli Non-uniform arrangement and K Zli k is a real number; x It is the x-component of the scattered field spectrum at the receiving antenna, k y It is the y-component of the scattered field spectrum at the receiving antenna, where x and y are the horizontal and vertical axes, respectively, and k is the wave number corresponding to a certain radar frequency;

[0027] By merging the same K Zli Value pair K Zli The contrast function spectrum is updated and arranged in non-decreasing order to obtain the spectrum distributed on a uniform grid. And on Perform three-dimensional linear interpolation to obtain the spectrum of the contrast function distributed in Cartesian coordinates.

[0028] Iterate through all k' xl and k' yi Repeat the coordinate transformation steps described above, and iterate through the obtained coordinates. By merging the results, we obtain the spectrum of the contrast function after coordinate transformation.

[0029] In one embodiment, the dielectric constant spectrum and conductivity spectrum of the target multi-frequency aliasing are obtained by sequentially performing inverse fast Fourier transform and three-dimensional fast Fourier transform on the contrast function spectrum after coordinate transformation, including:

[0030] By performing an inverse fast Fourier transform on the contrast function spectra at different frequencies after coordinate transformation, the dielectric constant and conductivity at each frequency are obtained, expressed as follows:

[0031] χ εn (r)=Re{χ n (r)},χ σn (r)=-Im{χ n (r)};

[0032] Where, χ εn (r) represents the dielectric constant at each frequency, and χ σn (r) represents the conductivity at each frequency, r represents the coordinates of the target, Re{} represents taking the real part, and Im{} represents taking the imaginary part; χ n (r) is the contrast function at the nth frequency, χ n (r) is the spectrum of the contrast function at the nth frequency after coordinate transformation. The result is obtained by inverse fast Fourier transform, where n = 1, 2, ..., N, and N = (f max -f min ) / Δf+1 is the total number of frequencies, f max For the maximum frequency, f min The minimum frequency is Δf, where Δf is the frequency step size.

[0033] For χ εn (r) and χ σn (r) Perform a three-dimensional fast Fourier transform to obtain the dielectric constant spectrum of multi-frequency aliasing at N frequencies. and conductivity spectrum

[0034] In one embodiment, a multi-frequency aliasing spectrum correction algorithm is used to correct the dielectric constant spectrum and conductivity spectrum of multi-frequency aliasing, resulting in corrected dielectric constant spectrum and conductivity spectrum, including:

[0035] A multi-frequency aliasing spectrum correction algorithm is used to analyze the dielectric constant spectrum of multi-frequency aliasing at N frequencies. and conductivity spectrum After correction, the corrected dielectric constant spectrum is obtained. and the corrected conductivity spectrum They are respectively represented as

[0036]

[0037] Where, ω n =2π(f min +nΔf) is the nth angular frequency; The dielectric constant spectrum of multi-frequency aliasing at N frequencies The weighting factor at the nth frequency and Conductivity spectrum of multi-frequency aliasing at N frequencies The weighting factor at the nth frequency and and They are respectively and Phase information, and They are respectively and The maximum amplitude.

[0038] In one embodiment, the corrected dielectric constant spectrum and conductivity spectrum are weighted by a range-normalized two-dimensional coherence factor based on the target's scattering field to obtain the reconstructed dielectric constant profile and reconstructed conductivity profile of the target, respectively expressed as:

[0039]

[0040]

[0041] in, To reconstruct the dielectric constant profile, To reconstruct the conductivity profile, ε rb =1 represents the relative permittivity in free space, r represents the target's coordinates, k represents the wavenumber corresponding to a certain radar frequency, and IFT represents the inverse Fourier transform. The distance-normalized two-dimensional coherence factor is represented as:

[0042]

[0043] in, Let represent the coherence factor, q and p represent the discrete positions of the q-th transmitting antenna and the p-th receiving antenna of the radar, respectively, and Q and P represent the number of discrete positions of the transmitting antenna and the receiving antenna of the radar, respectively. k represents the coherent signal in spatial subsets. min k max The minimum frequency f are respectively min Corresponding wave number and maximum frequency f max The corresponding wave number, where n represents the nth frequency, N is the total number of frequencies, j represents the imaginary unit, and r R The coordinates of the radar receiving antenna, r TThis represents the coordinates of the radar transmitting antenna, where c is the speed of light, and E is the speed of light. sct (r R ,r T (k) represents the target's scattered field, and f is the radar frequency. This represents the coherence factor of the incoherent summation at different frequencies. This represents a coherent signal within a frequency subset.

[0044] A polarization diffraction tomography device based on coherence factor, the device comprising:

[0045] The target detection module is used to sample the target in a three-dimensional electromagnetic inversion scenario using a fully polarized radar based on a sparse MIMO array, obtain the target's scattered field, and perform a Fourier transform to obtain the target's scattered field spectrum.

[0046] The polarization fusion transformation module is used to calculate the target's contrast function spectrum based on the linear relationship between the target's scattered field spectrum and the target's contrast function spectrum, and then perform polarization fusion transformation on the contrast function spectrum to obtain the polarization fusion transformed contrast function spectrum.

[0047] The coordinate transformation module is used to perform coordinate transformation on the contrast function spectrum after polarization fusion transformation to obtain the contrast function spectrum after coordinate transformation.

[0048] The decoupling correction module is used to decouple the dielectric constant spectrum and conductivity spectrum of the target multi-frequency aliasing by sequentially performing inverse fast Fourier transform and three-dimensional fast Fourier transform on the contrast function spectrum after coordinate transformation. Then, the multi-frequency aliasing spectrum correction algorithm is used to correct the dielectric constant spectrum and conductivity spectrum of the multi-frequency aliasing to obtain the corrected dielectric constant spectrum and conductivity spectrum.

[0049] The coherence factor weighting module is used to perform range-normalized two-dimensional coherence factor weighting on the corrected dielectric constant spectrum and conductivity spectrum based on the target's scattering field, thereby obtaining the reconstructed dielectric constant profile and reconstructed conductivity profile of the target and completing the polarization diffraction tomography imaging of the target.

[0050] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to perform the following steps:

[0051] In a three-dimensional electromagnetic inversion scenario, a fully polarimetric radar based on a sparse MIMO array samples the target, obtains the target's scattered field, performs a Fourier transform, and obtains the target's scattered field spectrum.

[0052] The contrast function spectrum of the target is calculated based on the linear relationship between the target's scattered field spectrum and the target's contrast function spectrum. Then, a polarization fusion transformation is performed on the contrast function spectrum to obtain the polarization fusion transformed contrast function spectrum.

[0053] The contrast function spectrum after polarization fusion transformation is subjected to coordinate transformation to obtain the contrast function spectrum after coordinate transformation;

[0054] By sequentially performing inverse fast Fourier transform and three-dimensional fast Fourier transform on the contrast function spectrum after coordinate transformation, the dielectric constant spectrum and conductivity spectrum of the target multi-frequency aliasing are decoupled and obtained. Then, a multi-frequency aliasing spectrum correction algorithm is used to correct the dielectric constant spectrum and conductivity spectrum of the multi-frequency aliasing, and the corrected dielectric constant spectrum and conductivity spectrum are obtained.

[0055] Based on the target's scattering field, the corrected dielectric constant spectrum and conductivity spectrum are weighted by a range-normalized two-dimensional coherence factor to obtain the reconstructed dielectric constant profile and reconstructed conductivity profile of the target, thus completing the polarization diffraction tomography imaging of the target.

[0056] The aforementioned polarization diffraction tomography method based on coherence factor has the following technical advantages:

[0057] 1. This application uses a fully polarimetric radar with a sparse MIMO array to sample targets. Since the fully polarimetric radar has four polarizations of target scattering data, including horizontal transmission and reception (HH), horizontal transmission and vertical reception (HV), vertical transmission and horizontal reception (VH), and vertical transmission and vertical reception (VV), the polarization signal carries more useful information about the target. It can make full use of the advantages of polarization diversity and avoid the adverse effects of spatial undersampling of sparse array on quantitative inversion. While simplifying the radar system hardware design and saving costs, it enhances the accuracy and detail of target detection and electromagnetic parameter inversion.

[0058] 2. This application employs a multi-frequency aliasing spectrum correction algorithm to correct the dielectric constant spectrum and conductivity spectrum of multi-frequency aliasing, thereby avoiding the adverse effects of redundant information (aliasing spectrum) on quantitative inversion, reducing the reconstruction error of dielectric constant profile and conductivity profile, and further improving the accuracy of electromagnetic parameter inversion and the quality of inversion imaging.

[0059] 3. This application uses a distance-normalized two-dimensional coherence factor to weight the corrected dielectric constant spectrum and conductivity spectrum, thereby enhancing coherence features to suppress grating lobe artifacts and noise in imaging, thus improving the reconstruction accuracy of the target dielectric constant and conductivity, and further improving the clarity of target inversion imaging. It is applicable to inversion imaging of weak and non-weak scatterers. Attached Figure Description

[0060] Figure 1 This is a schematic flowchart of a polarization diffraction tomography method based on coherence factor in one embodiment.

[0061] Figure 2 This is a schematic diagram of the geometric structure of a three-dimensional electromagnetic inversion in one embodiment;

[0062] Figure 3 For a specific k in one embodiment, from (o,k) x ,k' x ,k y ,k' y ) to (o,K X ,K Y ,K Z A schematic diagram of coordinate transformation; Figure 3 (a) is (o,k) x ,k' x ,k y ,k' y Coordinate system Figure 3 (b) is (o,K) X ,K Y ,K Z Coordinate system;

[0063] Figure 4 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0065] In one embodiment, such as Figure 1 As shown, a polarization diffraction tomography method based on coherence factor is provided, including the following steps:

[0066] Step S1: In the three-dimensional electromagnetic inversion scenario, the target is sampled by a fully polarimetric radar based on a sparse MIMO array to obtain the target's scattered field and perform a Fourier transform to obtain the target's scattered field spectrum.

[0067] Step S2: Calculate the target's contrast function spectrum based on the linear relationship between the target's scattered field spectrum and the target's contrast function spectrum, and perform a polarization fusion transformation on the contrast function spectrum to obtain the polarization fusion transformed contrast function spectrum.

[0068] Step S3: Perform coordinate transformation on the contrast function spectrum after polarization fusion transformation to obtain the contrast function spectrum after coordinate transformation.

[0069] Step S4: By sequentially performing inverse fast Fourier transform and three-dimensional fast Fourier transform on the contrast function spectrum after coordinate transformation, the dielectric constant spectrum and conductivity spectrum of the target multi-frequency aliasing are decoupled and obtained. Then, a multi-frequency aliasing spectrum correction algorithm is used to correct the dielectric constant spectrum and conductivity spectrum of the multi-frequency aliasing, and the corrected dielectric constant spectrum and conductivity spectrum are obtained.

[0070] Step S5: Based on the target's scattering field, the corrected dielectric constant spectrum and conductivity spectrum are weighted by a range-normalized two-dimensional coherence factor to obtain the reconstructed dielectric constant profile and reconstructed conductivity profile of the target, thus completing the polarization diffraction tomography imaging of the target.

[0071] In one embodiment, in a three-dimensional electromagnetic inversion scenario, a fully polarimetric radar based on a sparse MIMO array samples the target to obtain the target's scattered field, including:

[0072] like Figure 2 As shown, in a three-dimensional electromagnetic inversion scenario, a fully polarized radar based on a sparse MIMO array samples a target located within the detection region Ω in free space. The radar transmitting antenna (Tx) radiates electromagnetic waves towards the target as the incident field, and the radar receiving antenna (Rx) samples and obtains the target's scattered field, denoted as...

[0073]

[0074] Among them, E tot For the total field, k = ω(ε0μ0) 1 / 2 Let ω be the wavenumber corresponding to a certain frequency of the radar, and ω be the angular frequency. From ω = 2πf, we know that the definition of k can also be written as k = 2πf(ε0μ0). 1 / 2 ε0 is a quantity that varies with frequency f; ε0 and μ0 are the permittivity and permeability of free space, respectively. For the dyadic Green's function, The coordinates of the radar receiving antenna, x R y R These are the coordinates on the x and y axes in the receiving antenna coordinate system. The coordinates of the radar transmitting antenna, x T y T These are the coordinates on the x-axis and y-axis in the transmitting antenna coordinate system. Let r represent the coordinates of the target and r∈Ω. Specifically, Tx and Rx are used to detect the region Ω on the plane Σ: z=z0, where z0 is the position of the antenna array, and each antenna is modeled as a dipole polarized along the x-axis or y-axis; χ(r,k) is the contrast function of the target and is defined as the following complex number:

[0075]

[0076] The unknown in the inversion problem is the relative permittivity ε. r (r) and conductivity σ(r);

[0077] The dyadic Green's function is expressed as:

[0078]

[0079] in, k is the first intermediate variable. x It is the x-component of the scattered field spectrum at the receiving antenna, k y It is the y-component of the scattered field spectrum at the receiving antenna, and the spectral domain form of the dyadic Green's function is:

[0080]

[0081] Among them, z R The coordinates are on the z-axis in the receiving antenna coordinate system.

[0082] In one embodiment, the contrast function spectrum of the target is obtained by calculating based on the linear relationship between the target's scattered field spectrum and the target's contrast function spectrum, and is expressed as follows:

[0083]

[0084] Where j represents the imaginary unit, The scattered field spectrum of the target. As the first intermediate variable, The second intermediate variable is z0, which represents the position of the antenna array, and k is the second intermediate variable. x It is the x-component of the scattered field spectrum at the receiving antenna, k' x It is the x-component of the scattered field spectrum at the transmitting antenna, k y With k' y These are the y-components of the scattered field spectrum at the receiving antenna and the y-component of the scattered field spectrum at the transmitting antenna, respectively, with x and y being the horizontal and vertical axes, respectively; I(ω) is the spectral amplitude of the incident field at a certain frequency. Indicates the polarization direction of the receiving antenna. Indicates the polarization direction of the transmitting antenna; This represents the spectral domain form of the receiving antenna's dyadic Green's function. K represents the spectral domain form of the dyadic Green's function of the transmitting antenna; X =k x -k′ x As the first component, K Y =k y -k′ y For the second component, K Z =γres +γ′ res This is the third component.

[0085] Furthermore, the contrast function calculated from the spectrum of the target's contrast function can be expressed as follows:

[0086]

[0087] The reason for using approximate equality in the above formula is due to the limitations of radar observation aperture and spectrum range, so regarding K... X K X and K Z The triple integral range cannot completely cover the spectral domain space of the target object's contrast.

[0088] In one embodiment, a polarization fusion transform is performed on the contrast function spectrum to obtain the polarization fusion transformed contrast function spectrum, denoted as:

[0089]

[0090] Where PFT{·} represents polarization fusion transformation. Specifically, this application considers co-polarization fusion (COPF), cross-polarization fusion (CRPF), and full polarization fusion (FPF) diffraction tomography, based on the target's contrast function spectrum. The polarization direction is from To simplify the description, this application performs a polarization fusion transform on the contrast function spectrum to obtain the polarization fusion transformed contrast function spectrum. The purpose of the polarization fusion transform is to improve the inversion performance. Furthermore, for multiple polarization measurements, the transformation relationships of the three polarization fusion methods are shown in Table 1.

[0091] Table 1. Transformation Relationships of Three Polarization Fusion

[0092]

[0093] in, It is a unit vector.

[0094] In one embodiment, a coordinate transformation is performed on the contrast function spectrum after polarization fusion transformation to obtain the coordinate-transformed contrast function spectrum, including:

[0095] Spectrum of contrast function after polarization fusion transformation Discretization is performed to obtain the x component k′ of the scattered field spectrum at the transmitting antenna. xx Discretized into k′ x0 ,k' x1 ,k' x2 ,…,k' xl ,…,k' xL-1And the y component k′ of the scattered field spectrum at the transmitting antenna. y Discretized into k′ y0 ,k' y1 ,k' y2 ,…,k' yi ,…,k' yI-1 Among them, k' xl and k' yi They represent k′ respectively x The l-th discrete component and k′ y The i-th discrete component, l = 0, 1, ..., L-1 and L is k′ x The number of discrete numbers, i = 0, 1, ..., I-1 and I is k′ y The number of discrete numbers;

[0096] According to k' xl and k' yi The discretized first, second, and third components are calculated and represented as follows:

[0097] K Xl =k x -k' xl ,K Yi =k y -k' yi ;

[0098]

[0099] Among them, K Xl For the first component K X Discrete components, K Yi For the second component K Y The discrete components, and K Xl and K Yi Uniform arrangement; K Zli For the third component K Z Discrete components, K Zli Non-uniform arrangement and K Zli k is a real number; x It is the x-component of the scattered field spectrum at the receiving antenna, k y It is the y-component of the scattered field spectrum at the receiving antenna, where x and y are the horizontal and vertical axes, respectively, and k is the wave number corresponding to a certain radar frequency;

[0100] By merging the same K Zli Value pair K Zli The contrast function spectrum is updated and arranged in non-decreasing order to obtain the spectrum distributed on a uniform grid. And on Perform three-dimensional linear interpolation to obtain the spectrum of the contrast function distributed in Cartesian coordinates.

[0101] Iterate through all k' xl and k' yi Repeat the coordinate transformation steps described above, and iterate through the obtained coordinates. By merging the results, we obtain the spectrum of the contrast function after coordinate transformation.

[0102] It is understandable that, based on the expression for the spectrum of the target's contrast function, and The coordinates are inconsistent. Because the sampling points have non-Cartesian coordinates in the spectral domain, it is necessary to first interpolate the non-Cartesian sampling data to a uniformly distributed grid of Cartesian coordinates. In this application, a specific k-value is obtained from (o,k) x ,k' x ,k y ,k' y ) to (o,K X ,K Y ,K Z Coordinate transformations such as Figure 3 As shown; where, Figure 3 (a) is (o,k) x ,k' x ,k y ,k' y Coordinate system Figure 3 (b) is (o,K) X ,K Y ,K Z Coordinate system.

[0103] In one embodiment, the dielectric constant spectrum and conductivity spectrum of the target multi-frequency aliasing are obtained by sequentially performing inverse fast Fourier transform and three-dimensional fast Fourier transform on the contrast function spectrum after coordinate transformation, including:

[0104] By performing an inverse fast Fourier transform on the contrast function spectra at different frequencies after coordinate transformation, the dielectric constant and conductivity at each frequency are obtained, expressed as follows:

[0105] χ εn (r)=Re{χ n (r)},χ σn (r)=-Im{χ n (r)};

[0106] Where, χ εn (r) represents the dielectric constant at each frequency, and χ σn (r) represents the conductivity at each frequency, r represents the coordinates of the target, Re{} represents taking the real part, and Im{} represents taking the imaginary part; χ n (r) is the contrast function at the nth frequency, χ n(r) is the spectrum of the contrast function at the nth frequency after coordinate transformation. The result is obtained by inverse fast Fourier transform, where n = 1, 2, ..., N, and N = (f max -f min ) / Δf+1 is the total number of frequencies, f max For the maximum frequency, f min The minimum frequency is Δf, where Δf is the frequency step size.

[0107] For χ εn (r) and χ σn (r) Perform a three-dimensional fast Fourier transform to obtain the dielectric constant spectrum of multi-frequency aliasing at N frequencies. and conductivity spectrum

[0108] In one embodiment, a multi-frequency aliasing spectrum correction algorithm is used to correct the dielectric constant spectrum and conductivity spectrum of multi-frequency aliasing, resulting in corrected dielectric constant spectrum and conductivity spectrum, including:

[0109] A multi-frequency aliasing spectrum correction algorithm is used to analyze the dielectric constant spectrum of multi-frequency aliasing at N frequencies. and conductivity spectrum After correction, the corrected dielectric constant spectrum is obtained. and the corrected conductivity spectrum They are respectively represented as

[0110]

[0111] Where, ω n =2π(f min +nΔf) is the nth angular frequency; The dielectric constant spectrum of multi-frequency aliasing at N frequencies The weighting factor at the nth frequency and Conductivity spectrum of multi-frequency aliasing at N frequencies The weighting factor at the nth frequency and and They are respectively and Phase information, and They are respectively and The maximum amplitude. Due to χ ε and χ σ They are all real functions, and can be easily obtained: for Conjugate; Similarly.

[0112] It is understandable that in a multi-viewpoint, multi-base, multi-frequency configuration, a "speaker aliasing region" exists in the multi-frequency spatial spectrum. It is important to note that aliasing exists within the spectrum of any two different frequencies. The actual multi-frequency aliasing region is a superposition of multiple "speaker aliasing regions," with partial overlap in spectral coverage. Without fine processing, this can introduce reconstruction errors into the given inversion. Therefore, a multi-frequency aliasing spectrum correction algorithm is needed to correct the dielectric constant and conductivity spectra of the multi-frequency aliasing.

[0113] In one embodiment, the corrected dielectric constant spectrum and conductivity spectrum are weighted by a range-normalized two-dimensional coherence factor based on the target's scattering field to obtain the reconstructed dielectric constant profile and reconstructed conductivity profile of the target, respectively expressed as:

[0114]

[0115]

[0116] in, To reconstruct the dielectric constant profile, To reconstruct the conductivity profile, ε rb =1 represents the relative permittivity in free space, r represents the target's coordinates, k represents the wavenumber corresponding to a certain radar frequency, and IFT represents the inverse Fourier transform. The distance-normalized two-dimensional coherence factor is represented as:

[0117]

[0118] in, Let represent the coherence factor, q and p represent the discrete positions of the q-th transmitting antenna and the p-th receiving antenna of the radar, respectively, and Q and P represent the number of discrete positions of the transmitting antenna and the receiving antenna of the radar, respectively. k represents the coherent signal in spatial subsets. min k max The minimum frequency f are respectively min Corresponding wave number and maximum frequency f max The corresponding wave number, where n represents the nth frequency, N is the total number of frequencies, j represents the imaginary unit, and r R The coordinates of the radar receiving antenna, r T This represents the coordinates of the radar transmitting antenna, where c is the speed of light, and E is the speed of light. sct (r R ,r T (k) represents the target's scattered field, and f is the radar frequency. This represents the coherence factor of the incoherent summation at different frequencies. This represents a coherent signal within a frequency subset.

[0119] It is understood that coherence factor weighting improves image sharpness by suppressing low-coherence features in spatial and frequency diversity. For the main lobe, since the coherent and incoherent powers are almost equal, their ratio is 1; for the grating lobe and noise, the scattered data are not completely coherent, resulting in a ratio less than 1. Based on this, this application introduces two-dimensional coherence factor weighting, which combines spatial diversity and frequency diversity. It can use the ratio of coherent power to incoherent power as a mask to enhance coherent signals, suppress incoherent signals, and suppress the artifacts caused by strong grating lobes, thereby improving focusing accuracy and imaging quality.

[0120] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0121] In one embodiment, a polarization diffraction tomography apparatus based on coherence factor is provided, comprising:

[0122] The target detection module is used to sample the target in a three-dimensional electromagnetic inversion scenario using a fully polarized radar based on a sparse MIMO array, obtain the target's scattered field, and perform a Fourier transform to obtain the target's scattered field spectrum.

[0123] The polarization fusion transformation module is used to calculate the target's contrast function spectrum based on the linear relationship between the target's scattered field spectrum and the target's contrast function spectrum, and then perform polarization fusion transformation on the contrast function spectrum to obtain the polarization fusion transformed contrast function spectrum.

[0124] The coordinate transformation module is used to perform coordinate transformation on the contrast function spectrum after polarization fusion transformation to obtain the contrast function spectrum after coordinate transformation.

[0125] The decoupling correction module is used to decouple the dielectric constant spectrum and conductivity spectrum of the target multi-frequency aliasing by sequentially performing inverse fast Fourier transform and three-dimensional fast Fourier transform on the contrast function spectrum after coordinate transformation. Then, the multi-frequency aliasing spectrum correction algorithm is used to correct the dielectric constant spectrum and conductivity spectrum of the multi-frequency aliasing to obtain the corrected dielectric constant spectrum and conductivity spectrum.

[0126] The coherence factor weighting module is used to perform range-normalized two-dimensional coherence factor weighting on the corrected dielectric constant spectrum and conductivity spectrum based on the target's scattering field, thereby obtaining the reconstructed dielectric constant profile and reconstructed conductivity profile of the target and completing the polarization diffraction tomography imaging of the target.

[0127] Specific limitations regarding the polarization diffraction tomography apparatus based on coherence factor can be found in the limitations of the polarization diffraction tomography method based on coherence factor described above, and will not be repeated here. Each module in the aforementioned polarization diffraction tomography apparatus based on coherence factor can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the operations corresponding to each module.

[0128] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 4 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage medium. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements a polarization diffraction tomography method based on coherence factor. The display screen can be a liquid crystal display (LCD) or an e-ink display. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0129] Those skilled in the art will understand that Figure 4 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0130] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to perform the following steps:

[0131] In a three-dimensional electromagnetic inversion scenario, a fully polarimetric radar based on a sparse MIMO array samples the target, obtains the target's scattered field, performs a Fourier transform, and obtains the target's scattered field spectrum.

[0132] The contrast function spectrum of the target is calculated based on the linear relationship between the target's scattered field spectrum and the target's contrast function spectrum. Then, a polarization fusion transformation is performed on the contrast function spectrum to obtain the polarization fusion transformed contrast function spectrum.

[0133] The contrast function spectrum after polarization fusion transformation is subjected to coordinate transformation to obtain the contrast function spectrum after coordinate transformation;

[0134] By sequentially performing inverse fast Fourier transform and three-dimensional fast Fourier transform on the contrast function spectrum after coordinate transformation, the dielectric constant spectrum and conductivity spectrum of the target multi-frequency aliasing are decoupled and obtained. Then, a multi-frequency aliasing spectrum correction algorithm is used to correct the dielectric constant spectrum and conductivity spectrum of the multi-frequency aliasing, and the corrected dielectric constant spectrum and conductivity spectrum are obtained.

[0135] Based on the target's scattering field, the corrected dielectric constant spectrum and conductivity spectrum are weighted by a range-normalized two-dimensional coherence factor to obtain the reconstructed dielectric constant profile and reconstructed conductivity profile of the target, thus completing the polarization diffraction tomography imaging of the target.

[0136] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0137] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A polarization diffraction tomography method based on coherence factor, characterized in that, The method includes: In a three-dimensional electromagnetic inversion scenario, a fully polarimetric radar based on a sparse MIMO (multiple-input multiple-output) array samples the target, obtains the target's scattered field, performs a Fourier transform, and obtains the target's scattered field spectrum. The contrast function spectrum of the target is calculated based on the linear relationship between the target's scattered field spectrum and the target's contrast function spectrum. Then, the contrast function spectrum is subjected to polarization fusion transformation to obtain the contrast function spectrum after polarization fusion transformation. The contrast function spectrum after polarization fusion transformation is subjected to coordinate transformation to obtain the contrast function spectrum after coordinate transformation. By sequentially performing inverse fast Fourier transform and three-dimensional fast Fourier transform on the contrast function spectrum after coordinate transformation, the dielectric constant spectrum and conductivity spectrum of the target multi-frequency aliasing are decoupled and obtained. Then, the dielectric constant spectrum and conductivity spectrum of the multi-frequency aliasing are corrected by the multi-frequency aliasing spectrum correction algorithm to obtain the corrected dielectric constant spectrum and conductivity spectrum. Based on the target's scattering field, the corrected dielectric constant spectrum and conductivity spectrum are weighted by a range-normalized two-dimensional coherence factor to obtain the reconstructed dielectric constant profile and reconstructed conductivity profile of the target, thus completing the polarization diffraction tomography imaging of the target. Specifically, the corrected dielectric constant spectrum and conductivity spectrum are weighted by a range-normalized two-dimensional coherence factor based on the target's scattering field to obtain the reconstructed dielectric constant profile and reconstructed conductivity profile of the target, respectively expressed as: ； ； in, To reconstruct the dielectric constant profile, To reconstruct the conductivity profile, The relative permittivity in free space, The coordinates of the target The wave number corresponding to a certain radar frequency. This represents the inverse Fourier transform. The corrected dielectric constant spectrum. This is the corrected conductivity spectrum. They are the first component, the second component, and the third component, respectively. The distance-normalized two-dimensional coherence factor is represented as: ； in, Represents the coherence factor. q , p The radar number is respectively q The discrete positions of the first transmitting antenna and the second... p Discrete positions of each receiving antenna Q , P These represent the number of discrete positions of the radar transmitting antenna and the number of discrete positions of the radar receiving antenna, respectively. Represents coherent signals in spatial concentration. , Minimum frequency Corresponding wave number and maximum frequency The corresponding wave number, n Indicates the first n One frequency, N The total number of frequencies. Represents the imaginary unit. Indicates the coordinates of the radar receiving antenna. Indicates the coordinates of the radar transmitting antenna. At the speed of light, Represents the scattered field of the target. The frequency of the radar; This represents the coherence factor of the incoherent summation at different frequencies. This represents a coherent signal within a frequency subset.

2. The method according to claim 1, characterized in that, In a three-dimensional electromagnetic inversion scenario, a fully polarimetric radar based on a sparse MIMO array samples the target to obtain its scattered field, including: In a three-dimensional electromagnetic inversion scenario, a fully polarized radar based on a sparse MIMO array can detect objects in free space located within the detection region. The radar samples the target within its range. The radar transmitting antenna radiates electromagnetic waves towards the target as the incident field, and the radar receiving antenna samples the scattered field of the target, which is represented as... ； in, For the main field, The wave number corresponding to a certain radar frequency. Angular frequency, and These are the permittivity and permeability of free space, respectively. For the dyadic Green's function, Indicates the coordinates of the radar receiving antenna. Indicates the coordinates of the radar transmitting antenna. Represents the coordinates of the target and , The contrast function is the target.

3. The method according to claim 2, characterized in that, The contrast function spectrum of the target is obtained by calculating the linear relationship between the target's scattered field spectrum and the target's contrast function spectrum, and is expressed as follows: ； in, Represents the imaginary unit. The scattered field spectrum of the target. As the first intermediate variable, As the second intermediate variable, The location for the antenna array. It is the spectrum of the scattered field at the receiving antenna. Quantity, It is the spectrum of the scattered field at the transmitting antenna. Quantity, and These are the scattered field spectra at the receiving antenna. Components and the scattered field spectrum at the transmitting antenna Quantity, and These are the horizontal and vertical axes, respectively; It is the spectral amplitude of the incident field at a certain frequency; Indicates the polarization direction of the receiving antenna. Indicates the polarization direction of the transmitting antenna; This represents the spectral domain form of the receiving antenna's dyadic Green's function. Represent the spectral domain form of the dyadic Green's function of the transmitting antenna; As the first component, For the second component, This is the third component.

4. The method according to claim 3, characterized in that, The contrast function spectrum is subjected to polarization fusion transformation to obtain the contrast function spectrum after polarization fusion transformation, which is expressed as follows: ； Where PFT{·} represents polarization fusion transformation.

5. The method according to claim 4, characterized in that, Perform a coordinate transformation on the contrast function spectrum after the polarization fusion transformation to obtain the coordinate-transformed contrast function spectrum, including: Spectrum of contrast function after polarization fusion transformation Discretization is performed to obtain the scattered field spectrum at the transmitting antenna. Quantity Discretized and the scattered field spectrum at the transmitting antenna Quantity Discretized in, and They represent The discrete components and The Discrete components and L for The number of discrete numbers, and I for The number of discrete numbers; According to the above and The discretized first, second, and third components are calculated and represented as follows: ； ； in, The first component discrete components, For the second component The discrete components, and and Evenly arranged; The third component discrete components, Non-uniform arrangement and It is a real number; It is the spectrum of the scattered field at the receiving antenna. Quantity, It is the spectrum of the scattered field at the receiving antenna. Quantity, and The horizontal and vertical axes are respectively. The wave number corresponding to a certain radar frequency; By merging the same value pair The contrast function spectrum is updated and arranged in non-decreasing order to obtain the spectrum distributed on a uniform grid. and the above Perform three-dimensional linear interpolation to obtain the spectrum of the contrast function distributed in Cartesian coordinates. ; Traverse all and Repeat the coordinate transformation steps described above, and iterate through the obtained coordinates. By merging the results, we obtain the spectrum of the contrast function after coordinate transformation. .

6. The method according to claim 1, characterized in that, By sequentially performing inverse fast Fourier transform and three-dimensional fast Fourier transform on the contrast function spectrum after the coordinate transformation, the dielectric constant spectrum and conductivity spectrum of the target's multi-frequency aliasing are decoupled and obtained, including: By performing an inverse fast Fourier transform on the contrast function spectra at different frequencies after coordinate transformation, the dielectric constant and conductivity at each frequency are obtained, expressed as follows: ； in, Here is the dielectric constant at each frequency. The conductivity at various frequencies, Represents the coordinates of the target. Indicates taking the real part, Indicates taking the imaginary part; For the first n Contrast function at each frequency It is the first after coordinate transformation Contrast function spectrum at each frequency It is obtained through inverse fast Fourier transform, where , The total number of frequencies. For the maximum frequency, For the minimum frequency, This represents the frequency step size. Regarding the and Perform a three-dimensional fast Fourier transform to obtain N Dielectric constant spectrum of multi-frequency aliasing at various frequencies and conductivity spectrum .

7. The method according to claim 6, characterized in that, A multi-frequency aliasing spectrum correction algorithm is used to correct the dielectric constant spectrum and conductivity spectrum of the multi-frequency aliasing, resulting in corrected dielectric constant spectrum and conductivity spectrum, including: A multi-frequency aliasing spectrum correction algorithm is used to correct the aliasing spectrum. N Dielectric constant spectrum of multi-frequency aliasing at various frequencies and conductivity spectrum After correction, the corrected dielectric constant spectrum is obtained. and the corrected conductivity spectrum , respectively represented as ； in, For the first n angular frequency; for N Dielectric constant spectrum of multi-frequency aliasing at various frequencies In the Weighting factors at each frequency and , for N Conductivity spectrum of multi-frequency aliasing at various frequencies In the Weighting factors at each frequency and , and They are respectively and Phase information, and They are respectively and The maximum amplitude.

8. A polarization diffraction tomography imaging device based on coherence factor, characterized in that, The device includes: The target detection module is used to sample the target in a three-dimensional electromagnetic inversion scenario using a fully polarized radar based on a sparse MIMO array, obtain the target's scattered field, and perform a Fourier transform to obtain the target's scattered field spectrum. The polarization fusion transformation module is used to calculate the contrast function spectrum of the target based on the linear relationship between the target's scattered field spectrum and the target's contrast function spectrum, and to perform polarization fusion transformation on the contrast function spectrum to obtain the polarization fusion transformed contrast function spectrum. The coordinate transformation module is used to perform coordinate transformation on the contrast function spectrum after polarization fusion transformation to obtain the contrast function spectrum after coordinate transformation. The decoupling correction module is used to decouple the dielectric constant spectrum and conductivity spectrum of the target multi-frequency aliasing by sequentially performing inverse fast Fourier transform and three-dimensional fast Fourier transform on the contrast function spectrum after coordinate transformation, and then using a multi-frequency aliasing spectrum correction algorithm to correct the dielectric constant spectrum and conductivity spectrum of the multi-frequency aliasing to obtain the corrected dielectric constant spectrum and conductivity spectrum. The coherence factor weighting module is used to perform range-normalized two-dimensional coherence factor weighting on the corrected dielectric constant spectrum and conductivity spectrum based on the target's scattering field, so as to obtain the reconstructed dielectric constant profile and reconstructed conductivity profile of the target and complete the polarization diffraction tomography imaging of the target. Specifically, the corrected dielectric constant spectrum and conductivity spectrum are weighted by a range-normalized two-dimensional coherence factor based on the target's scattering field to obtain the reconstructed dielectric constant profile and reconstructed conductivity profile of the target, respectively expressed as: ； ； in, To reconstruct the dielectric constant profile, To reconstruct the conductivity profile, The relative permittivity in free space, The coordinates of the target The wave number corresponding to a certain radar frequency. This represents the inverse Fourier transform. The corrected dielectric constant spectrum. This is the corrected conductivity spectrum. They are the first component, the second component, and the third component, respectively. The distance-normalized two-dimensional coherence factor is represented as: ； in, Represents the coherence factor. q , p The radar number is respectively q The discrete positions of the first transmitting antenna and the second... p Discrete positions of each receiving antenna Q , P These represent the number of discrete positions of the radar transmitting antenna and the number of discrete positions of the radar receiving antenna, respectively. Represents coherent signals in spatial concentration. , Minimum frequency Corresponding wave number and maximum frequency The corresponding wave number, n Indicates the first n One frequency, N The total number of frequencies. Represents the imaginary unit. Indicates the coordinates of the radar receiving antenna. Indicates the coordinates of the radar transmitting antenna. At the speed of light, Represents the scattered field of the target. The frequency of the radar; This represents the coherence factor of the incoherent summation at different frequencies. This represents a coherent signal within a frequency subset.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

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